{"logics": [{"logic": "E", "axioms": {"T": {"status": false, "ref": "LogicE.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicE.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicE.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicE.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicE.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicE.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicE.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicE.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicE.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicE.not_provable_axiomFour"}}}, {"logic": "E4", "axioms": {"T": {"status": false, "ref": "LogicE4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicE4.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicE4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicE4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicE4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicE4.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicE4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicE4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicE4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicE4", "derived": false}}}, {"logic": "E5", "axioms": {"T": {"status": false, "ref": "LogicE5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicE5.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicE5.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicE5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicE5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicE5.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicE5.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicE5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicE5", "derived": false}, "4": {"status": false, "ref": "LogicE5.not_provable_axiomFour"}}}, {"logic": "EB", "axioms": {"T": {"status": false, "ref": "LogicEB.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEB.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEB.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEB.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEB.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEB.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEB", "derived": false}, "5": {"status": false, "ref": "LogicEB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEB.not_provable_axiomFour"}}}, {"logic": "EC", "axioms": {"T": {"status": false, "ref": "LogicEC.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEC.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEC.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEC.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEC.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEC.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicEC", "derived": false}, "B": {"status": false, "ref": "LogicEC.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEC.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEC.not_provable_axiomFour"}}}, {"logic": "ED", "axioms": {"T": {"status": false, "ref": "LogicED.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicED.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicED.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicED.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicED.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicED", "derived": false}, "C": {"status": false, "ref": "LogicED.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicED.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicED.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicED.not_provable_axiomFour"}}}, {"logic": "EK", "axioms": {"T": {"status": false, "ref": "LogicEK.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEK.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEK.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEK.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEK", "derived": false}, "D": {"status": false, "ref": "LogicEK.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEK.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEK.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEK.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEK.not_provable_axiomFour"}}}, {"logic": "EM", "axioms": {"T": {"status": false, "ref": "LogicEM.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEM.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEM.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEM", "derived": false}, "K": {"status": false, "ref": "LogicEM.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEM.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEM.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEM.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEM.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEM.not_provable_axiomFour"}}}, {"logic": "EN", "axioms": {"T": {"status": false, "ref": "LogicEN.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEN.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicEN", "derived": false}, "M": {"status": false, "ref": "LogicEN.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEN.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEN.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEN.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEN.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEN.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEN.not_provable_axiomFour"}}}, {"logic": "EP", "axioms": {"T": {"status": false, "ref": "LogicEP.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEP", "derived": false}, "N": {"status": false, "ref": "LogicEP.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEP.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEP.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEP.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEP.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEP.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEP.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEP.not_provable_axiomFour"}}}, {"logic": "ET", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicET", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicET.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicET.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicET.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicET.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicET.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicET.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicET.not_provable_axiomFour"}}}, {"logic": "E45", "axioms": {"T": {"status": false, "ref": "LogicE45.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicE45.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicE45.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicE45.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicE45.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicE45.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicE45.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicE45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicE45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicE45", "derived": false}}}, {"logic": "EB4", "axioms": {"T": {"status": false, "ref": "LogicEB4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEB4.not_provable_axiomP"}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomBOfHasAxiomFour", "derived": true}, "M": {"status": false, "ref": "LogicEB4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEB4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEB4.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEB4.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEB4", "derived": false}, "5": {"status": false, "ref": "LogicEB4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEB4", "derived": false}}}, {"logic": "EB5", "axioms": {"T": {"status": false, "ref": "LogicEB5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEB5.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEB5.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEB5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEB5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEB5.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEB5.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEB5", "derived": false}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEB5", "derived": false}, "4": {"status": false, "ref": "LogicEB5.not_provable_axiomFour"}}}, {"logic": "EC4", "axioms": {"T": {"status": false, "ref": "LogicEC4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEC4.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEC4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEC4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEC4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEC4.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicEC4", "derived": false}, "B": {"status": false, "ref": "LogicEC4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEC4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEC4", "derived": false}}}, {"logic": "EC5", "axioms": {"T": {"status": false, "ref": "LogicEC5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEC5.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEC5.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEC5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEC5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEC5.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicEC5", "derived": false}, "B": {"status": false, "ref": "LogicEC5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEC5", "derived": false}, "4": {"status": false, "ref": "LogicEC5.not_provable_axiomFour"}}}, {"logic": "ECB", "axioms": {"T": {"status": false, "ref": "LogicECB.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECB.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECB.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECB.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicECB.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECB", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECB", "derived": false}, "5": {"status": false, "ref": "LogicECB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECB.not_provable_axiomFour"}}}, {"logic": "ECD", "axioms": {"T": {"status": false, "ref": "LogicECD.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECD.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECD.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECD.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECD.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicECD", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECD", "derived": false}, "B": {"status": false, "ref": "LogicECD.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECD.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECD.not_provable_axiomFour"}}}, {"logic": "ECK", "axioms": {"T": {"status": false, "ref": "LogicECK.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECK.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECK.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECK.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicECK", "derived": false}, "D": {"status": false, "ref": "LogicECK.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECK", "derived": false}, "B": {"status": false, "ref": "LogicECK.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECK.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECK.not_provable_axiomFour"}}}, {"logic": "ECN", "axioms": {"T": {"status": false, "ref": "LogicECN.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECN.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicECN", "derived": false}, "M": {"status": false, "ref": "LogicECN.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECN.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicECN.