%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0. % 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 : Sat Jul 16 10:51:40 EDT 2022 % Result : Unsatisfiable 0.76s 0.90s % Output : Proof 0.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0. % 0.08/0.14 % Command : moca.sh %s % 0.14/0.36 % Computer : n021.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Tue Jun 14 06:06:42 EDT 2022 % 0.14/0.37 % CPUTime : % 0.76/0.90 % SZS status Unsatisfiable % 0.76/0.90 % SZS output start Proof % 0.76/0.90 The input problem is unsatisfiable because % 0.76/0.90 % 0.76/0.90 [1] the following set of Horn clauses is unsatisfiable: % 0.76/0.90 % 0.76/0.90 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.76/0.90 multiply(identity, X) = X % 0.76/0.90 multiply(X, X) = identity % 0.76/0.90 multiply(a, b) = c % 0.76/0.90 multiply(b, a) = c ==> \bottom % 0.76/0.90 % 0.76/0.90 This holds because % 0.76/0.90 % 0.76/0.90 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.76/0.90 % 0.76/0.90 E: % 0.76/0.90 f1(c) = false__ % 0.76/0.90 f1(multiply(b, a)) = true__ % 0.76/0.90 multiply(X, X) = identity % 0.76/0.90 multiply(a, b) = c % 0.76/0.90 multiply(identity, X) = X % 0.76/0.90 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.76/0.90 G: % 0.76/0.90 true__ = false__ % 0.76/0.90 % 0.76/0.90 This holds because % 0.76/0.90 % 0.76/0.90 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.76/0.90 % 0.76/0.90 multiply(X1, multiply(Y0, X1)) = multiply(Y1, multiply(Y0, Y1)) % 0.76/0.90 multiply(Y0, X1) = multiply(X1, Y0) % 0.76/0.90 multiply(Y0, identity) = multiply(X1, multiply(Y0, X1)) % 0.76/0.90 multiply(Y1, multiply(Y0, Y2)) = multiply(Y0, multiply(Y1, Y2)) % 0.76/0.90 multiply(Y2, multiply(Y0, Y1)) = multiply(Y0, multiply(Y1, Y2)) % 0.76/0.90 c -> multiply(a, b) % 0.76/0.90 f1(c) -> false__ % 0.76/0.90 f1(multiply(a, b)) -> false__ % 0.76/0.90 f1(multiply(b, a)) -> true__ % 0.76/0.90 multiply(X, X) -> identity % 0.76/0.90 multiply(X0, multiply(X1, multiply(Y1, multiply(X0, multiply(X1, Y2))))) -> multiply(Y1, Y2) % 0.76/0.90 multiply(X0, multiply(X1, multiply(Y1, multiply(Y2, multiply(X0, X1))))) -> multiply(Y1, Y2) % 0.76/0.90 multiply(X1, multiply(Y0, multiply(Y1, X1))) -> multiply(Y0, Y1) % 0.76/0.90 multiply(Y0, multiply(X0, multiply(X1, multiply(Y0, Y2)))) -> multiply(X0, multiply(X1, Y2)) % 0.76/0.90 multiply(Y0, multiply(X0, multiply(X1, multiply(Y0, multiply(X0, multiply(X1, Y2)))))) -> Y2 % 0.76/0.90 multiply(Y0, multiply(X1, multiply(Y0, multiply(X1, identity)))) -> identity % 0.76/0.90 multiply(Y0, multiply(Y1, multiply(X1, multiply(Y0, Y1)))) -> X1 % 0.76/0.90 multiply(Y0, multiply(Y1, multiply(X1, multiply(Y0, multiply(Y1, X1))))) -> identity % 0.76/0.90 multiply(Y0, multiply(Y1, multiply(Y0, X1))) -> multiply(Y1, X1) % 0.76/0.90 multiply(Y0, multiply(Y1, multiply(Y0, Y1))) -> identity % 0.76/0.90 multiply(Y0, multiply(Y1, multiply(Y0, multiply(X1, multiply(Y1, X1))))) -> identity % 0.76/0.90 multiply(Y0, multiply(Y1, multiply(Y0, multiply(Y1, X1)))) -> X1 % 0.76/0.90 multiply(Y1, identity) -> Y1 % 0.76/0.90 multiply(Y1, multiply(Y0, Y1)) -> Y0 % 0.76/0.90 multiply(Y1, multiply(Y1, Y2)) -> Y2 % 0.76/0.90 multiply(identity, X) -> X % 0.76/0.90 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 0.76/0.90 true__ -> false__ % 0.76/0.90 with the LPO induced by % 0.76/0.90 f1 > c > a > b > multiply > identity > true__ > false__ % 0.76/0.90 % 0.76/0.90 % SZS output end Proof % 0.76/0.90 %------------------------------------------------------------------------------