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load("conjecturing.py")
3+4
7
def independence_number(g): return len(g.independent_set())
#to generate conjectures you need: #(1) examples of graphs (OBJECTS) #(2) function names of graph invariants that will appear in the conjectures (INVARIANTS) #(3) a choice of an invariant to make conjectures about #list some common graphs p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() objects = [p3, k3, pete] invariants = [independence_number, Graph.order, Graph.size] conjecture(objects, invariants, invariants.index(independence_number))
[independence_number(x) <= floor(10^sin(size(x))), independence_number(x) <= size(x), independence_number(x) <= ceil(sqrt(order(x)))]
show(k3) k3.order() k3.size() independence_number(k3)
3 3 1
10^sin(2)
10^sin(2)
n(10^sin(2))
8.11516635222698
n(10^sin(3))
1.38394875099483
n(10^sin(15))
4.46979741648266
#k1 is a counterexample to the conjecture alpha <= size #alpha = 1, size = 0 #add k1 to the objects (get new conjectures) p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) objects = [p3, k3, pete, k1] invariants = [independence_number, Graph.order, Graph.size] conjecture(objects, invariants, invariants.index(independence_number))
[independence_number(x) <= order(x), independence_number(x) <= 1/2*order(x) + 1/2, independence_number(x) <= ceil(sqrt(order(x))), independence_number(x) <= floor(10^sin(size(x)))]
#its possible to add theoretical knowledge. #the program is required to make conjectures that are better than the provided knowledge FOR AT LEAST ONE INPUT GRAPH #add knowledge using the #theory" parameter #we proved alpha <= order, add that as theoretical knowledge p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) objects = [p3, k3, pete, k1] invariants = [independence_number, Graph.order, Graph.size] theorems = [Graph.order] conjecture(objects, invariants, invariants.index(independence_number), theory = theorems)
[independence_number(x) <= 1/2*order(x) + 1/2, independence_number(x) <= ceil(sqrt(order(x))), independence_number(x) <= floor(10^sin(size(x)))]
s = graphs.StarGraph(4) show(s)
#s4, the star graph with 4 rays is a counterexample to the conjecture alpha <= ceil(sqrt(order)) #add s4 to the objects, generate new conjectures #DEBUG repeated alpha <= order conjecture p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) s4 = graphs.StarGraph(4) objects = [p3, k3, pete, k1, s4] invariants = [independence_number, Graph.order, Graph.size] theorems = [Graph.order] conjecture(objects, invariants, invariants.index(independence_number), theory = theorems)
[independence_number(x) <= (order(x) - size(x) + 1)^2, independence_number(x) <= maximum(size(x), 1/order(x)), independence_number(x) <= order(x), independence_number(x) <= 2*ceil(arctan(order(x)))]
#DEBUG repeated alpha <= order conjecture #try to fix this minor problem by adding the actual conjecture that Sage made: alpha <= (sqrt(order))^2 p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) s4 = graphs.StarGraph(4) def order_theorem(g): return sqrt(g.order())^2 order_theorem = lambda g: (sqrt(g.order()))^2 objects = [p3, k3, pete, k1, s4] invariants = [independence_number, Graph.order, Graph.size] theorems = [Graph.order, order_theorem] conjecture(objects, invariants, invariants.index(independence_number), theory = theorems)
[independence_number(x) <= (order(x) - size(x) + 1)^2, independence_number(x) <= maximum(size(x), 1/order(x)), independence_number(x) <= order(x), independence_number(x) <= 2*ceil(arctan(order(x)))]
c5 = graphs.CycleGraph(5) show(c5)
#c5, the cycle (cycle graph) on 5 vertices is a counterexample to: alpha <= (order-size+1)^2 #add c5 and iterate p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) s4 = graphs.StarGraph(4) c5 = graphs.CycleGraph(5) objects = [p3, k3, pete, k1, s4, c5] invariants = [independence_number, Graph.order, Graph.size] theorems = [Graph.order] conjecture(objects, invariants, invariants.index(independence_number), theory = theorems)
[independence_number(x) <= floor(10^abs(sin(size(x)))), independence_number(x) <= 2*ceil(arctan(order(x))), independence_number(x) <= order(x), independence_number(x) <= ceil(cosh(tan(2*size(x)))), independence_number(x) <= maximum(size(x), 1/order(x))]
#DEBUG repeated alpha <= order conjecture p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) s4 = graphs.StarGraph(4) objects = [p3, k3, pete, k1, s4] invariants = [independence_number, Graph.order, Graph.size] theorems = [Graph.order] conjecture(objects, invariants, invariants.index(independence_number), theory = theorems, debug=true, verbose=true)
> Known theory Invariant 1 Invariant 2 Invariant 3 > 1) 3.000000 2.000000 3.000000 2.000000 > 2) 3.000000 1.000000 3.000000 3.000000 > 3) 10.000000 4.000000 10.000000 15.000000 > 4) 1.000000 1.000000 1.000000 0.000000 > 5) 5.000000 4.000000 5.000000 4.000000 > Generating trees with 0 unary nodes and 0 binary nodes. > Status: 1 unlabeled tree, 2 labeled trees, 1 expression > Generating trees with 1 unary node and 0 binary nodes. > Status: 2 unlabeled trees, 56 labeled trees, 18 expressions > Generating trees with 0 unary nodes and 1 binary node. > Status: 3 unlabeled trees, 66 labeled trees, 21 expressions > Generating trees with 2 unary nodes and 0 binary nodes. > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.352410 > Saving expression > independence_number <= cosh((order) / 2) > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.324555 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.472136 > Conjecture is more significant for object 3. > 74.209949 vs. 6.324555 > Conjecture is more significant for object 5. > 6.132289 vs. 4.472136 > Saving expression > independence_number <= (sqrt(order)) * 2 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 3.000000 > Conjecture is more significant for object 4. > 1.127626 vs. 1.000000 > Saving expression > independence_number <= (sqrt(order)) ^ 2 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624796 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.731673 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.996446 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624877 > Conjecture is more significant for object 3. > 6.324555 vs. 5.996446 > Saving expression > independence_number <= (asinh(order)) * 2 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant for object 1. > 2.352410 vs. 2.236068 > Conjecture is more significant for object 5. > 4.472136 vs. 4.123106 > Saving expression > independence_number <= cosh(asinh(size)) > Status: 4 unlabeled trees, 1524 labeled trees, 365 expressions > Generating trees with 1 unary node and 1 binary node. > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant for object 3. > 5.996446 vs. 5.000000 > Saving expression > independence_number <= ((order) * 2) - (size) > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.250000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.200000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant for object 1. > 2.236068 vs. 2.000000 > Conjecture is more significant for object 5. > 4.123106 vs. 4.000000 > Saving expression > independence_number <= max(1 / (order), size) > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.463019 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.243198 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.583853 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.240312 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.346356 > Conjecture is more significant for object 2. > 2.352410 vs. 2.010008 > Saving expression > independence_number <= (cos(size)) + (order) > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.141486 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.698970 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.522879 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.823909 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.397940 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.090703 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.858880 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.349712 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.035972 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.004945 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000671 > Conjecture is more significant for object 2. > 2.010008 vs. 2.004945 > Saving expression > independence_number <= (order) - (tanh(size)) > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.883753 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.983745 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.994606 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.141486 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.641589 > Conjecture is more significant for object 3. > 5.000000 vs. 4.641589 > Saving expression > independence_number <= 10 ^ ((order) / (size)) > Status: 7 unlabeled trees, 2334 labeled trees, 587 expressions > Generating trees with 3 unary nodes and 0 binary nodes. > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.999999 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.055385 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.500000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.488955 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.276859 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.488921 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.276473 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.633250 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.898979 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.393545 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.078167 > Conjecture is more significant for object 3. > 4.641589 vs. 4.393545 > Saving expression > independence_number <= exp(atan((order) + 1)) > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.186204 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.983560 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.567281 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.177940 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.955777 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.541735 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.324555 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.472136 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.991465 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.605170 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.684613 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.684610 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.472136 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.162278 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.944272 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.991465 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.605170 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.576058 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.354142 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.379008 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.376508 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.500000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.356469 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.860488 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000000 > Conjecture is more significant for object 2. > 2.004945 vs. 2.000000 > Saving expression > independence_number <= floor(cosh((order) / 2)) > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.997910 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.991471 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.605270 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.991458 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.605070 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.605170 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.218876 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.596703 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.596703 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.046855 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.762614 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.621954 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.298342 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.912423 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.298292 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.911623 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.885626 