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECN", "derived": false}, "B": {"status": false, "ref": "LogicECN.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECN.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECN.not_provable_axiomFour"}}}, {"logic": "ECP", "axioms": {"T": {"status": false, "ref": "LogicECP.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicECP", "derived": false}, "N": {"status": false, "ref": "LogicECP.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECP.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECP.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomCOfHasAxiomP", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECP", "derived": false}, "B": {"status": false, "ref": "LogicECP.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECP.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECP.not_provable_axiomFour"}}}, {"logic": "ECT", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicECT", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicECT.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECT.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECT.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECT", "derived": false}, "B": {"status": false, "ref": "LogicECT.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECT.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECT.not_provable_axiomFour"}}}, {"logic": "ED4", "axioms": {"T": {"status": false, "ref": "LogicED4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicED4.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicED4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicED4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicED4.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicED4", "derived": false}, "C": {"status": false, "ref": "LogicED4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicED4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicED4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicED4", "derived": false}}}, {"logic": "ED5", "axioms": {"T": {"status": false, "ref": "LogicED5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicED5.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicED5.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicED5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicED5.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicED5", "derived": false}, "C": {"status": false, "ref": "LogicED5.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicED5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicED5", "derived": false}, "4": {"status": false, "ref": "LogicED5.not_provable_axiomFour"}}}, {"logic": "EDB", "axioms": {"T": {"status": false, "ref": "LogicEDB.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEDB.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEDB.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEDB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEDB.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEDB", "derived": false}, "C": {"status": false, "ref": "LogicEDB.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEDB", "derived": false}, "5": {"status": false, "ref": "LogicEDB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEDB.not_provable_axiomFour"}}}, {"logic": "EDP", "axioms": {"T": {"status": false, "ref": "LogicEDP.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEDP", "derived": false}, "N": {"status": false, "ref": "LogicEDP.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEDP.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEDP.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEDP", "derived": false}, "C": {"status": false, "ref": "LogicEDP.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEDP.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEDP.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEDP.not_provable_axiomFour"}}}, {"logic": "EK4", "axioms": {"T": {"status": false, "ref": "LogicEK4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEK4.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEK4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEK4.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEK4", "derived": false}, "D": {"status": false, "ref": "LogicEK4.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEK4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEK4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEK4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEK4", "derived": false}}}, {"logic": "EK5", "axioms": {"T": {"status": false, "ref": "LogicEK5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEK5.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEK5.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEK5.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEK5", "derived": false}, "D": {"status": false, "ref": "LogicEK5.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEK5.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEK5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEK5", "derived": false}, "4": {"status": false, "ref": "LogicEK5.not_provable_axiomFour"}}}, {"logic": "EKB", "axioms": {"T": {"status": false, "ref": "LogicEKB.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEKB.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEKB.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEKB.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEKB", "derived": false}, "D": {"status": false, "ref": "LogicEKB.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEKB.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEKB", "derived": false}, "5": {"status": false, "ref": "LogicEKB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEKB.not_provable_axiomFour"}}}, {"logic": "EKD", "axioms": {"T": {"status": false, "ref": "LogicEKD.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEKD.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEKD.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEKD.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEKD", "derived": false}, "D": {"status": true, "ref": "instHasAxiomDLogicEKD", "derived": false}, "C": {"status": false, "ref": "LogicEKD.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEKD.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEKD.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEKD.not_provable_axiomFour"}}}, {"logic": "EKP", "axioms": {"T": {"status": false, "ref": "LogicEKP.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEKP", "derived": false}, "N": {"status": false, "ref": "LogicEKP.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEKP.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEKP", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomKOfHasAxiomP", "derived": true}, "C": {"status": false, "ref": "LogicEKP.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEKP.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEKP.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEKP.not_provable_axiomFour"}}}, {"logic": "EKT", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEKT", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicEKT.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEKT.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEKT", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicEKT.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEKT.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEKT.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEKT.not_provable_axiomFour"}}}, {"logic": "EM4", "axioms": {"T": {"status": false, "ref": "LogicEM4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEM4.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEM4.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEM4", "derived": false}, "K": {"status": false, "ref": "LogicEM4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEM4.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEM4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEM4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEM4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEM4", "derived": false}}}, {"logic": "EM5", "axioms": {"T": {"status": false, "ref": "LogicEM5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEM5.not_provable_axiomP"}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomMOfHasAxiomFive", "derived": true}, "M": {"status": true, "ref": "instHasAxiomMLogicEM5", "derived": false}, "K": {"status": false, "ref": "LogicEM5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEM5.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEM5.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEM5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEM5", "derived": false}, "4": {"status": false, "ref": "LogicEM5.not_provable_axiomFour"}}}, {"logic": "EMB", "axioms": {"T": {"status": false, "ref": "LogicEMB.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEMB.not_provable_axiomP"}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomMOfHasAxiomB", "derived": true}, "M": {"status": true, "ref": "instHasAxiomMLogicEMB", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": false, "ref": "LogicEMB.not_provable_axiomD"}, "C": {"status": true, "ref": "Logic.instHasAxiomCOfHasAxiomMOfHasAxiomB", "derived": true}, "B": {"status": true, "ref": "instHasAxiomBLogicEMB", "derived": false}, "5": {"status": false, "ref": "LogicEMB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMB.not_provable_axiomFour"}}}, {"logic": "EMC", "axioms": {"T": {"status": false, "ref": "LogicEMC.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEMC.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEMC.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMC", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": false, "ref": "LogicEMC.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicEMC", "derived": false}, "B": {"status": false, "ref": "LogicEMC.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMC.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMC.not_provable_axiomFour"}}}, {"logic": "EMD", "axioms": {"T": {"status": false, "ref": "LogicEMD.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomMOfHasAxiomD", "derived": true}, "N": {"status": false, "ref": "LogicEMD.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMD", "derived": false}, "K": {"status": false, "ref": "LogicEMD.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEMD", "derived": false}, "C": {"status": false, "ref": "LogicEMD.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMD.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMD.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMD.not_provable_axiomFour"}}}, {"logic": "EMK", "equivalentTo": "EMC"}, {"logic": "EMN", "axioms": {"T": {"status": false, "ref": "LogicEMN.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEMN.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicEMN", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMN", "derived": false}, "K": {"status": false, "ref": "LogicEMN.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEMN.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEMN.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMN.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMN.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMN.not_provable_axiomFour"}}}, {"logic": "EMP", "axioms": {"T": {"status": false, "ref": "LogicEMP.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEMP", "derived": false}, "N": {"status": false, "ref": "LogicEMP.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMP", "derived": false}, "K": {"status": false, "ref": "LogicEMP.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEMP.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEMP.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMP.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMP.