%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : REL049-1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n021.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Mon Jul 18 19:47:38 EDT 2022 % Result : Unsatisfiable 1.80s 1.93s % Output : Proof 1.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : REL049-1 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.13 % Command : moca.sh %s % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Fri Jul 8 09:57:50 EDT 2022 % 0.12/0.34 % CPUTime : % 1.80/1.93 % SZS status Unsatisfiable % 1.80/1.93 % SZS output start Proof % 1.80/1.93 The input problem is unsatisfiable because % 1.80/1.93 % 1.80/1.93 [1] the following set of Horn clauses is unsatisfiable: % 1.80/1.93 % 1.80/1.93 join(A, B) = join(B, A) % 1.80/1.93 join(A, join(B, C)) = join(join(A, B), C) % 1.80/1.93 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) % 1.80/1.93 meet(A, B) = complement(join(complement(A), complement(B))) % 1.80/1.93 composition(A, composition(B, C)) = composition(composition(A, B), C) % 1.80/1.93 composition(A, one) = A % 1.80/1.93 composition(join(A, B), C) = join(composition(A, C), composition(B, C)) % 1.80/1.93 converse(converse(A)) = A % 1.80/1.93 converse(join(A, B)) = join(converse(A), converse(B)) % 1.80/1.93 converse(composition(A, B)) = composition(converse(B), converse(A)) % 1.80/1.93 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B) % 1.80/1.93 top = join(A, complement(A)) % 1.80/1.93 zero = meet(A, complement(A)) % 1.80/1.93 join(sk1, sk2) = sk2 % 1.80/1.93 join(sk3, sk2) = sk2 % 1.80/1.93 join(join(sk1, sk3), sk2) = sk2 ==> \bottom % 1.80/1.93 % 1.80/1.93 This holds because % 1.80/1.93 % 1.80/1.93 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.80/1.93 % 1.80/1.93 E: % 1.80/1.93 A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) % 1.80/1.93 composition(A, composition(B, C)) = composition(composition(A, B), C) % 1.80/1.93 composition(A, one) = A % 1.80/1.93 composition(join(A, B), C) = join(composition(A, C), composition(B, C)) % 1.80/1.93 converse(composition(A, B)) = composition(converse(B), converse(A)) % 1.80/1.93 converse(converse(A)) = A % 1.80/1.93 converse(join(A, B)) = join(converse(A), converse(B)) % 1.80/1.93 f1(join(join(sk1, sk3), sk2)) = true__ % 1.80/1.93 f1(sk2) = false__ % 1.80/1.93 join(A, B) = join(B, A) % 1.80/1.93 join(A, join(B, C)) = join(join(A, B), C) % 1.80/1.93 join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B) % 1.80/1.93 join(sk1, sk2) = sk2 % 1.80/1.93 join(sk3, sk2) = sk2 % 1.80/1.93 meet(A, B) = complement(join(complement(A), complement(B))) % 1.80/1.93 top = join(A, complement(A)) % 1.80/1.93 zero = meet(A, complement(A)) % 1.80/1.93 G: % 1.80/1.93 true__ = false__ % 1.80/1.93 % 1.80/1.93 This holds because % 1.80/1.93 % 1.80/1.93 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.80/1.93 % 1.80/1.93 join(A, B) = join(B, A) % 1.80/1.93 composition(A, one) -> A % 1.80/1.93 composition(composition(A, B), C) -> composition(A, composition(B, C)) % 1.80/1.93 composition(join(A, B), C) -> join(composition(A, C), composition(B, C)) % 1.80/1.93 composition(one, Y1) -> Y1 % 1.80/1.93 converse(composition(A, B)) -> composition(converse(B), converse(A)) % 1.80/1.93 converse(converse(A)) -> A % 1.80/1.93 converse(join(A, B)) -> join(converse(A), converse(B)) % 1.80/1.93 converse(one) -> one % 1.80/1.93 f1(join(join(sk1, sk3), sk2)) -> true__ % 1.80/1.93 f1(join(sk2, join(sk1, sk3))) -> true__ % 1.80/1.93 f1(join(sk2, join(sk3, sk1))) -> true__ % 1.80/1.93 f1(sk2) -> false__ % 1.80/1.93 join(A, complement(A)) -> top % 1.80/1.93 join(X0, converse(complement(converse(X0)))) -> converse(top) % 1.80/1.93 join(complement(Y1), composition(X0, complement(composition(converse(X0), Y1)))) -> complement(Y1) % 1.80/1.93 join(complement(join(complement(A), complement(B))), complement(join(complement(A), B))) -> A % 1.80/1.93 join(complement(one), complement(one)) -> complement(one) % 1.80/1.93 join(complement(one), composition(X0, complement(converse(X0)))) -> complement(one) % 1.80/1.93 join(complement(one), composition(converse(Y0), complement(Y0))) -> complement(one) % 1.80/1.93 join(composition(converse(A), complement(composition(A, B))), complement(B)) -> complement(B) % 1.80/1.93 join(composition(converse(Y0), complement(Y0)), complement(one)) -> complement(one) % 1.80/1.93 join(converse(Y0), converse(complement(Y0))) -> converse(top) % 1.80/1.93 join(converse(sk1), converse(sk2)) -> converse(sk2) % 1.80/1.93 join(converse(sk1), converse(top)) -> converse(top) % 1.80/1.93 join(converse(sk2), converse(sk1)) -> converse(sk2) % 1.80/1.93 join(converse(sk2), converse(sk3)) -> converse(sk2) % 1.80/1.93 join(converse(top), converse(sk1)) -> converse(top) % 1.80/1.93 join(join(A, B), C) -> join(A, join(B, C)) % 1.80/1.93 join(one, converse(complement(one))) -> converse(top) % 1.80/1.93 join(sk1, join(sk2, Y2)) -> join(sk2, Y2) % 1.80/1.93 join(sk1, sk2) -> sk2 % 1.80/1.93 join(sk1, top) -> top % 1.80/1.93 join(sk2, sk1) -> sk2 % 1.80/1.93 join(sk2, sk3) -> sk2 % 1.80/1.93 join(sk3, join(sk2, Y2)) -> join(sk2, Y2) % 1.80/1.93 join(sk3, sk2) -> sk2 % 1.80/1.93 join(sk3, top) -> top % 1.80/1.93 join(top, sk1) -> top % 1.80/1.93 meet(A, B) -> complement(join(complement(A), complement(B))) % 1.80/1.93 meet(A, complement(A)) -> zero % 1.80/1.93 true__ -> false__ % 1.80/1.93 with the LPO induced by % 1.80/1.93 sk1 > meet > complement > zero > converse > composition > join > top > sk3 > one > sk2 > f1 > true__ > false__ % 1.80/1.93 % 1.80/1.93 % SZS output end Proof % 1.80/1.93 %------------------------------------------------------------------------------