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.162278 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.236068 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.324555 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.324555 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.324555 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.472136 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.731673 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.919662 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.460892 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.826117 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.826117 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.678235 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.281413 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.974561 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.974560 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.324555 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.472136 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624796 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.731673 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624796 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.731673 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.917972 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.478902 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.685558 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.162278 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.236068 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.605170 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.605170 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.218876 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.546006 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.028633 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.028633 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.777778 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.777778 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.552807 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.552807 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.741683 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.741683 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.554281 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.596703 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.596703 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.046855 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.436564 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.023359 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.596703 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.596703 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.046855 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.878882 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.878882 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.941782 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.399766 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.787261 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.787261 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.100960 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.074125 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.779298 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.779298 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.775561 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.015259 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.888387 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.888387 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.609806 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.485621 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.810259 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.778174 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.810477 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.810429 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.324555 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.472136 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624796 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.731673 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.996446 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624877 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.324555 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.472136 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624796 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.731673 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.996446 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624877 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.324555 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.472136 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624796 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.731673 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.996446 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624877 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.858407 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.858407 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.292037 > Conjecture is more significant for object 3. > 4.393545 vs. 4.292037 > Saving expression > independence_number <= (acos(sin(order))) * 2 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.550745 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.207436 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.207436 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.333847 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.657511 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.942255 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.746802 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.106472 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.875648 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.960138 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.884511 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.656867 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.452905 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.505651 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.439561 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.860718 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.707778 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.783554 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.354142 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.948757 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.708285 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.439561 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.860718 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant for object 3. > 4.292037 vs. 4.000000 > Saving expression > independence_number <= (ceil(atan(order))) * 2 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.886378 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.414347 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.863549 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.583809 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.202001 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.252826 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.414203 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.893761 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.896344 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.026005 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.997418 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.148339 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.939485 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.720391 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.720391 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.810041 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.746088 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.726254 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.726254 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.810041 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.746094 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.436564 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.544137 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.610125 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.998955 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.941782 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.746501 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.745025 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.810041 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.746088 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.100960 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.678982 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.678483 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.775561 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.609806 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.998223 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.312438 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.996446 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.996446 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.996446 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624877 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.989341 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.649334 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.575291 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.903663 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.596811 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.596810 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.996446 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624877 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.886378 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.158815 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.831837 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.993223 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.292432 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.986446 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.986446 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.959383 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.641180 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.545228 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.885245 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.149072 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.793480 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.543081 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.381098 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.232630 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.446352 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.472136 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624796 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.731673 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.933422 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624877 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.125000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.062500 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.652829 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.247970 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.500000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.113250 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.669618 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.478591 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.518144 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.501738 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.175201 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.626860 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.543081 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.762196 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.381098 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.232630 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.446352 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.999986 