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMP.not_provable_axiomFour"}}}, {"logic": "EMT", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEMT", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicEMT.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMT", "derived": false}, "K": {"status": false, "ref": "LogicEMT.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicEMT.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMT.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMT.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMT.not_provable_axiomFour"}}}, {"logic": "EN4", "axioms": {"T": {"status": false, "ref": "LogicEN4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEN4.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicEN4", "derived": false}, "M": {"status": false, "ref": "LogicEN4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEN4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEN4.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEN4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEN4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEN4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEN4", "derived": false}}}, {"logic": "EN5", "axioms": {"T": {"status": false, "ref": "LogicEN5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEN5.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicEN5", "derived": false}, "M": {"status": false, "ref": "LogicEN5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEN5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEN5.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEN5.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEN5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEN5", "derived": false}, "4": {"status": false, "ref": "LogicEN5.not_provable_axiomFour"}}}, {"logic": "ENB", "axioms": {"T": {"status": false, "ref": "LogicENB.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicENB.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicENB", "derived": false}, "M": {"status": false, "ref": "LogicENB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicENB.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicENB.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicENB.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicENB", "derived": false}, "5": {"status": false, "ref": "LogicENB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicENB.not_provable_axiomFour"}}}, {"logic": "END", "axioms": {"T": {"status": false, "ref": "LogicEND.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicEND", "derived": false}, "M": {"status": false, "ref": "LogicEND.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEND.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEND", "derived": false}, "C": {"status": false, "ref": "LogicEND.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEND.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEND.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEND.not_provable_axiomFour"}}}, {"logic": "ENK", "axioms": {"T": {"status": false, "ref": "LogicEMCN.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEMCN.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicENK", "derived": false}, "M": {"status": true, "ref": "Logic.instHasAxiomMOfHasAxiomKOfHasAxiomN", "derived": true}, "K": {"status": true, "ref": "instHasAxiomKLogicENK", "derived": false}, "D": {"status": false, "ref": "LogicEMCN.not_provable_axiomD"}, "C": {"status": true, "ref": "Logic.instHasAxiomCOfHasAxiomMOfHasAxiomK", "derived": true}, "B": {"status": false, "ref": "LogicEMCN.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMCN.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMCN.not_provable_axiomFour"}}}, {"logic": "ENP", "axioms": {"T": {"status": false, "ref": "LogicENP.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicENP", "derived": false}, "N": {"status": true, "ref": "instHasAxiomNLogicENP", "derived": false}, "M": {"status": false, "ref": "LogicENP.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicENP.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicENP.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicENP.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicENP.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicENP.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicENP.not_provable_axiomFour"}}}, {"logic": "ENT", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicENT", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicENT", "derived": false}, "M": {"status": false, "ref": "LogicENT.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicENT.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicENT.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicENT.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicENT.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicENT.not_provable_axiomFour"}}}, {"logic": "EP4", "axioms": {"T": {"status": false, "ref": "LogicEP4.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEP4", "derived": false}, "N": {"status": false, "ref": "LogicEP4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEP4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEP4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEP4.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEP4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEP4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEP4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEP4", "derived": false}}}, {"logic": "EP5", "axioms": {"T": {"status": false, "ref": "LogicEP5.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEP5", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": false, "ref": "LogicEP5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEP5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEP5.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEP5.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEP5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEP5", "derived": false}, "4": {"status": false, "ref": "LogicEP5.not_provable_axiomFour"}}}, {"logic": "EPB", "axioms": {"T": {"status": false, "ref": "LogicEPB.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEPB", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomB", "derived": true}, "M": {"status": false, "ref": "LogicEPB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEPB.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEPB.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEPB.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEPB", "derived": false}, "5": {"status": false, "ref": "LogicEPB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEPB.not_provable_axiomFour"}}}, {"logic": "ET4", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicET4", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicET4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicET4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicET4.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicET4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicET4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicET4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicET4", "derived": false}}}, {"logic": "ET5", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicET5", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "LogicET5.instHasAxiomN", "derived": true}, "M": {"status": false, "ref": "LogicET5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicET5.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicET5.not_provable_axiomC"}, "B": {"status": true, "ref": "Logic.instHasAxiomBOfHasAxiomTOfHasAxiomFive", "derived": true}, "5": {"status": true, "ref": "instHasAxiomFiveLogicET5", "derived": false}, "4": {"status": true, "ref": "Logic.instHasAxiomFourOfHasAxiomTOfHasAxiomFive", "derived": true}}}, {"logic": "ETB", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicETB", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomTOfHasAxiomB", "derived": true}, "M": {"status": false, "ref": "LogicETB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicETB.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicETB.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicETB", "derived": false}, "5": {"status": false, "ref": "LogicETB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicETB.not_provable_axiomFour"}}}, {"logic": "ETD", "equivalentTo": "ET"}, {"logic": "ETP", "equivalentTo": "ET"}, {"logic": "EB45", "axioms": {"T": {"status": false, "ref": "LogicEB45.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEB45.not_provable_axiomP"}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomBOfHasAxiomFour", "derived": true}, "M": {"status": false, "ref": "LogicEB45.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEB45.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEB45.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEB45.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEB45", "derived": false}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEB45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicEB45", "derived": false}}}, {"logic": "EC45", "axioms": {"T": {"status": false, "ref": "LogicEC45.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEC45.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEC45.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEC45.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEC45.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEC45.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicEC45", "derived": false}, "B": {"status": false, "ref": "LogicEC45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEC45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicEC45", "derived": false}}}, {"logic": "ECB4", "axioms": {"T": {"status": false, "ref": "LogicECB4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECB4.not_provable_axiomP"}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomBOfHasAxiomFour", "derived": true}, "M": {"status": false, "ref": "LogicECB4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECB4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicECB4.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECB4", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECB4", "derived": false}, "5": {"status": false, "ref": "LogicECB4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicECB4", "derived": false}}}, {"logic": "ECB5", "axioms": {"T": {"status": false, "ref": "LogicECB5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECB5.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECB5.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECB5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECB5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicECB5.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECB5", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECB5", "derived": false}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECB5", "derived": false}, "4": {"status": false, "ref": "LogicECB5.not_provable_axiomFour"}}}, {"logic": "ECD4", "axioms": {"T": {"status": false, "ref": "LogicECD4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECD4.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECD4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECD4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECD4.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicECD4", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECD4", "derived": false}, "B": {"status": false, "ref": "LogicECD4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECD4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicECD4", "derived": false}}}, {"logic": "ECD5", "axioms": {"T": {"status": false, "ref": "LogicECD5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECD5.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECD5.