Exercise logic.propositional.consequence
Description
Prove that formula is a logical consequence of a set of formulas
Firsts
Rule logic.propositional.genoroverand Location [1,1] Term "Just (TList [TList [TCon logic1.equivalent [TVar \"p\",TVar \"r\"],TCon logic1.equivalent [TVar \"q\",TVar \"s\"]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]]],TCon logic1.not [TCon logic1.and [TVar \"p\",TVar \"q\"]]],TCon logic1.and [TCon logic1.or [TVar \"p\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.and [TCon logic1.or [TVar \"q\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.and [TCon logic1.or [TVar \"r\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TVar \"s\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]]]]])" Focus "Just (TCon logic1.and [TCon logic1.or [TVar \"p\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.and [TCon logic1.or [TVar \"q\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.and [TCon logic1.or [TVar \"r\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TVar \"s\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]]])" Environment Rule logic.propositional.genoroverand Location [1,1] Term "Just (TList [TList [TCon logic1.equivalent [TVar \"p\",TVar \"r\"],TCon logic1.equivalent [TVar \"q\",TVar \"s\"]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]]],TCon logic1.not [TCon logic1.and [TVar \"p\",TVar \"q\"]]],TCon logic1.and [TCon logic1.or [TVar \"p\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.and [TCon logic1.or [TVar \"q\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TCon logic1.and [TVar \"r\",TVar \"s\"],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]]]])" Focus "Just (TCon logic1.and [TCon logic1.or [TVar \"p\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.and [TCon logic1.or [TVar \"q\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TCon logic1.and [TVar \"r\",TVar \"s\"],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]])" Environment Rule logic.propositional.genoroverand Location [1,1] Term "Just (TList [TList [TCon logic1.equivalent [TVar \"p\",TVar \"r\"],TCon logic1.equivalent [TVar \"q\",TVar \"s\"]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]]],TCon logic1.not [TCon logic1.and [TVar \"p\",TVar \"q\"]]],TCon logic1.and [TCon logic1.or [TVar \"p\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"q\",TVar \"r\"],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TVar \"s\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]]]])" Focus "Just (TCon logic1.and [TCon logic1.or [TVar \"p\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"q\",TVar \"r\"],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TVar \"s\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]])" Environment Rule logic.propositional.genoroverand Location [1,1] Term "Just (TList [TList [TCon logic1.equivalent [TVar \"p\",TVar \"r\"],TCon logic1.equivalent [TVar \"q\",TVar \"s\"]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]]],TCon logic1.not [TCon logic1.and [TVar \"p\",TVar \"q\"]]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TVar \"q\"],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.and [TCon logic1.or [TVar \"r\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TVar \"s\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]]]])" Focus "Just (TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TVar \"q\"],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.and [TCon logic1.or [TVar \"r\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TVar \"s\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]])" Environment Rule logic.propositional.oroverand Location [1,1] Term "Just (TList [TList [TCon logic1.equivalent [TVar \"p\",TVar \"r\"],TCon logic1.equivalent [TVar \"q\",TVar \"s\"]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]]],TCon logic1.not [TCon logic1.and [TVar \"p\",TVar \"q\"]]],TCon logic1.and [TCon logic1.or [TVar \"p\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]]])" Focus "Just (TCon logic1.and [TCon logic1.or [TVar \"p\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]])" Environment Rule logic.propositional.oroverand Location [1,1] Term "Just (TList [TList [TCon logic1.equivalent [TVar \"p\",TVar \"r\"],TCon logic1.equivalent [TVar \"q\",TVar \"s\"]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]]],TCon logic1.not [TCon logic1.and [TVar \"p\",TVar \"q\"]]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TVar \"q\"],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TCon logic1.and [TVar \"r\",TVar \"s\"],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]]])" Focus "Just (TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TVar \"q\"],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TCon logic1.and [TVar \"r\",TVar \"s\"],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]])" Environment Rule logic.propositional.oroverand Location [1,1] Term "Just (TList [TList [TCon logic1.equivalent [TVar \"p\",TVar \"r\"],TCon logic1.equivalent [TVar \"q\",TVar \"s\"]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]]],TCon logic1.not [TCon logic1.and [TVar \"p\",TVar \"q\"]]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TVar \"r\"]],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TVar \"s\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]]]])" Focus "Just (TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TVar \"r\"]],TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]],TCon logic1.or [TVar \"s\",TCon logic1.or [TCon logic1.not [TVar \"r\"],TCon logic1.not [TVar \"s\"]]]])" Environment Rule logic.propositional.oroverand Location [1,1] Term "Just (TList [TList [TCon logic1.equivalent [TVar \"p\",TVar \"r\"],TCon logic1.equivalent [TVar \"q\",TVar \"s\"]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]]],TCon logic1.not [TCon logic1.and [TVar \"p\",TVar \"q\"]]],TCon logic1.or [TCon logic1.and [TCon logic1.or [TVar \"p\",TCon logic1.not [TVar \"r\"]],TCon logic1.or [TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]],TCon logic1.not [TVar \"r\"]]],TCon logic1.not [TVar \"s\"]]]])" Focus "Just (TCon logic1.or [TCon logic1.and [TCon logic1.or [TVar \"p\",TCon logic1.not [TVar \"r\"]],TCon logic1.or [TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]],TCon logic1.not [TVar \"r\"]]],TCon logic1.not [TVar \"s\"]])" Environment Rule logic.propositional.oroverand Location [1,1] Term "Just (TList [TList [TCon logic1.equivalent [TVar \"p\",TVar \"r\"],TCon logic1.equivalent [TVar \"q\",TVar \"s\"]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]]],TCon logic1.not [TCon logic1.and [TVar \"p\",TVar \"q\"]]],TCon logic1.or [TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TVar \"q\"],TCon logic1.not [TVar \"r\"]],TCon logic1.or [TCon logic1.and [TVar \"r\",TVar \"s\"],TCon logic1.not [TVar \"r\"]]],TCon logic1.not [TVar \"s\"]]]])" Focus "Just (TCon logic1.or [TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TVar \"q\"],TCon logic1.not [TVar \"r\"]],TCon logic1.or [TCon logic1.and [TVar \"r\",TVar \"s\"],TCon logic1.not [TVar \"r\"]]],TCon logic1.not [TVar \"s\"]])" Environment Rule logic.propositional.oroverand Location [1,1] Term "Just (TList [TList [TCon logic1.equivalent [TVar \"p\",TVar \"r\"],TCon logic1.equivalent [TVar \"q\",TVar \"s\"]],TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TCon logic1.and [TVar \"r\",TVar \"s\"]]],TCon logic1.not [TCon logic1.and [TVar \"p\",TVar \"q\"]]],TCon logic1.or [TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TVar \"r\"]],TCon logic1.not [TVar \"r\"]],TCon logic1.or [TVar \"s\",TCon logic1.not [TVar \"r\"]]],TCon logic1.not [TVar \"s\"]]]])" Focus "Just (TCon logic1.or [TCon logic1.and [TCon logic1.or [TCon logic1.and [TVar \"p\",TCon logic1.and [TVar \"q\",TVar \"r\"]],TCon logic1.not [TVar \"r\"]],TCon logic1.or [TVar \"s\",TCon logic1.not [TVar \"r\"]]],TCon logic1.not [TVar \"s\"]])" Environment