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.414214 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.236068 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.125000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.789145 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.519392 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.109253 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.466711 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.163953 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.082988 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.872983 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.745967 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.745967 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.156276 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.113250 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.935067 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.626860 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.762196 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.980112 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.872983 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.236068 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.866747 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.810252 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.125000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.500000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.250000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.083928 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.896387 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.823609 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.711378 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.816504 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.711216 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.383545 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.828427 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.645751 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.810476 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.723182 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.810477 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.809996 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.383949 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.469797 > Conjecture is more significant for object 2. > 2.000000 vs. 1.383949 > Saving expression > independence_number <= 10 ^ (|(sin(size))|) > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.250425 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.686604 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.291772 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.607035 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.750266 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.504469 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.309468 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.743950 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.954915 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.047899 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.404116 > Conjecture is more significant for object 2. > 1.383949 vs. 1.047899 > Saving expression > independence_number <= 10 ^ ((tan(size)) ^ 2) > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.388502 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.177834 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.746087 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.011985 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.008456 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.651635 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.271159 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.076187 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.157926 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.650854 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.601600 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.609021 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.621604 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.500678 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.765263 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.001357 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.650854 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.601600 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.949131 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.640336 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.493022 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.722867 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.030849 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.816051 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.576369 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.061935 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.052104 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.626860 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.151014 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.813430 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.904432 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.810474 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.637471 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.381098 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.182246 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.264702 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.036612 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.242645 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.035988 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.743062 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.715684 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.693566 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.706852 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.693399 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.881098 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.939638 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.325003 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.307188 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.013999 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.810474 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.637585 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.436564 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.389056 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.544137 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.610125 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.941782 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.746501 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.735620 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.810474 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.637471 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.100960 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.678982 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.675297 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.775561 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.609806 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.402307 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.094713 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.804613 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.804613 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.325153 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.251671 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.949131 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.948529 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.415880 > Status: 8 unlabeled trees, 41700 labeled trees, 8312 expressions > Generating trees with 2 unary nodes and 1 binary node. > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.828427 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.665144 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.154195 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.376842 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.720054 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.585786 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.267949 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.127017 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.901388 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.291950 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.613706 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.823909 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.842179 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.892851 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.750954 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.495772 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.674182 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.312720 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.525509 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.163978 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.878365 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.773925 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.250000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.250000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.250000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.250000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.250000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.200000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.174581 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.589400 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.210012 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.715249 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.061457 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.633432 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.231726 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.641589 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.141486 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.698970 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.522879 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.823909 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.397940 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.090703 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.858880 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.349712 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.035972 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.004945 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000671 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.883753 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.983745 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.994606 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.141486 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.698970 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.522879 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.823909 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.397940 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.090703 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.858880 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.349712 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.035972 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.004945 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000671 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.883753 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.983745 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.994606 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.141486 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.698970 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.522879 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.823909 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.397940 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.090703 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.858880 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.349712 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.035972 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.004945 