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECD5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECD5.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicECD5", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECD5", "derived": false}, "B": {"status": false, "ref": "LogicECD5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECD5", "derived": false}, "4": {"status": false, "ref": "LogicECD5.not_provable_axiomFour"}}}, {"logic": "ECDB", "axioms": {"T": {"status": false, "ref": "LogicECDB.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECDB.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECDB.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECDB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECDB.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicECDB", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECDB", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECDB", "derived": false}, "5": {"status": false, "ref": "LogicECDB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECDB.not_provable_axiomFour"}}}, {"logic": "ECDP", "equivalentTo": "ECP"}, {"logic": "ECK4", "axioms": {"T": {"status": false, "ref": "LogicECK4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECK4.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECK4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECK4.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicECK4", "derived": false}, "D": {"status": false, "ref": "LogicECK4.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECK4", "derived": false}, "B": {"status": false, "ref": "LogicECK4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECK4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicECK4", "derived": false}}}, {"logic": "ECK5", "axioms": {"T": {"status": false, "ref": "LogicECK5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECK5.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECK5.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECK5.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicECK5", "derived": false}, "D": {"status": false, "ref": "LogicECK5.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECK5", "derived": false}, "B": {"status": false, "ref": "LogicECK5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECK5", "derived": false}, "4": {"status": false, "ref": "LogicECK5.not_provable_axiomFour"}}}, {"logic": "ECKB", "axioms": {"T": {"status": false, "ref": "LogicECKB.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECKB.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECKB.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECKB.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicECKB", "derived": false}, "D": {"status": false, "ref": "LogicECKB.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECKB", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECKB", "derived": false}, "5": {"status": false, "ref": "LogicECKB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECKB.not_provable_axiomFour"}}}, {"logic": "ECKD", "axioms": {"T": {"status": false, "ref": "LogicECKD.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECKD.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECKD.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECKD.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicECKD", "derived": false}, "D": {"status": true, "ref": "instHasAxiomDLogicECKD", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECKD", "derived": false}, "B": {"status": false, "ref": "LogicECKD.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECKD.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECKD.not_provable_axiomFour"}}}, {"logic": "ECKP", "axioms": {"T": {"status": false, "ref": "LogicECKP.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicECKP", "derived": false}, "N": {"status": false, "ref": "LogicECKP.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECKP.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicECKP", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomKOfHasAxiomP", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECKP", "derived": false}, "B": {"status": false, "ref": "LogicECKP.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECKP.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECKP.not_provable_axiomFour"}}}, {"logic": "ECKT", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicECKT", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicECKT.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECKT.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicECKT", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECKT", "derived": false}, "B": {"status": false, "ref": "LogicECKT.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECKT.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECKT.not_provable_axiomFour"}}}, {"logic": "ECN4", "axioms": {"T": {"status": false, "ref": "LogicECN4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECN4.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicECN4", "derived": false}, "M": {"status": false, "ref": "LogicECN4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECN4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicECN4.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECN4", "derived": false}, "B": {"status": false, "ref": "LogicECN4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECN4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicECN4", "derived": false}}}, {"logic": "ECN5", "axioms": {"T": {"status": false, "ref": "LogicECN5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECN5.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicECN5", "derived": false}, "M": {"status": false, "ref": "LogicECN5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECN5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicECN5.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECN5", "derived": false}, "B": {"status": false, "ref": "LogicECN5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECN5", "derived": false}, "4": {"status": false, "ref": "LogicECN5.not_provable_axiomFour"}}}, {"logic": "ECNB", "axioms": {"T": {"status": false, "ref": "LogicECNB.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECNB.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicECNB", "derived": false}, "M": {"status": false, "ref": "LogicECNB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECNB.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicECNB.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECNB", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECNB", "derived": false}, "5": {"status": false, "ref": "LogicECNB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECNB.not_provable_axiomFour"}}}, {"logic": "ECND", "axioms": {"T": {"status": false, "ref": "LogicECND.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicECND", "derived": false}, "M": {"status": false, "ref": "LogicECND.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECND.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicECND", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECND", "derived": false}, "B": {"status": false, "ref": "LogicECND.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECND.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECND.not_provable_axiomFour"}}}, {"logic": "ECNK", "equivalentTo": "ENK"}, {"logic": "ECNP", "equivalentTo": "ECND"}, {"logic": "ECNT", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicECNT", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicECNT", "derived": false}, "M": {"status": false, "ref": "LogicECNT.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECNT.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECNT", "derived": false}, "B": {"status": false, "ref": "LogicECNT.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECNT.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECNT.not_provable_axiomFour"}}}, {"logic": "ECP4", "axioms": {"T": {"status": false, "ref": "LogicECP4.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicECP4", "derived": false}, "N": {"status": false, "ref": "LogicECP4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECP4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECP4.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomCOfHasAxiomP", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECP4", "derived": false}, "B": {"status": false, "ref": "LogicECP4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECP4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicECP4", "derived": false}}}, {"logic": "ECP5", "axioms": {"T": {"status": false, "ref": "LogicECP5.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicECP5", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": false, "ref": "LogicECP5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECP5.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomCOfHasAxiomP", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECP5", "derived": false}, "B": {"status": false, "ref": "LogicECP5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECP5", "derived": false}, "4": {"status": false, "ref": "LogicECP5.not_provable_axiomFour"}}}, {"logic": "ECPB", "axioms": {"T": {"status": false, "ref": "LogicECPB.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicECPB", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomB", "derived": true}, "M": {"status": false, "ref": "LogicECPB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECPB.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomCOfHasAxiomP", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECPB", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECPB", "derived": false}, "5": {"status": false, "ref": "LogicECPB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECPB.not_provable_axiomFour"}}}, {"logic": "ECT4", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicECT4", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicECT4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECT4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECT4.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECT4", "derived": false}, "B": {"status": false, "ref": "LogicECT4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECT4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicECT4", "derived": false}}}, {"logic": "ECT5", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicECT5", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomTOfHasAxiomB", "derived": true}, "M": {"status": false, "ref": "LogicECT5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECT5.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECT5", "derived": false}, "B": {"status": true, "ref": "Logic.instHasAxiomBOfHasAxiomTOfHasAxiomFive", "derived": true}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECT5", "derived": false}, "4": {"status": true, "ref": "Logic.instHasAxiomFourOfHasAxiomTOfHasAxiomFive", "derived": true}}}, {"logic": "ECTB", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicECTB", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomTOfHasAxiomB", "derived": true}, "M": {"status": false, "ref": "LogicECTB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECTB.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECTB", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECTB", "derived": false}, "5": {"status": false, "ref": "LogicECTB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECTB.not_provable_axiomFour"}}}, {"logic": "ECTD", "equivalentTo": "ECT"}, {"logic": "ECTP", "equivalentTo": "ECT"}, {"logic": "ED45", "axioms": {"T": {"status": false, "ref": "LogicED45.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicED45.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicED45.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicED45.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicED45.