hasCounterexample

P64864
predicate

Indicates that there exists at least one specific case or instance that disproves or violates a given claim, rule, or general statement.

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All labels observed (7)

Label Occurrences
hasCounterexample canonical 4
disproofMethod 3
counterexampleInvolves 2

Description generation (PDg)

The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.

Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning.  
# Instructions
Focus on describing the relationship, not the entities themselves. 
# Response Format
Begin the description with \' Indicates...\'
Input
Predicate: hasCounterexample
Generated description
Indicates that there exists at least one specific case or instance that disproves or violates a given claim, rule, or general statement.

Sample triples (13)

Subject Object
Fermat's theorem on sums of two squares 3 ≡ 3 (mod 4) and 3 is not a sum of two squares ⓘ
Fermat's theorem on sums of two squares 7 ≡ 3 (mod 4) and 7 is not a sum of two squares ⓘ
Hilbert’s fourteenth problem Masayoshi Nagata via predicate surface "hasCounterexampleProvidedBy" ⓘ
Hilbert’s fourteenth problem non-finitely generated ring of invariants via predicate surface "counterexampleInvolves" ⓘ
Hilbert’s fourteenth problem action of an algebraic group on affine space via predicate surface "counterexampleInvolves" ⓘ
Whitney umbrella naive generalizations of manifold properties to singular varieties via predicate surface "isUsedAsCounterexampleTo" ⓘ
Connes embedding problem construction of non-hyperlinear II₁ factors via predicate surface "disproofMethod" ⓘ
Connes embedding problem use of nonlocal games and quantum correlations via predicate surface "disproofMethod" ⓘ
Szekeres snark 3-edge-colorability of bridgeless cubic graphs via predicate surface "isCounterexampleTo" ⓘ
Pólya’s conjecture existence of counterexamples for large x via predicate surface "disproofMethod" ⓘ
Pólya’s conjecture values of x for which M(x) > 0 via predicate surface "hasCounterexamples" ⓘ
Hilbert's third problem pairs of polyhedra of equal volume that are not equidecomposable ⓘ
Hilbert's third problem cube and regular tetrahedron of equal volume ⓘ