%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT088-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n029.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 4.98s 5.11s % Output : Proof 4.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : LAT088-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n029.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Thu Jun 30 00:10:23 EDT 2022 % 0.13/0.34 % CPUTime : % 4.98/5.11 % SZS status Unsatisfiable % 4.98/5.11 % SZS output start Proof % 4.98/5.11 The input problem is unsatisfiable because % 4.98/5.11 % 4.98/5.11 [1] the following set of Horn clauses is unsatisfiable: % 4.98/5.11 % 4.98/5.11 join(meet(A, B), meet(A, join(A, B))) = A % 4.98/5.11 join(meet(A, A), meet(B, join(A, A))) = A % 4.98/5.11 join(meet(A, B), meet(B, join(A, B))) = B % 4.98/5.11 meet(meet(join(A, B), join(C, A)), A) = A % 4.98/5.11 join(join(meet(A, B), meet(C, A)), A) = A % 4.98/5.11 meet(a, a) = a ==> \bottom % 4.98/5.11 % 4.98/5.11 This holds because % 4.98/5.11 % 4.98/5.11 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.98/5.11 % 4.98/5.11 E: % 4.98/5.11 f1(a) = false__ % 4.98/5.11 f1(meet(a, a)) = true__ % 4.98/5.11 join(join(meet(A, B), meet(C, A)), A) = A % 4.98/5.11 join(meet(A, A), meet(B, join(A, A))) = A % 4.98/5.11 join(meet(A, B), meet(A, join(A, B))) = A % 4.98/5.11 join(meet(A, B), meet(B, join(A, B))) = B % 4.98/5.11 meet(meet(join(A, B), join(C, A)), A) = A % 4.98/5.11 G: % 4.98/5.11 true__ = false__ % 4.98/5.11 % 4.98/5.11 This holds because % 4.98/5.11 % 4.98/5.11 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.98/5.11 % 4.98/5.11 % 4.98/5.11 f1(a) -> false__ % 4.98/5.11 f1(meet(a, a)) -> true__ % 4.98/5.11 join(Y0, join(Y0, Y0)) -> Y0 % 4.98/5.11 join(Y0, meet(Y1, join(Y0, Y0))) -> Y0 % 4.98/5.11 join(Y1, meet(Y1, join(Y1, Y1))) -> Y1 % 4.98/5.11 join(Y1, meet(Y1, join(meet(join(Y1, X1), Y1), Y1))) -> Y1 % 4.98/5.11 join(Y1, meet(Y1, join(meet(join(Y1, X1), join(X2, Y1)), Y1))) -> Y1 % 4.98/5.11 join(join(Y1, Y1), Y1) -> Y1 % 4.98/5.11 join(join(Y1, meet(Y1, join(X1, Y1))), meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1)) % 4.98/5.11 join(join(Y1, meet(join(Y1, X1), Y1)), meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1) % 4.98/5.11 join(join(meet(A, B), meet(C, A)), A) -> A % 4.98/5.11 join(join(meet(Y0, Y1), Y0), Y0) -> Y0 % 4.98/5.11 join(meet(A, A), meet(B, join(A, A))) -> A % 4.98/5.11 join(meet(A, B), meet(A, join(A, B))) -> A % 4.98/5.11 join(meet(A, B), meet(B, join(A, B))) -> B % 4.98/5.11 join(meet(Y0, Y0), join(Y0, Y0)) -> Y0 % 4.98/5.11 join(meet(Y0, meet(Y0, join(meet(join(Y0, X1), Y0), Y0))), meet(Y0, Y0)) -> Y0 % 4.98/5.11 join(meet(join(meet(Y1, X1), Y1), Y1), meet(Y1, Y1)) -> Y1 % 4.98/5.11 join(meet(join(meet(Y1, X1), meet(X2, Y1)), Y1), meet(Y1, Y1)) -> Y1 % 4.98/5.11 join(meet(meet(X0, X0), join(X0, X0)), meet(join(X0, X0), X0)) -> join(X0, X0) % 4.98/5.11 join(meet(meet(X0, X0), join(X0, X0)), meet(meet(X0, X0), X0)) -> X0 % 4.98/5.11 join(meet(meet(X0, X0), meet(X1, join(X0, X0))), meet(meet(X0, X0), X0)) -> X0 % 4.98/5.11 join(meet(meet(X0, X1), meet(X0, join(X0, X1))), meet(meet(X0, X1), X0)) -> meet(X0, X1) % 4.98/5.11 join(meet(meet(X0, X1), meet(X1, join(X0, X1))), meet(meet(X0, X1), X1)) -> meet(X0, X1) % 4.98/5.11 meet(Y1, Y1) -> Y1 % 4.98/5.11 meet(meet(X0, join(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1) % 4.98/5.11 meet(meet(X0, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1) % 4.98/5.11 meet(meet(X1, join(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1) % 4.98/5.11 meet(meet(X1, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1) % 4.98/5.11 meet(meet(Y0, X0), meet(Y0, join(X0, X0))) -> meet(Y0, join(X0, X0)) % 4.98/5.11 meet(meet(Y0, Y0), meet(Y0, join(X0, Y0))) -> meet(Y0, join(X0, Y0)) % 4.98/5.11 meet(meet(Y0, Y0), meet(Y0, join(Y0, X1))) -> meet(Y0, join(Y0, X1)) % 4.98/5.11 meet(meet(Y0, join(Y1, Y0)), Y0) -> Y0 % 4.98/5.11 meet(meet(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1) % 4.98/5.11 meet(meet(join(A, B), join(C, A)), A) -> A % 4.98/5.11 meet(meet(join(X0, X0), X0), join(X0, X0)) -> join(X0, X0) % 4.98/5.11 meet(meet(join(X0, X0), X0), meet(Y2, join(X0, X0))) -> meet(Y2, join(X0, X0)) % 4.98/5.11 meet(meet(join(Y0, Y1), Y0), Y0) -> Y0 % 4.98/5.11 meet(meet(join(Y2, X1), Y2), meet(Y2, join(Y2, X1))) -> meet(Y2, join(Y2, X1)) % 4.98/5.11 meet(meet(join(join(X0, X0), Y1), X0), join(X0, X0)) -> join(X0, X0) % 4.98/5.11 meet(meet(meet(X0, X1), meet(X0, X1)), meet(meet(X0, X1), X0)) -> meet(meet(X0, X1), X0) % 4.98/5.11 meet(meet(meet(join(Y2, X1), Y2), join(Y1, Y2)), Y2) -> Y2 % 4.98/5.11 true__ -> false__ % 4.98/5.11 with the LPO induced by % 4.98/5.11 join > meet > a > f1 > true__ > false__ % 4.98/5.11 % 4.98/5.11 % SZS output end Proof % 4.98/5.11 %------------------------------------------------------------------------------