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000671 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.883753 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.983745 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.994606 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.433960 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.433960 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.240145 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.504469 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.504469 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.669646 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.017875 > Conjecture is more significant for object 2. > 1.047899 vs. 1.017875 > Saving expression > independence_number <= (sinh(order)) - ((size) ^ 2) > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.504469 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.113097 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.637701 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.516915 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.516915 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.677944 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.067662 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.516915 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.118629 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.638122 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.329550 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.817179 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.370898 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.966549 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.229283 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.669400 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.266776 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.803389 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.522879 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.301030 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.041076 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.983745 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.999269 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.619485 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.732051 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.236068 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.500000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.066667 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.250000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.035261 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.236068 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.463019 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.596703 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.463019 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.463019 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.463019 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.200000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.141486 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.200000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.141486 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.200000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.141486 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.243198 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.243198 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.243198 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.243198 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.583853 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.240312 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.346356 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.583853 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.240312 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.346356 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.583853 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.240312 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.346356 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.583853 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.240312 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.346356 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.508130 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.172105 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.663583 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.772203 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.068906 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.134280 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.084083 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.564584 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.330781 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.500000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.250000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.828427 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.463019 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.084083 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.066667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.094713 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.063437 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.449490 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.491780 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.477889 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.500000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.666667 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.400000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.481689 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.481689 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.250000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.352410 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.733333 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.111111 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.040000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.132006 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.666667 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.400000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.111111 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.040000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.577350 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.447214 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.154435 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.200000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.346254 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.202710 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.339837 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.201358 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.339541 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.201336 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.346574 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.202733 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.732051 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.472136 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.577350 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.447214 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.652234 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.624343 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.737656 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624796 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.914577 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.731673 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.098612 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.910239 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.621335 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.777778 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.181887 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.095903 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.596703 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.888321 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.765505 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.796840 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.481689 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.481689 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.313594 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.025851 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.464261 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.718998 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.718998 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.250000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.200000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.250000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.200000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.250000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.666667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.200000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 3.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.041076 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.383305 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.109920 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.042623 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.919324 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.371579 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.102331 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.020320 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.867147 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.034030 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.720201 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000416 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.142547 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.249046 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.498092 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.433960 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.800611 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.728120 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.560377 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.504469 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.669646 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.164736 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.516915 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.677944 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.166175 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.704872 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.373439 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.164736 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.363254 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.818446 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.624877 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.549920 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.432444 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 5.049876 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 5.