%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL059-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n028.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 : Fri Jul 15 00:37:16 EDT 2022 % Result : Unsatisfiable 24.48s 24.46s % Output : Proof 24.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COL059-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n028.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 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue May 31 15:56:06 EDT 2022 % 0.12/0.33 % CPUTime : % 24.48/24.46 % SZS status Unsatisfiable % 24.48/24.46 % SZS output start Proof % 24.48/24.46 The input problem is unsatisfiable because % 24.48/24.46 % 24.48/24.46 [1] the following set of Horn clauses is unsatisfiable: % 24.48/24.46 % 24.48/24.46 response(response(kestrel, X1), X2) = X1 % 24.48/24.46 response(response(lark, X1), X2) = response(X1, response(X2, X2)) % 24.48/24.46 response(response(response(lark, lark), X1), X2) = response(response(X1, X1), response(X2, X2)) % 24.48/24.46 response(response(response(response(lark, lark), lark), X1), X2) = response(response(response(X1, X1), response(X1, X1)), response(x2, x2)) % 24.48/24.46 response(l2, l2) = l2 ==> \bottom % 24.48/24.46 response(lark, lark) = l2 % 24.48/24.46 response(l2, lark) = l3 % 24.48/24.46 response(l3, l3) = l3 % 24.48/24.46 % 24.48/24.46 This holds because % 24.48/24.46 % 24.48/24.46 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 24.48/24.46 % 24.48/24.46 E: % 24.48/24.46 f1(l2) = false__ % 24.48/24.46 f1(response(l2, l2)) = true__ % 24.48/24.46 response(l2, lark) = l3 % 24.48/24.46 response(l3, l3) = l3 % 24.48/24.46 response(lark, lark) = l2 % 24.48/24.46 response(response(kestrel, X1), X2) = X1 % 24.48/24.46 response(response(lark, X1), X2) = response(X1, response(X2, X2)) % 24.48/24.46 response(response(response(lark, lark), X1), X2) = response(response(X1, X1), response(X2, X2)) % 24.48/24.46 response(response(response(response(lark, lark), lark), X1), X2) = response(response(response(X1, X1), response(X1, X1)), response(x2, x2)) % 24.48/24.46 G: % 24.48/24.46 true__ = false__ % 24.48/24.46 % 24.48/24.46 This holds because % 24.48/24.46 % 24.48/24.46 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 24.48/24.46 % 24.48/24.46 response(X0, response(response(Y1, Y1), response(Y1, Y1))) = response(response(lark, response(lark, X0)), Y1) % 24.48/24.46 response(l2, Y1) = response(lark, response(Y1, Y1)) % 24.48/24.46 response(l2, response(Y1, Y1)) = response(response(l2, lark), Y1) % 24.48/24.46 response(l2, response(response(lark, kestrel), X1)) = response(lark, response(X1, X1)) % 24.48/24.46 response(response(Y0, Y0), l2) = response(response(l2, Y0), lark) % 24.48/24.46 response(response(l2, X0), Y1) = response(response(X0, X0), response(Y1, Y1)) % 24.48/24.46 response(response(l2, X0), response(kestrel, Y1)) = response(response(X0, X0), Y1) % 24.48/24.46 response(response(l2, X0), response(l2, kestrel)) = response(response(X0, X0), kestrel) % 24.48/24.46 response(response(lark, X0), Y1) = response(response(X0, X0), response(Y1, Y1)) % 24.48/24.46 response(response(lark, X1), X2) = response(X1, response(X2, X2)) % 24.48/24.46 response(response(response(lark, lark), X1), X2) = response(response(X1, X1), response(X2, X2)) % 24.48/24.46 response(response(response(response(lark, lark), lark), X1), X2) = response(response(response(X1, X1), response(X1, X1)), response(x2, x2)) % 24.48/24.46 f1(l2) -> false__ % 24.48/24.46 f1(response(l2, l2)) -> true__ % 24.48/24.46 f1(response(lark, l2)) -> true__ % 24.48/24.46 l3 -> response(l2, lark) % 24.48/24.46 response(kestrel, l2) -> kestrel % 24.48/24.46 response(kestrel, response(Y1, Y1)) -> kestrel % 24.48/24.46 response(l2, Y1) -> response(lark, Y1) % 24.48/24.46 response(l2, kestrel) -> response(lark, kestrel) % 