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Let H  := Hollow Earth Theory is true
Let F  := Flat Earth Theory is true
apparent contradiction
H ∧ F  ⊢  ⊥
existence of a reconciling condition
∃C  ( C → (H ∧ F) )  ∧  ¬(C → ⊥)
synthesis
( H ∧ F  ⊢  ⊥ )  ∧  ◇∃C  [ C → (H ∧ F) ∧ ¬⊥ ]
possibly (modal operator)
contradiction / absurdity
there exists
logical conjunction (and)
material implication (if … then)
logical entailment (derives)
¬
negation (not)