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.762747 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.567296 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.436218 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.828427 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.949874 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.583853 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.010008 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.243198 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.712097 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.041076 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.346356 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.042341 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.243198 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.720585 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.011968 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.346356 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.854500 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.583853 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.243198 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.069905 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.712097 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.346356 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.088870 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.042341 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.547684 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.467885 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.090703 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.858880 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.349712 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.583853 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.240312 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.346356 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.035972 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.004945 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000671 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.500000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.066667 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.250000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.698970 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.522879 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.823909 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.397940 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 4.641589 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.332095 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.839443 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.255754 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.583853 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.079442 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.698970 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.522879 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.823909 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.397940 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.796352 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.718282 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.666667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.333333 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.463019 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.071232 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.850506 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.629338 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.493634 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.694386 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.486806 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.047845 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.412786 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.327585 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.463019 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.243198 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.583853 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.240312 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.346356 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.463019 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.243198 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.583853 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.240312 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.346356 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.463019 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.243198 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.583853 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.010008 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.240312 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.346356 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.621599 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.090703 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.858880 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.349712 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.313400 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.055616 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.141593 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.352159 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.168857 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.360810 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.301420 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.011312 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.791927 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.505004 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.620156 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.673178 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.595761 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.163978 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.311305 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.391917 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.558041 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.476348 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.050142 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.234030 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.570796 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.570796 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.137167 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.287611 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.605652 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.219631 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.350327 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.421068 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.571737 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.840183 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.165102 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.298807 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.606321 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.242641 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.359107 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.425882 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.595015 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.125721 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.299121 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.385723 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.182790 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.857936 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.244778 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.423660 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.856480 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.847813 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 1.030843 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.024984 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.858411 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.305812 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.533555 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.441068 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.115450 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.170786 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.446651 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.508130 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.418474 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.400494 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.186472 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.199630 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.431489 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.035972 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.004945 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000671 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.742230 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.754874 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.033794 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.499725 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.236068 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.123106 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.633916 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.800169 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.126874 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.500000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.928571 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.666667 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.158529 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.090703 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.009393 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.858880 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.369901 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.238406 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.035972 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.004945 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.308728 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.883753 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.960363 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.633432 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.522879 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.397940 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.795880 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.301030 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.304820 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.983745 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.997790 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 10.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.999269 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.397940 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.221849 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.522879 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.096910 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.010642 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.000671 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.000012 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.997790 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.999959 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.999998 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.500000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.250000 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.250000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.000000 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.594535 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 7.985097 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.306853 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.823909 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.124939 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.698970 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.158529 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.002505 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.062000 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.090703 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.520483 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.991755 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 8.669618 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.320874 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 6.952919 > Conjecture is more significant than known theory for object 5. > 5.000000 vs. 4.516105 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.369901 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.943824 > Conjecture is more significant than known theory for object 1. > 3.000000 vs. 2.238406 > Conjecture is more significant than known theory for object 2. > 3.000000 vs. 2.094852 > Conjecture is more significant than known theory for object 3. > 10.000000 vs. 9.000001
Output too long: 150785 -- MAX_OUTPUT (=150000) exceeded (type 'smc?' to learn how to raise this limit): attempting to terminate...
