%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT090-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.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 : Sun Jul 17 06:04:34 EDT 2022 % Result : Unsatisfiable 5.58s 5.72s % Output : Proof 5.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : LAT090-1 : TPTP v8.1.0. Released v2.6.0. % 0.04/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n011.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 : Thu Jun 30 10:50:48 EDT 2022 % 0.12/0.34 % CPUTime : % 5.58/5.72 % SZS status Unsatisfiable % 5.58/5.72 % SZS output start Proof % 5.58/5.72 The input problem is unsatisfiable because % 5.58/5.72 % 5.58/5.72 [1] the following set of Horn clauses is unsatisfiable: % 5.58/5.72 % 5.58/5.72 join(meet(A, B), meet(A, join(A, B))) = A % 5.58/5.72 join(meet(A, A), meet(B, join(A, A))) = A % 5.58/5.72 join(meet(A, B), meet(B, join(A, B))) = B % 5.58/5.72 meet(meet(join(A, B), join(C, A)), A) = A % 5.58/5.72 join(join(meet(A, B), meet(C, A)), A) = A % 5.58/5.72 join(a, a) = a ==> \bottom % 5.58/5.72 % 5.58/5.72 This holds because % 5.58/5.72 % 5.58/5.72 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.58/5.72 % 5.58/5.72 E: % 5.58/5.72 f1(a) = false__ % 5.58/5.72 f1(join(a, a)) = true__ % 5.58/5.72 join(join(meet(A, B), meet(C, A)), A) = A % 5.58/5.72 join(meet(A, A), meet(B, join(A, A))) = A % 5.58/5.72 join(meet(A, B), meet(A, join(A, B))) = A % 5.58/5.72 join(meet(A, B), meet(B, join(A, B))) = B % 5.58/5.72 meet(meet(join(A, B), join(C, A)), A) = A % 5.58/5.72 G: % 5.58/5.72 true__ = false__ % 5.58/5.72 % 5.58/5.72 This holds because % 5.58/5.72 % 5.58/5.72 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.58/5.72 % 5.58/5.72 % 5.58/5.72 f1(a) -> false__ % 5.58/5.72 f1(join(a, a)) -> true__ % 5.58/5.72 join(Y0, meet(Y1, Y0)) -> Y0 % 5.58/5.72 join(Y0, meet(Y1, join(Y0, Y0))) -> Y0 % 5.58/5.72 join(Y1, Y1) -> Y1 % 5.58/5.72 join(Y1, meet(Y1, join(meet(Y1, join(X1, Y1)), Y1))) -> Y1 % 5.58/5.72 join(Y1, meet(Y1, join(meet(join(Y1, X1), Y1), Y1))) -> Y1 % 5.58/5.72 join(Y1, meet(Y1, join(meet(join(Y1, X1), join(X2, Y1)), Y1))) -> Y1 % 5.58/5.72 join(join(Y1, meet(Y1, join(X1, Y1))), meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1)) % 5.58/5.72 join(join(Y1, meet(Y2, Y1)), Y1) -> Y1 % 5.58/5.72 join(join(Y1, meet(join(Y1, X1), Y1)), meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1) % 5.58/5.72 join(join(meet(A, B), meet(C, A)), A) -> A % 5.58/5.72 join(join(meet(Y0, Y1), Y0), Y0) -> Y0 % 5.58/5.72 join(meet(A, B), meet(A, join(A, B))) -> A % 5.58/5.72 join(meet(A, B), meet(B, join(A, B))) -> B % 5.58/5.72 join(meet(Y0, meet(Y0, join(meet(join(Y0, X1), Y0), Y0))), meet(Y0, Y0)) -> Y0 % 5.58/5.72 join(meet(join(meet(Y0, Y1), Y0), Y0), Y0) -> Y0 % 5.58/5.72 join(meet(join(meet(Y1, X1), meet(X2, Y1)), Y1), meet(Y1, Y1)) -> Y1 % 5.58/5.72 join(meet(meet(X0, X0), meet(X1, join(X0, X0))), meet(meet(X0, X0), X0)) -> X0 % 5.58/5.72 join(meet(meet(X0, X1), meet(X0, join(X0, X1))), meet(meet(X0, X1), X0)) -> meet(X0, X1) % 5.58/5.72 join(meet(meet(X0, X1), meet(X1, join(X0, X1))), meet(meet(X0, X1), X1)) -> meet(X0, X1) % 5.58/5.72 meet(Y1, Y1) -> Y1 % 5.58/5.72 meet(join(meet(Y1, X1), Y1), Y1) -> join(meet(Y1, X1), Y1) % 5.58/5.72 meet(meet(X0, join(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1) % 5.58/5.72 meet(meet(X0, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1) % 5.58/5.72 meet(meet(X1, join(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1) % 5.58/5.72 meet(meet(X1, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1) % 5.58/5.72 meet(meet(Y0, Y0), meet(Y0, join(X0, Y0))) -> meet(Y0, join(X0, Y0)) % 5.58/5.72 meet(meet(Y0, Y0), meet(Y0, join(Y0, X1))) -> meet(Y0, join(Y0, X1)) % 5.58/5.72 meet(meet(Y0, join(Y1, Y0)), Y0) -> Y0 % 5.58/5.72 meet(meet(Y1, join(Y1, meet(X1, Y1))), join(Y1, meet(X1, Y1))) -> join(Y1, meet(X1, Y1)) % 5.58/5.72 meet(meet(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1) % 5.58/5.72 meet(meet(join(A, B), join(C, A)), A) -> A % 5.58/5.72 meet(meet(join(X0, X0), X0), meet(Y2, join(X0, X0))) -> meet(Y2, X0) % 5.58/5.72 meet(meet(join(Y0, Y1), Y0), Y0) -> Y0 % 5.58/5.72 meet(meet(join(Y2, X1), Y2), meet(Y2, join(Y2, X1))) -> meet(Y2, join(Y2, X1)) % 5.58/5.72 meet(meet(meet(X0, X1), meet(X0, X1)), meet(meet(X0, X1), X0)) -> meet(meet(X0, X1), X0) % 5.58/5.72 meet(meet(meet(X0, join(X0, X1)), X0), meet(X0, join(X0, X1))) -> meet(X0, join(X0, X1)) % 5.58/5.72 meet(meet(meet(X1, Y1), Y1), meet(X1, Y1)) -> meet(X1, Y1) % 5.58/5.72 meet(meet(meet(join(Y2, X1), Y2), join(Y1, Y2)), Y2) -> Y2 % 5.58/5.72 true__ -> false__ % 5.58/5.72 with the LPO induced by % 5.58/5.72 join > meet > a > f1 > true__ > false__ % 5.58/5.72 % 5.58/5.72 % SZS output end Proof % 5.58/5.72 %------------------------------------------------------------------------------