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicED45", "derived": false}, "C": {"status": false, "ref": "LogicED45.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicED45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicED45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicED45", "derived": false}}}, {"logic": "EDB4", "equivalentTo": "ET5"}, {"logic": "EDB5", "axioms": {"T": {"status": false, "ref": "LogicEDB5.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomDOfHasAxiomBOfHasAxiomFive", "derived": true}, "M": {"status": false, "ref": "LogicEDB5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEDB5.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEDB5", "derived": false}, "C": {"status": false, "ref": "LogicEDB5.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEDB5", "derived": false}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEDB5", "derived": false}, "4": {"status": false, "ref": "LogicEDB5.not_provable_axiomFour"}}}, {"logic": "EDP4", "axioms": {"T": {"status": false, "ref": "LogicEDP4.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEDP4", "derived": false}, "N": {"status": false, "ref": "LogicEDP4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEDP4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEDP4.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEDP4", "derived": false}, "C": {"status": false, "ref": "LogicEDP4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEDP4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEDP4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEDP4", "derived": false}}}, {"logic": "EDP5", "axioms": {"T": {"status": false, "ref": "LogicEND5.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEDP5", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": false, "ref": "LogicEND5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEND5.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEDP5", "derived": false}, "C": {"status": false, "ref": "LogicEND5.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEND5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEDP5", "derived": false}, "4": {"status": false, "ref": "LogicEND5.not_provable_axiomFour"}}}, {"logic": "EDPB", "axioms": {"T": {"status": false, "ref": "LogicENDB.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEDPB", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomB", "derived": true}, "M": {"status": false, "ref": "LogicENDB.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicENDB.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEDPB", "derived": false}, "C": {"status": false, "ref": "LogicENDB.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEDPB", "derived": false}, "5": {"status": false, "ref": "LogicENDB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicENDB.not_provable_axiomFour"}}}, {"logic": "EK45", "axioms": {"T": {"status": false, "ref": "LogicEK45.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEK45.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEK45.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEK45.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEK45", "derived": false}, "D": {"status": false, "ref": "LogicEK45.not_provable_axiomD"}, "C": null, "B": {"status": false, "ref": "LogicEK45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEK45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicEK45", "derived": false}}}, {"logic": "EKB4", "axioms": {"T": {"status": false, "ref": "LogicEMB4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEMB4.not_provable_axiomP"}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomBOfHasAxiomFour", "derived": true}, "M": {"status": true, "ref": "Logic.instHasAxiomMOfHasAxiomKOfHasAxiomN", "derived": true}, "K": {"status": true, "ref": "instHasAxiomKLogicEKB4", "derived": false}, "D": {"status": false, "ref": "LogicEMB4.not_provable_axiomD"}, "C": {"status": true, "ref": "Logic.instHasAxiomCOfHasAxiomMOfHasAxiomB", "derived": true}, "B": {"status": true, "ref": "instHasAxiomBLogicEKB4", "derived": false}, "5": {"status": true, "ref": "Logic.instHasAxiomFiveOfHasAxiomMOfHasAxiomBOfHasAxiomFour", "derived": true}, "4": {"status": true, "ref": "instHasAxiomFourLogicEKB4", "derived": false}}}, {"logic": "EKB5", "axioms": {"T": {"status": false, "ref": "LogicEKB5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEKB5.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEKB5.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEKB5.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEKB5", "derived": false}, "D": {"status": false, "ref": "LogicEKB5.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEKB5.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEKB5", "derived": false}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEKB5", "derived": false}, "4": {"status": false, "ref": "LogicEKB5.not_provable_axiomFour"}}}, {"logic": "EKD4", "axioms": {"T": {"status": false, "ref": "LogicEKD4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEKD4.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEKD4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEKD4.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEKD4", "derived": false}, "D": {"status": true, "ref": "instHasAxiomDLogicEKD4", "derived": false}, "C": {"status": false, "ref": "LogicEKD4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEKD4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEKD4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEKD4", "derived": false}}}, {"logic": "EKD5", "axioms": {"T": {"status": false, "ref": "LogicEKD5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEKD5.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEKD5.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEKD5.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEKD5", "derived": false}, "D": {"status": true, "ref": "instHasAxiomDLogicEKD5", "derived": false}, "C": null, "B": {"status": false, "ref": "LogicEKD5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEKD5", "derived": false}, "4": {"status": false, "ref": "LogicEKD5.not_provable_axiomFour"}}}, {"logic": "EKDB", "axioms": {"T": {"status": false, "ref": "LogicEKDB.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEKDB.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEKDB.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEKDB.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEKDB", "derived": false}, "D": {"status": true, "ref": "instHasAxiomDLogicEKDB", "derived": false}, "C": null, "B": {"status": true, "ref": "instHasAxiomBLogicEKDB", "derived": false}, "5": {"status": false, "ref": "LogicEKDB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEKDB.not_provable_axiomFour"}}}, {"logic": "EKDP", "equivalentTo": "EKP"}, {"logic": "EKP4", "axioms": {"T": {"status": false, "ref": "LogicEKP4.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEKP4", "derived": false}, "N": {"status": false, "ref": "LogicEKP4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEKP4.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEKP4", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomKOfHasAxiomP", "derived": true}, "C": {"status": false, "ref": "LogicEKP4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEKP4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEKP4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEKP4", "derived": false}}}, {"logic": "EKP5", "axioms": {"T": {"status": false, "ref": "LogicEKP5.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEKP5", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": true, "ref": "Logic.instHasAxiomMOfHasAxiomKOfHasAxiomN", "derived": true}, "K": {"status": true, "ref": "instHasAxiomKLogicEKP5", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomKOfHasAxiomP", "derived": true}, "C": {"status": true, "ref": "Logic.instHasAxiomCOfHasAxiomMOfHasAxiomK", "derived": true}, "B": {"status": false, "ref": "LogicEKP5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEKP5", "derived": false}, "4": {"status": false, "ref": "LogicEKP5.not_provable_axiomFour"}}}, {"logic": "EKPB", "axioms": {"T": {"status": false, "ref": "LogicEMDB.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEKPB", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomB", "derived": true}, "M": {"status": true, "ref": "Logic.instHasAxiomMOfHasAxiomKOfHasAxiomN", "derived": true}, "K": {"status": true, "ref": "instHasAxiomKLogicEKPB", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomKOfHasAxiomP", "derived": true}, "C": {"status": true, "ref": "Logic.instHasAxiomCOfHasAxiomMOfHasAxiomB", "derived": true}, "B": {"status": true, "ref": "instHasAxiomBLogicEKPB", "derived": false}, "5": {"status": false, "ref": "LogicEMDB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMDB.not_provable_axiomFour"}}}, {"logic": "EKT4", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEKT4", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicEKT4.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicEKT4.not_provable_axiomM"}, "K": {"status": true, "ref": "instHasAxiomKLogicEKT4", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicEKT4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEKT4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEKT4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEKT4", "derived": false}}}, {"logic": "EKT5", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEKT5", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomTOfHasAxiomB", "derived": true}, "M": {"status": true, "ref": "Logic.instHasAxiomMOfHasAxiomKOfHasAxiomN", "derived": true}, "K": {"status": true, "ref": "instHasAxiomKLogicEKT5", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "Logic.instHasAxiomCOfHasAxiomMOfHasAxiomB", "derived": true}, "B": {"status": true, "ref": "Logic.instHasAxiomBOfHasAxiomTOfHasAxiomFive", "derived": true}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEKT5", "derived": false}, "4": {"status": true, "ref": "Logic.instHasAxiomFourOfHasAxiomTOfHasAxiomFive", "derived": true}}}, {"logic": "EKTB", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEKTB", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomTOfHasAxiomB", "derived": true}, "M": {"status": true, "ref": "Logic.instHasAxiomMOfHasAxiomKOfHasAxiomN", "derived": true}, "K": {"status": true, "ref": "instHasAxiomKLogicEKTB", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "Logic.instHasAxiomCOfHasAxiomMOfHasAxiomB", "derived": true}, "B": {"status": true, "ref": "instHasAxiomBLogicEKTB", "derived": false}, "5": {"status": false, "ref": "LogicEMTB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMTB.not_provable_axiomFour"}}}, {"logic": "EKTD", "equivalentTo": "EKT"}, {"logic": "EKTP", "equivalentTo": "EKT"}, {"logic": "EM45", "axioms": {"T": {"status": false, "ref": "LogicEM45.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEM45.not_provable_axiomP"}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomMOfHasAxiomFive", "derived": true}, "M": {"status": true, "ref": "instHasAxiomMLogicEM45", "derived": false}, "K": {"status": false, "ref": "LogicEM45.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEM45.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEM45.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEM45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEM45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicEM45", "derived": false}}}, {"logic": "EMB4", "equivalentTo": "EKB4"}, {"logic": "EMB5", "equivalentTo": "EKB4"}, {"logic": "EMC4", "axioms": {"T": {"status": false, "ref": "LogicEMC4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEMC4.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicEMC4.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMC4", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": false, "ref": "LogicEMC4.