p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) s4 = graphs.StarGraph(4) def min_degree(g): return min(g.degree()) def max_degree(g): return max(g.degree()) min_degree_thm = lambda g: g.order() - min_degree(g) objects = [p3, k3, pete, k1, s4] invariants = [independence_number, Graph.order, Graph.size, max_degree, min_degree] theorems = [Graph.order, min_degree_thm] conjecture(objects, invariants, invariants.index(independence_number), theory = theorems)
[independence_number(x) <= max_degree(x) + 1, independence_number(x) <= maximum(max_degree(x), min_degree(x) + 1), independence_number(x) <= -2*min_degree(x) + order(x) + 2]
c8 = graphs.CycleGraph(8) show(c8)
#c8, the cycle on 8 vertices, is a counterexample to alpha <= max_degree + 1 #DEBUG!!!! alpha <= order - min_degree p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) s4 = graphs.StarGraph(4) c8 = graphs.CycleGraph(8) def min_degree(g): return min(g.degree()) def max_degree(g): return max(g.degree()) min_degree_thm = lambda g: g.order() - min_degree(g) objects = [p3, k3, pete, k1, s4, c8] invariants = [independence_number, Graph.order, Graph.size, max_degree, min_degree] theorems = [Graph.order, min_degree_thm] conjecture(objects, invariants, invariants.index(independence_number), theory = theorems)
[independence_number(x) <= max_degree(x)^min_degree(x), independence_number(x) <= -min_degree(x) + order(x), independence_number(x) <= ceil(order(x)/min_degree(x))]
#an example for making lower bound conjectures #don't need the known upper bounds here p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) s4 = graphs.StarGraph(4) c8 = graphs.CycleGraph(8) def min_degree(g): return min(g.degree()) def max_degree(g): return max(g.degree()) objects = [p3, k3, pete, k1, s4, c8] invariants = [independence_number, Graph.order, Graph.size, max_degree, min_degree] lower_bounds = [] conjecture(objects, invariants, invariants.index(independence_number), theory = lower_bounds, upperBound = False)
[independence_number(x) >= (1/order(x)), independence_number(x) >= max_degree(x) - 1, independence_number(x) >= ceil(tan(min_degree(x))), independence_number(x) >= 1/2*order(x) - 1, independence_number(x) >= 1/4*max_degree(x)^2, independence_number(x) >= -2*max_degree(x) + order(x)]
#k5 is a counterexample to alpha >= order/2 - 1 p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) s4 = graphs.StarGraph(4) c8 = graphs.CycleGraph(8) k5 = graphs.CompleteGraph(5) def min_degree(g): return min(g.degree()) def max_degree(g): return max(g.degree()) objects = [p3, k3, pete, k1, s4, c8, k5] invariants = [independence_number, Graph.order, Graph.size, max_degree, min_degree] lower_bounds = [] conjecture(objects, invariants, invariants.index(independence_number), theory = lower_bounds, upperBound = False)
[independence_number(x) >= (1/order(x)), independence_number(x) >= log(size(x))/log(10), independence_number(x) >= ceil(1/order(x)), independence_number(x) >= max_degree(x) - min_degree(x) + 1, independence_number(x) >= -2*max_degree(x) + order(x)]
#PROVED: alpha >= 1/order for any connected graph #add this as a theorem #DEBUG!!! the lower bound theorem p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() k1 = graphs.CompleteGraph(1) s4 = graphs.StarGraph(4) c8 = graphs.CycleGraph(8) k5 = graphs.CompleteGraph(5) def min_degree(g): return min(g.degree()) def max_degree(g): return max(g.degree()) thm1 = lambda g: 1/g.order() objects = [p3, k3, pete, k1, s4, c8, k5] invariants = [independence_number, Graph.order, Graph.size, max_degree, min_degree] lower_bounds = [thm1] conjecture(objects, invariants, invariants.index(independence_number), theory = lower_bounds, upperBound = False)
[independence_number(x) >= (1/order(x)), independence_number(x) >= log(size(x))/log(10), independence_number(x) >= ceil(1/order(x)), independence_number(x) >= max_degree(x) - min_degree(x) + 1, independence_number(x) >= -2*max_degree(x) + order(x)]