24.48/24.46 response(l2, response(Y0, Y0)) -> response(l2, Y0) % 24.48/24.46 response(l2, response(kestrel, X0)) -> response(lark, X0) % 24.48/24.46 response(l2, response(l2, kestrel)) -> response(lark, kestrel) % 24.48/24.46 response(l2, response(l2, l2)) -> response(l2, l2) % 24.48/24.46 response(l2, response(lark, l2)) -> response(lark, response(lark, l2)) % 24.48/24.46 response(l2, response(lark, response(kestrel, X0))) -> response(lark, X0) % 24.48/24.46 response(l2, response(lark, response(l2, kestrel))) -> response(lark, kestrel) % 24.48/24.46 response(l2, response(response(X1, X1), response(X1, X1))) -> response(l2, X1) % 24.48/24.46 response(l3, l3) -> l3 % 24.48/24.46 response(lark, l2) -> l2 % 24.48/24.46 response(lark, lark) -> l2 % 24.48/24.46 response(lark, response(Y0, Y0)) -> response(lark, Y0) % 24.48/24.46 response(lark, response(kestrel, Y0)) -> response(lark, Y0) % 24.48/24.46 response(lark, response(lark, X0)) -> response(lark, X0) % 24.48/24.46 response(lark, response(lark, kestrel)) -> response(lark, kestrel) % 24.48/24.46 response(lark, response(lark, l2)) -> response(lark, l2) % 24.48/24.46 response(response(kestrel, X1), X2) -> X1 % 24.48/24.46 response(response(l2, kestrel), Y1) -> kestrel % 24.48/24.46 response(response(l2, lark), response(l2, lark)) -> response(l2, lark) % 24.48/24.46 response(response(l2, response(l2, kestrel)), lark) -> response(kestrel, l2) % 24.48/24.46 response(response(l2, response(lark, l2)), lark) -> response(l2, response(l2, l2)) % 24.48/24.46 response(response(lark, Y0), Y1) -> Y0 % 24.48/24.46 response(response(lark, Y0), response(kestrel, X0)) -> response(Y0, X0) % 24.48/24.46 response(response(lark, Y0), response(l2, kestrel)) -> response(Y0, kestrel) % 24.48/24.46 response(response(lark, Y0), response(lark, kestrel)) -> response(Y0, kestrel) % 24.48/24.46 response(response(lark, Y0), response(lark, l2)) -> response(Y0, response(lark, l2)) % 24.48/24.46 response(response(lark, Y0), response(lark, response(kestrel, X0))) -> response(Y0, X0) % 24.48/24.46 response(response(lark, Y0), response(lark, response(l2, kestrel))) -> response(Y0, kestrel) % 24.48/24.46 response(response(lark, kestrel), Y0) -> kestrel % 24.48/24.46 response(response(lark, l2), Y1) -> response(l2, Y1) % 24.48/24.46 response(response(lark, l2), kestrel) -> response(lark, kestrel) % 24.48/24.46 response(response(lark, l2), response(Y1, Y1)) -> response(response(lark, l2), Y1) % 24.48/24.46 response(response(lark, l2), response(l2, kestrel)) -> response(l2, kestrel) % 24.48/24.46 response(response(lark, l2), response(lark, l2)) -> response(l2, response(lark, l2)) % 24.48/24.46 response(response(lark, l2), response(lark, l2)) -> response(lark, l2) % 24.48/24.46 response(response(lark, l2), response(lark, response(kestrel, X0))) -> response(l2, X0) % 24.48/24.46 response(response(lark, l2), response(lark, response(l2, kestrel))) -> response(l2, kestrel) % 24.48/24.46 response(response(lark, response(kestrel, X0)), Y1) -> X0 % 24.48/24.46 response(response(lark, response(l2, kestrel)), Y1) -> kestrel % 24.48/24.46 response(response(lark, response(lark, kestrel)), Y0) -> kestrel % 24.48/24.46 response(response(lark, response(lark, response(kestrel, X0))), Y1) -> X0 % 24.48/24.46 response(response(lark, response(lark, response(l2, kestrel))), Y1) -> kestrel % 24.48/24.46 response(response(lark, response(response(lark, kestrel), X1)), Y1) -> response(X1, X1) % 24.48/24.46 response(response(response(lark, kestrel), X1), Y1) -> response(X1, X1) % 24.48/24.46 true__ -> false__ % 24.48/24.46 with the LPO induced by % 24.48/24.46 f1 > kestrel > l3 > response > l2 > lark > x2 > true__ > false__ % 24.48/24.46 % 24.48/24.46 % SZS output end Proof % 24.48/24.46 %------------------------------------------------------------------------------