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicEMC4", "derived": false}, "B": {"status": false, "ref": "LogicEMC4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMC4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMC4", "derived": false}}}, {"logic": "EMC5", "axioms": {"T": {"status": false, "ref": "LogicEMC5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEMC5.not_provable_axiomP"}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomMOfHasAxiomFive", "derived": true}, "M": {"status": true, "ref": "instHasAxiomMLogicEMC5", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": false, "ref": "LogicEMC5.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicEMC5", "derived": false}, "B": {"status": false, "ref": "LogicEMC5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEMC5", "derived": false}, "4": {"status": false, "ref": "LogicEMC5.not_provable_axiomFour"}}}, {"logic": "EMCB", "equivalentTo": "EMB"}, {"logic": "EMCD", "axioms": {"T": {"status": false, "ref": "LogicEMCD.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomMOfHasAxiomD", "derived": true}, "N": {"status": false, "ref": "LogicEMCD.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMCD", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": true, "ref": "instHasAxiomDLogicEMCD", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicEMCD", "derived": false}, "B": {"status": false, "ref": "LogicEMCD.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMCD.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMCD.not_provable_axiomFour"}}}, {"logic": "EMCK", "equivalentTo": "EMC"}, {"logic": "EMCN", "equivalentTo": "ENK"}, {"logic": "EMCP", "equivalentTo": "EMCD"}, {"logic": "EMCT", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEMCT", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicEMCT.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMCT", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicEMCT", "derived": false}, "B": {"status": false, "ref": "LogicEMCT.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMCT.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMCT.not_provable_axiomFour"}}}, {"logic": "EMD4", "axioms": {"T": {"status": false, "ref": "LogicEMD4.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomMOfHasAxiomD", "derived": true}, "N": {"status": false, "ref": "LogicEMD4.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMD4", "derived": false}, "K": {"status": false, "ref": "LogicEMD4.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEMD4", "derived": false}, "C": {"status": false, "ref": "LogicEMD4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMD4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMD4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMD4", "derived": false}}}, {"logic": "EMD5", "axioms": {"T": {"status": false, "ref": "LogicEMD5.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": true, "ref": "instHasAxiomMLogicEMD5", "derived": false}, "K": {"status": false, "ref": "LogicEMD5.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEMD5", "derived": false}, "C": {"status": false, "ref": "LogicEMD5.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMD5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEMD5", "derived": false}, "4": {"status": false, "ref": "LogicEMD5.not_provable_axiomFour"}}}, {"logic": "EMDB", "equivalentTo": "EKPB"}, {"logic": "EMDP", "equivalentTo": "EMD"}, {"logic": "EMK4", "equivalentTo": "EMC4"}, {"logic": "EMK5", "equivalentTo": "EMC5"}, {"logic": "EMKB", "equivalentTo": "EMB"}, {"logic": "EMKD", "equivalentTo": "EMCD"}, {"logic": "EMKP", "equivalentTo": "EMCD"}, {"logic": "EMKT", "equivalentTo": "EMCT"}, {"logic": "EMN4", "axioms": {"T": {"status": false, "ref": "LogicEMN4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEMN4.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicEMN4", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMN4", "derived": false}, "K": {"status": false, "ref": "LogicEMN4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEMN4.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEMN4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMN4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMN4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMN4", "derived": false}}}, {"logic": "EMN5", "equivalentTo": "EM5"}, {"logic": "EMNB", "equivalentTo": "EMB"}, {"logic": "EMND", "axioms": {"T": {"status": false, "ref": "LogicEMND.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicEMND", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMND", "derived": false}, "K": {"status": false, "ref": "LogicEMND.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEMND", "derived": false}, "C": {"status": false, "ref": "LogicEMND.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMND.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMND.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMND.not_provable_axiomFour"}}}, {"logic": "EMNK", "equivalentTo": "ENK"}, {"logic": "EMNP", "axioms": {"T": {"status": false, "ref": "LogicEMNP.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEMNP", "derived": false}, "N": {"status": true, "ref": "instHasAxiomNLogicEMNP", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMNP", "derived": false}, "K": {"status": false, "ref": "LogicEMNP.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEMNP.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEMNP.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMNP.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMNP.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMNP.not_provable_axiomFour"}}}, {"logic": "EMNT", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEMNT", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicEMNT", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMNT", "derived": false}, "K": {"status": false, "ref": "LogicEMNT.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicEMNT.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMNT.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMNT.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMNT.not_provable_axiomFour"}}}, {"logic": "EMP4", "axioms": {"T": {"status": false, "ref": "LogicEMP4.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEMP4", "derived": false}, "N": {"status": false, "ref": "LogicEMP4.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMP4", "derived": false}, "K": {"status": false, "ref": "LogicEMP4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEMP4.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEMP4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMP4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMP4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMP4", "derived": false}}}, {"logic": "EMP5", "axioms": {"T": {"status": false, "ref": "LogicEMP5.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEMP5", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": true, "ref": "instHasAxiomMLogicEMP5", "derived": false}, "K": {"status": false, "ref": "LogicEMP5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEMP5.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEMP5.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMP5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEMP5", "derived": false}, "4": {"status": false, "ref": "LogicEMP5.not_provable_axiomFour"}}}, {"logic": "EMPB", "equivalentTo": "EKPB"}, {"logic": "EMT4", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEMT4", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicEMT4.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMT4", "derived": false}, "K": {"status": false, "ref": "LogicEMT4.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicEMT4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMT4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMT4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMT4", "derived": false}}}, {"logic": "EMT5", "equivalentTo": "EKT5"}, {"logic": "EMTB", "equivalentTo": "EKTB"}, {"logic": "EMTD", "equivalentTo": "EMT"}, {"logic": "EMTP", "equivalentTo": "EMT"}, {"logic": "EN45", "axioms": {"T": {"status": false, "ref": "LogicEN45.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicEN45.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicEN45", "derived": false}, "M": {"status": false, "ref": "LogicEN45.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEN45.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEN45.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEN45.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEN45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEN45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicEN45", "derived": false}}}, {"logic": "ENB4", "equivalentTo": "EB4"}, {"logic": "ENB5", "axioms": {"T": {"status": false, "ref": "LogicENB5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicENB5.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicENB5", "derived": false}, "M": {"status": false, "ref": "LogicENB5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicENB5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicENB5.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicENB5.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicENB5", "derived": false}, "5": {"status": true, "ref": "instHasAxiomFiveLogicENB5", "derived": false}, "4": {"status": false, "ref": "LogicENB5.not_provable_axiomFour"}}}, {"logic": "END4", "axioms": {"T": {"status": false, "ref": "LogicEND4.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicEND4", "derived": false}, "M": {"status": false, "ref": "LogicEND4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEND4.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicEND4", "derived": false}, "C": {"status": false, "ref": "LogicEND4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEND4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEND4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEND4", "derived": false}}}, {"logic": "END5", "equivalentTo": "EDP5"}, {"logic": "ENDB", "equivalentTo": "EDPB"}, {"logic": "ENDP", "equivalentTo": "END"}, {"logic": "ENK4", "axioms": {"T": {"status": false, "ref": "LogicENK4.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicENK4.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicENK4", "derived": false}, "M": {"status": true, "ref": "Logic.instHasAxiomMOfHasAxiomKOfHasAxiomN", "derived": true}, "K": {"status": true, "ref": "instHasAxiomKLogicENK4", "derived": false}, "D": {"status": false, "ref": "LogicENK4.not_provable_axiomD"}, "C": {"status": true, "ref": "Logic.instHasAxiomCOfHasAxiomMOfHasAxiomK", "derived": true}, "B": {"status": false, "ref": "LogicENK4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicENK4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicENK4", "derived": false}}}, {"logic": "ENK5", "equivalentTo": "EMC5"}, {"logic": "ENKB", "equivalentTo": "EMB"}, {"logic": "ENKD", "axioms": {"T": {"status": false, "ref": "LogicENKD.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicENKD", "derived": false}, "M": {"status": true, "ref": "Logic.instHasAxiomMOfHasAxiomKOfHasAxiomN", "derived": true}, "K": {"status": true, "ref": "instHasAxiomKLogicENKD", "derived": false}, "D": {"status": true, "ref": "instHasAxiomDLogicENKD", "derived": false}, "C": {"status": true, "ref": "Logic.instHasAxiomCOfHasAxiomMOfHasAxiomK", "derived": true}, "B": {"status": false, "ref": "LogicENKD.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicENKD.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicENKD.not_provable_axiomFour"}}}, {"logic": "ENKP", "equivalentTo": "ENKD"}, {"logic": "ENKT", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicENKT", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicENKT", "derived": false}, "M": {"status": true, "ref": "Logic.instHasAxiomMOfHasAxiomKOfHasAxiomN", "derived": true}, "K": {"status": true, "ref": "instHasAxiomKLogicENKT", "derived": false}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "Logic.instHasAxiomCOfHasAxiomMOfHasAxiomK", "derived": true}, "B": {"status": false, "ref": "LogicENKT.