load("conjecturing.py") p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() objects = [p3, k3, pete] invariants = [independence_number, Graph.order, Graph.size] conjs = conjecture(objects, invariants, invariants.index(independence_number)) for c in conjs: print c
independence_number(x) <= floor(10^sin(size(x))) independence_number(x) <= size(x) independence_number(x) <= ceil(sqrt(order(x)))
p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() def independence_number(g): return len(g.independent_set()) objects = [p3, k3, pete] invariants = [independence_number, Graph.order, Graph.size] conjs2 = conjecture(objects, invariants, invariants.index(independence_number))
conjs[0].expression == conjs2[0].expression
True
conjs[0] conjs2[0]
independence_number(x) <= floor(10^sin(size(x))) independence_number(x) <= floor(10^sin(size(x)))
latex(conjs[0])==latex(conjs2[0])
True
latex(conjs2[0])
{\rm independence}_{{\rm number}}\left(x\right) \leq \left \lfloor 10^{\sin\left({\rm size}\left(x\right)\right)} \right \rfloor
conjs[0].__eq__(conjs2[0])
False
type(conjs[0])
<class 'Conjecture'>
c0 = conjs2[0]
c0._repr_
<bound method Conjecture._repr_ of independence_number(x) <= floor(10^sin(size(x)))>
c0.stack
[(<function <lambda> at 0x7fb5fc54b1b8>, 0), (<function <lambda> at 0x7fb5fc54b488>, 0), (sin, 1), (<function <lambda> at 0x7fb5fc54b500>, 1), (floor, 1), (<built-in function le>, 2)]
load("conjecturing.py") p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() def independence_number(g): return len(g.independent_set()) objects = [p3, k3, pete] invariants = [independence_number, Graph.order, Graph.size] conjs2 = conjecture(objects, invariants, invariants.index(independence_number)) for c in conjs2: print c
independence_number(x) <= floor(10^sin(size(x))) independence_number(x) <= size(x) independence_number(x) <= ceil(sqrt(order(x)))
type(conjs[0])
<class 'Conjecture'>
c = conjs[0]
c.expression()
independence_number(x) <= floor(10^sin(size(x)))
cexp = c.expression()
ctest= lambda x: cexp
type(ctest)
<type 'function'>
ctest(p3)
independence_number(x) <= floor(10^sin(size(x)))
save(conjs[0], "save_test.sobj")
Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 995, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "sage/structure/sage_object.pyx", line 1087, in sage.structure.sage_object.save (/projects/sage/sage-7.5/src/build/cythonized/sage/structure/sage_object.c:13349) s = cPickle.dumps(obj, protocol=2) TypeError: expected string or Unicode object, NoneType found
cexp.substitute(x=p3)
Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 995, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "sage/symbolic/expression.pyx", line 4972, in sage.symbolic.expression.Expression.substitute (/projects/sage/sage-7.5/src/build/cythonized/sage/symbolic/expression.cpp:29999) (<Expression>self.coerce_in(v))._gobj)) File "sage/symbolic/expression.pyx", line 2885, in sage.symbolic.expression.Expression.coerce_in (/projects/sage/sage-7.5/src/build/cythonized/sage/symbolic/expression.cpp:21670) return self._parent._coerce_(z) File "sage/structure/parent_old.pyx", line 240, in sage.structure.parent_old.Parent._coerce_ (/projects/sage/sage-7.5/src/build/cythonized/sage/structure/parent_old.c:4949) return self.coerce(x) File "sage/structure/parent.pyx", line 1195, in sage.structure.parent.Parent.coerce (/projects/sage/sage-7.5/src/build/cythonized/sage/structure/parent.c:11166) raise TypeError("no canonical coercion from %s to %s" % (parent_c(x), self)) TypeError: no canonical coercion from <class 'sage.graphs.graph.Graph'> to Symbolic Ring
min(x^2 for x in range(3))
0
p3 = graphs.PathGraph(3) k3 = graphs.CompleteGraph(3) pete = graphs.PetersenGraph() objects = [p3, k3, pete] invariants = [independence_number, Graph.order, Graph.size] conjs = conjecture(objects, invariants, invariants.index(independence_number))
c0 = conjs[0]
for g in objects: print g.name(), c0.__call__(g, returnBoundValue = true)
Path graph 8.0 Complete graph 1.0 Petersen graph 4.0