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicENKT.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicENKT.not_provable_axiomFour"}}}, {"logic": "ENP4", "axioms": {"T": {"status": false, "ref": "LogicENP4.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicENP4", "derived": false}, "N": {"status": true, "ref": "instHasAxiomNLogicENP4", "derived": false}, "M": {"status": false, "ref": "LogicENP4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicENP4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicENP4.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicENP4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicENP4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicENP4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicENP4", "derived": false}}}, {"logic": "ENP5", "equivalentTo": "EP5"}, {"logic": "ENPB", "equivalentTo": "EPB"}, {"logic": "ENT4", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicENT4", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicENT4", "derived": false}, "M": {"status": false, "ref": "LogicENT4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicENT4.not_provable_axiomK"}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicENT4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicENT4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicENT4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicENT4", "derived": false}}}, {"logic": "ENT5", "equivalentTo": "ET5"}, {"logic": "ENTB", "equivalentTo": "ETB"}, {"logic": "ENTD", "equivalentTo": "ENT"}, {"logic": "ENTP", "equivalentTo": "ENT"}, {"logic": "EP45", "axioms": {"T": {"status": false, "ref": "LogicEP45.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEP45", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": false, "ref": "LogicEP45.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEP45.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEP45.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEP45.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEP45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEP45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicEP45", "derived": false}}}, {"logic": "EPB4", "axioms": {"T": {"status": false, "ref": "LogicEPB4.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEPB4", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomBOfHasAxiomFour", "derived": true}, "M": {"status": false, "ref": "LogicEPB4.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEPB4.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEPB4.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEPB4.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEPB4", "derived": false}, "5": {"status": false, "ref": "LogicEPB4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEPB4", "derived": false}}}, {"logic": "EPB5", "axioms": {"T": {"status": false, "ref": "LogicEPB5.not_provable_axiomT"}, "P": {"status": true, "ref": "instHasAxiomPLogicEPB5", "derived": false}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": false, "ref": "LogicEPB5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicEPB5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicEPB5.not_provable_axiomD"}, "C": {"status": false, "ref": "LogicEPB5.not_provable_axiomC"}, "B": {"status": true, "ref": "instHasAxiomBLogicEPB5", "derived": false}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEPB5", "derived": false}, "4": {"status": false, "ref": "LogicEPB5.not_provable_axiomFour"}}}, {"logic": "ET45", "equivalentTo": "ET5"}, {"logic": "ETB4", "equivalentTo": "ET5"}, {"logic": "ETB5", "equivalentTo": "ET5"}, {"logic": "ETD4", "equivalentTo": "ET4"}, {"logic": "ETD5", "equivalentTo": "ET5"}, {"logic": "ETDB", "equivalentTo": "ETB"}, {"logic": "ETDP", "equivalentTo": "ET"}, {"logic": "ETP4", "equivalentTo": "ET4"}, {"logic": "ETP5", "equivalentTo": "ET5"}, {"logic": "ETPB", "equivalentTo": "ETB"}, {"logic": "ECB45", "axioms": {"T": {"status": false, "ref": "LogicECB45.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECB45.not_provable_axiomP"}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomBOfHasAxiomFour", "derived": true}, "M": {"status": false, "ref": "LogicECB45.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECB45.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicECB45.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECB45", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECB45", "derived": false}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECB45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicECB45", "derived": false}}}, {"logic": "ECD45", "axioms": {"T": {"status": false, "ref": "LogicECD45.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECD45.not_provable_axiomP"}, "N": {"status": false, "ref": "LogicECD45.not_provable_axiomN"}, "M": {"status": false, "ref": "LogicECD45.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECD45.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicECD45", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECD45", "derived": false}, "B": {"status": false, "ref": "LogicECD45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECD45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicECD45", "derived": false}}}, {"logic": "ECDB4", "equivalentTo": "ECT5"}, {"logic": "ECDB5", "equivalentTo": "ECT5"}, {"logic": "ECN45", "axioms": {"T": {"status": false, "ref": "LogicECN45.not_provable_axiomT"}, "P": null, "N": {"status": true, "ref": "instHasAxiomNLogicECN45", "derived": false}, "M": {"status": false, "ref": "LogicECN45.not_provable_axiomM"}, "K": null, "D": {"status": false, "ref": "LogicECN45.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECN45", "derived": false}, "B": {"status": false, "ref": "LogicECN45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECN45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicECN45", "derived": false}}}, {"logic": "ECNB4", "equivalentTo": "ECB4"}, {"logic": "ECNB5", "axioms": {"T": {"status": false, "ref": "LogicECNB5.not_provable_axiomT"}, "P": {"status": false, "ref": "LogicECNB5.not_provable_axiomP"}, "N": {"status": true, "ref": "instHasAxiomNLogicECNB5", "derived": false}, "M": {"status": false, "ref": "LogicECNB5.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECNB5.not_provable_axiomK"}, "D": {"status": false, "ref": "LogicECNB5.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicECNB5", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECNB5", "derived": false}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECNB5", "derived": false}, "4": {"status": false, "ref": "LogicECNB5.not_provable_axiomFour"}}}, {"logic": "ECND4", "axioms": {"T": {"status": false, "ref": "LogicECND4.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicECND4", "derived": false}, "M": {"status": false, "ref": "LogicECND4.not_provable_axiomM"}, "K": null, "D": {"status": true, "ref": "instHasAxiomDLogicECND4", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECND4", "derived": false}, "B": {"status": false, "ref": "LogicECND4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECND4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicECND4", "derived": false}}}, {"logic": "ECND5", "axioms": {"T": {"status": false, "ref": "LogicECND5.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicECND5", "derived": false}, "M": {"status": false, "ref": "LogicECND5.not_provable_axiomM"}, "K": null, "D": {"status": true, "ref": "instHasAxiomDLogicECND5", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECND5", "derived": false}, "B": {"status": false, "ref": "LogicECND5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECND5", "derived": false}, "4": {"status": false, "ref": "LogicECND5.not_provable_axiomFour"}}}, {"logic": "ECNDB", "axioms": {"T": {"status": false, "ref": "LogicECNDB.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicECNDB", "derived": false}, "M": {"status": false, "ref": "LogicECNDB.not_provable_axiomM"}, "K": null, "D": {"status": true, "ref": "instHasAxiomDLogicECNDB", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECNDB", "derived": false}, "B": {"status": true, "ref": "instHasAxiomBLogicECNDB", "derived": false}, "5": {"status": false, "ref": "LogicECNDB.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicECNDB.not_provable_axiomFour"}}}, {"logic": "ECNT4", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicECNT4", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicECNT4", "derived": false}, "M": {"status": false, "ref": "LogicECNT4.not_provable_axiomM"}, "K": null, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicECNT4", "derived": false}, "B": {"status": false, "ref": "LogicECNT4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicECNT4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicECNT4", "derived": false}}}, {"logic": "ECNT5", "equivalentTo": "ECT5"}, {"logic": "ECNTB", "equivalentTo": "ECTB"}, {"logic": "ECNTD", "equivalentTo": "ECNT"}, {"logic": "ECT45", "equivalentTo": "ECT5"}, {"logic": "ECTB4", "equivalentTo": "ECT5"}, {"logic": "ECTB5", "equivalentTo": "ECT5"}, {"logic": "ECTD4", "equivalentTo": "ECT4"}, {"logic": "ECTD5", "equivalentTo": "ECT5"}, {"logic": "ECTDB", "equivalentTo": "ECTB"}, {"logic": "EDB45", "equivalentTo": "ET5"}, {"logic": "EMB45", "equivalentTo": "EKB4"}, {"logic": "EMC45", "axioms": {"T": {"status": false, "ref": "LogicEMC45.not_provable_axiomT"}, "P": null, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomMOfHasAxiomFive", "derived": true}, "M": {"status": true, "ref": "instHasAxiomMLogicEMC45", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": false, "ref": "LogicEMC45.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicEMC45", "derived": false}, "B": {"status": false, "ref": "LogicEMC45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEMC45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMC45", "derived": false}}}, {"logic": "EMCB4", "equivalentTo": "EKB4"}, {"logic": "EMCB5", "equivalentTo": "EKB4"}, {"logic": "EMCD4", "axioms": {"T": {"status": false, "ref": "LogicEMCD4.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomMOfHasAxiomD", "derived": true}, "N": {"status": false, "ref": "LogicEMCD4.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMCD4", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": true, "ref": "instHasAxiomDLogicEMCD4", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicEMCD4", "derived": false}, "B": {"status": false, "ref": "LogicEMCD4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMCD4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMCD4", "derived": false}}}, {"logic": "EMCD5", "axioms": {"T": {"status": false, "ref": "LogicEMCD5.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": true, "ref": "instHasAxiomMLogicEMCD5", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": true, "ref": "instHasAxiomDLogicEMCD5", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicEMCD5", "derived": false}, "B": {"status": false, "ref": "LogicEMCD5.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEMCD5", "derived": false}, "4": {"status": false, "ref": "LogicEMCD5.not_provable_axiomFour"}}}, {"logic": "EMCDB", "equivalentTo": "EKPB"}, {"logic": "EMCN4", "axioms": {"T": {"status": false, "ref": "LogicEMCN4.not_provable_axiomT"}, "P": null, "N": {"status": true, "ref": "instHasAxiomNLogicEMCN4", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMCN4", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": false, "ref": "LogicEMCN4.not_provable_axiomD"}, "C": {"status": true, "ref": "instHasAxiomCLogicEMCN4", "derived": false}, "B": {"status": false, "ref": "LogicEMCN4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMCN4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMCN4", "derived": false}}}, {"logic": "EMCN5", "equivalentTo": "EMC5"}, {"logic": "EMCNB", "equivalentTo": "EMB"}, {"logic": "EMCND", "axioms": {"T": {"status": false, "ref": "LogicEMCND.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicEMCND", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMCND", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": true, "ref": "instHasAxiomDLogicEMCND", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicEMCND", "derived": false}, "B": {"status": false, "ref": "LogicEMCND.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMCND.not_provable_axiomFive"}, "4": {"status": false, "ref": "LogicEMCND.not_provable_axiomFour"}}}, {"logic": "EMCNP", "equivalentTo": "EMCND"}, {"logic": "EMCNT", "equivalentTo": "ENKT"}, {"logic": "EMCT4", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEMCT4", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": false, "ref": "LogicEMCT4.not_provable_axiomN"}, "M": {"status": true, "ref": "instHasAxiomMLogicEMCT4", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicEMCT4", "derived": false}, "B": {"status": false, "ref": "LogicEMCT4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMCT4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMCT4", "derived": false}}}, {"logic": "EMCT5", "equivalentTo": "EKT5"}, {"logic": "EMCTB", "equivalentTo": "EKTB"}, {"logic": "EMCTD", "equivalentTo": "EMCT"}, {"logic": "EMD45", "axioms": {"T": {"status": false, "ref": "LogicEMD45.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": true, "ref": "instHasAxiomMLogicEMD45", "derived": false}, "K": null, "D": {"status": true, "ref": "instHasAxiomDLogicEMD45", "derived": false}, "C": {"status": false, "ref": "LogicEMD45.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMD45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEMD45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMD45", "derived": false}}}, {"logic": "EMDB4", "equivalentTo": "EKT5"}, {"logic": "EMDB5", "equivalentTo": "EKT5"}, {"logic": "EMN45", "equivalentTo": "EM45"}, {"logic": "EMNB4", "equivalentTo": "EKB4"}, {"logic": "EMNB5", "equivalentTo": "EKB4"}, {"logic": "EMND4", "axioms": {"T": {"status": false, "ref": "LogicEMND4.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicEMND4", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMND4", "derived": false}, "K": null, "D": {"status": true, "ref": "instHasAxiomDLogicEMND4", "derived": false}, "C": {"status": false, "ref": "LogicEMND4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMND4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMND4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMND4", "derived": false}}}, {"logic": "EMND5", "equivalentTo": "EMD5"}, {"logic": "EMNDB", "equivalentTo": "EKPB"}, {"logic": "EMNT4", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEMNT4", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicEMNT4", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMNT4", "derived": false}, "K": null, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": false, "ref": "LogicEMNT4.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEMNT4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMNT4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMNT4", "derived": false}}}, {"logic": "EMNT5", "equivalentTo": "EKT5"}, {"logic": "EMNTB", "equivalentTo": "EKTB"}, {"logic": "EMNTD", "equivalentTo": "EMNT"}, {"logic": "EMT45", "equivalentTo": "EKT5"}, {"logic": "EMTB4", "equivalentTo": "EKT5"}, {"logic": "EMTB5", "equivalentTo": "EKT5"}, {"logic": "EMTD4", "equivalentTo": "EMT4"}, {"logic": "EMTD5", "equivalentTo": "EKT5"}, {"logic": "EMTDB", "equivalentTo": "EKTB"}, {"logic": "ENB45", "equivalentTo": "EB45"}, {"logic": "END45", "axioms": {"T": {"status": false, "ref": "LogicEND45.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicEND45", "derived": false}, "M": {"status": false, "ref": "LogicEND45.not_provable_axiomM"}, "K": null, "D": {"status": true, "ref": "instHasAxiomDLogicEND45", "derived": false}, "C": {"status": false, "ref": "LogicEND45.not_provable_axiomC"}, "B": {"status": false, "ref": "LogicEND45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEND45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicEND45", "derived": false}}}, {"logic": "ENDB4", "equivalentTo": "ET5"}, {"logic": "ENDB5", "equivalentTo": "EDB5"}, {"logic": "ENT45", "equivalentTo": "ET5"}, {"logic": "ENTB4", "equivalentTo": "ET5"}, {"logic": "ENTB5", "equivalentTo": "ET5"}, {"logic": "ENTD4", "equivalentTo": "ENT4"}, {"logic": "ENTD5", "equivalentTo": "ET5"}, {"logic": "ENTDB", "equivalentTo": "ETB"}, {"logic": "ETB45", "equivalentTo": "ET5"}, {"logic": "ETD45", "equivalentTo": "ET5"}, {"logic": "ETDB4", "equivalentTo": "ET5"}, {"logic": "ETDB5", "equivalentTo": "ET5"}, {"logic": "ECDB45", "equivalentTo": "ECT5"}, {"logic": "ECNB45", "equivalentTo": "ECB45"}, {"logic": "ECND45", "axioms": {"T": {"status": false, "ref": "LogicECND45.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicECND45", "derived": false}, "M": {"status": false, "ref": "LogicECND45.not_provable_axiomM"}, "K": {"status": false, "ref": "LogicECND45.not_provable_axiomK"}, "D": {"status": true, "ref": "instHasAxiomDLogicECND45", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicECND45", "derived": false}, "B": {"status": false, "ref": "LogicECND45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicECND45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicECND45", "derived": false}}}, {"logic": "ECNDB4", "equivalentTo": "ECT5"}, {"logic": "ECNDB5", "equivalentTo": "ECT5"}, {"logic": "ECNT45", "equivalentTo": "ECT5"}, {"logic": "ECNTB4", "equivalentTo": "ECT5"}, {"logic": "ECNTB5", "equivalentTo": "ECT5"}, {"logic": "ECNTD4", "equivalentTo": "ECNT4"}, {"logic": "ECNTD5", "equivalentTo": "ECT5"}, {"logic": "ECNTDB", "equivalentTo": "ECTB"}, {"logic": "ECTB45", "equivalentTo": "ECT5"}, {"logic": "ECTD45", "equivalentTo": "ECT5"}, {"logic": "ECTDB4", "equivalentTo": "ECT5"}, {"logic": "ECTDB5", "equivalentTo": "ECT5"}, {"logic": "EMCB45", "equivalentTo": "EKB4"}, {"logic": "EMCD45", "axioms": {"T": {"status": false, "ref": "LogicEMCD45.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "Logic.instHasAxiomNOfHasAxiomPOfHasAxiomFive", "derived": true}, "M": {"status": true, "ref": "instHasAxiomMLogicEMCD45", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": true, "ref": "instHasAxiomDLogicEMCD45", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicEMCD45", "derived": false}, "B": {"status": false, "ref": "LogicEMCD45.not_provable_axiomB"}, "5": {"status": true, "ref": "instHasAxiomFiveLogicEMCD45", "derived": false}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMCD45", "derived": false}}}, {"logic": "EMCDB4", "equivalentTo": "EKT5"}, {"logic": "EMCDB5", "equivalentTo": "EKT5"}, {"logic": "EMCN45", "equivalentTo": "EMC45"}, {"logic": "EMCNB4", "equivalentTo": "EKB4"}, {"logic": "EMCNB5", "equivalentTo": "EKB4"}, {"logic": "EMCND4", "axioms": {"T": {"status": false, "ref": "LogicEMCND4.not_provable_axiomT"}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomNOfHasAxiomD", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicEMCND4", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMCND4", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": true, "ref": "instHasAxiomDLogicEMCND4", "derived": false}, "C": {"status": true, "ref": "instHasAxiomCLogicEMCND4", "derived": false}, "B": {"status": false, "ref": "LogicEMCND4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMCND4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMCND4", "derived": false}}}, {"logic": "EMCND5", "equivalentTo": "EMCD5"}, {"logic": "EMCNDB", "equivalentTo": "EKPB"}, {"logic": "EMCNT4", "axioms": {"T": {"status": true, "ref": "instHasAxiomTLogicEMCNT4", "derived": false}, "P": {"status": true, "ref": "Logic.instHasAxiomPOfHasAxiomT", "derived": true}, "N": {"status": true, "ref": "instHasAxiomNLogicEMCNT4", "derived": false}, "M": {"status": true, "ref": "instHasAxiomMLogicEMCNT4", "derived": false}, "K": {"status": true, "ref": "Logic.instHasAxiomKOfHasAxiomMOfHasAxiomC", "derived": true}, "D": {"status": true, "ref": "Logic.instHasAxiomDOfHasAxiomT", "derived": true}, "C": {"status": true, "ref": "instHasAxiomCLogicEMCNT4", "derived": false}, "B": {"status": false, "ref": "LogicEMCNT4.not_provable_axiomB"}, "5": {"status": false, "ref": "LogicEMCNT4.not_provable_axiomFive"}, "4": {"status": true, "ref": "instHasAxiomFourLogicEMCNT4", "derived": false}}}, {"logic": "EMCNT5", "equivalentTo": "EKT5"}, {"logic": "EMCNTB", "equivalentTo": "EKTB"}, {"logic": "EMCNTD", "equivalentTo": "ENKT"}, {"logic": "EMCT45", "equivalentTo": "EKT5"}, {"logic": "EMCTB4", "equivalentTo": "EKT5"}, {"logic": "EMCTB5", "equivalentTo": "EKT5"}, {"logic": "EMCTD4", "equivalentTo": "EMCT4"}, {"logic": "EMCTD5", "equivalentTo": "EKT5"}, {"logic": "EMCTDB", "equivalentTo": "EKTB"}, {"logic": "EMDB45", "equivalentTo": "EKT5"}, {"logic": "EMNB45", "equivalentTo": "EKB4"}, {"logic": "EMND45", "equivalentTo": "EMD45"}, {"logic": "EMNDB4", "equivalentTo": "EKT5"}, {"logic": "EMNDB5", "equivalentTo": "EKT5"}, {"logic": "EMNT45", "equivalentTo": "EKT5"}, {"logic": "EMNTB4", "equivalentTo": "EKT5"}, {"logic": "EMNTB5", "equivalentTo": "EKT5"}, {"logic": "EMNTD4", "equivalentTo": "EMNT4"}, {"logic": "EMNTD5", "equivalentTo": "EKT5"}, {"logic": "EMNTDB", "equivalentTo": "EKTB"}, {"logic": "EMTB45", "equivalentTo": "EKT5"}, {"logic": "EMTD45", "equivalentTo": "EKT5"}, {"logic": "EMTDB4", "equivalentTo": "EKT5"}, {"logic": "EMTDB5", "equivalentTo": "EKT5"}, {"logic": "ENDB45", "equivalentTo": "ET5"}, {"logic": "ENTB45", "equivalentTo": "ET5"}, {"logic": "ENTD45", "equivalentTo": "ET5"}, {"logic": "ENTDB4", "equivalentTo": "ET5"}, {"logic": "ENTDB5", "equivalentTo": "ET5"}, {"logic": "ETDB45", "equivalentTo": "ET5"}, {"logic": "ECNDB45", "equivalentTo": "ECT5"}, {"logic": "ECNTB45", "equivalentTo": "ECT5"}, {"logic": "ECNTD45", "equivalentTo": "ECT5"}, {"logic": "ECNTDB4", "equivalentTo": "ECT5"}, {"logic": "ECNTDB5", "equivalentTo": "ECT5"}, {"logic": "ECTDB45", "equivalentTo": "ECT5"}, {"logic": "EMCDB45", "equivalentTo": "EKT5"}, {"logic": "EMCNB45", "equivalentTo": "EKB4"}, {"logic": "EMCND45", "equivalentTo": "EMCD45"}, {"logic": "EMCNDB4", "equivalentTo": "EKT5"}, {"logic": "EMCNDB5", "equivalentTo": "EKT5"}, {"logic": "EMCNT45", "equivalentTo": "EKT5"}, {"logic": "EMCNTB4", "equivalentTo": "EKT5"}, {"logic": "EMCNTB5", "equivalentTo": "EKT5"}, {"logic": "EMCNTD4", "equivalentTo": "EMCNT4"}, {"logic": "EMCNTD5", "equivalentTo": "EKT5"}, {"logic": "EMCNTDB", "equivalentTo": "EKTB"}, {"logic": "EMCTB45", "equivalentTo": "EKT5"}, {"logic": "EMCTD45", "equivalentTo": "EKT5"}, {"logic": "EMCTDB4", "equivalentTo": "EKT5"}, {"logic": "EMCTDB5", "equivalentTo": "EKT5"}, {"logic": "EMNDB45", "equivalentTo": "EKT5"}, {"logic": "EMNTB45", "equivalentTo": "EKT5"}, {"logic": "EMNTD45", "equivalentTo": "EKT5"}, {"logic": "EMNTDB4", "equivalentTo": "EKT5"}, {"logic": "EMNTDB5", "equivalentTo": "EKT5"}, {"logic": "EMTDB45", "equivalentTo": "EKT5"}, {"logic": "ENTDB45", "equivalentTo": "ET5"}, {"logic": "ECNTDB45", "equivalentTo": "ECT5"}, {"logic": "EMCNDB45", "equivalentTo": "EKT5"}, {"logic": "EMCNTB45", "equivalentTo": "EKT5"}, {"logic": "EMCNTD45", "equivalentTo": "EKT5"}, {"logic": "EMCNTDB4", "equivalentTo": "EKT5"}, {"logic": "EMCNTDB5", "equivalentTo": "EKT5"}, {"logic": "EMCTDB45", "equivalentTo": "EKT5"}, {"logic": "EMNTDB45", "equivalentTo": "EKT5"}, {"logic": "EMCNTDB45", "equivalentTo": "EKT5"}], "axioms": ["K", "M", "C", "N", "T", "B", "D", "P", "4", "5"]}