%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP528-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n003.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 10:56:03 EDT 2022 % Result : Unsatisfiable 3.36s 3.43s % Output : Proof 3.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP528-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n003.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 : Tue Jun 14 06:09:55 EDT 2022 % 0.13/0.34 % CPUTime : % 3.36/3.43 % SZS status Unsatisfiable % 3.36/3.43 % SZS output start Proof % 3.36/3.43 The input problem is unsatisfiable because % 3.36/3.43 % 3.36/3.43 [1] the following set of Horn clauses is unsatisfiable: % 3.36/3.43 % 3.36/3.43 divide(A, divide(divide(A, B), divide(C, B))) = C % 3.36/3.43 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 3.36/3.43 inverse(A) = divide(divide(B, B), A) % 3.36/3.43 multiply(a, b) = multiply(b, a) ==> \bottom % 3.36/3.43 % 3.36/3.43 This holds because % 3.36/3.43 % 3.36/3.43 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.36/3.43 % 3.36/3.43 E: % 3.36/3.43 divide(A, divide(divide(A, B), divide(C, B))) = C % 3.36/3.43 f1(multiply(a, b)) = true__ % 3.36/3.43 f1(multiply(b, a)) = false__ % 3.36/3.43 inverse(A) = divide(divide(B, B), A) % 3.36/3.43 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 3.36/3.43 G: % 3.36/3.43 true__ = false__ % 3.36/3.43 % 3.36/3.43 This holds because % 3.36/3.43 % 3.36/3.43 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.36/3.43 % 3.36/3.43 divide(X1, Y0) = divide(g1, divide(Y0, X1)) % 3.36/3.43 divide(X1, divide(Y1, divide(g1, X1))) = divide(g1, Y1) % 3.36/3.43 divide(X1, divide(g1, Y1)) = divide(Y1, divide(g1, X1)) % 3.36/3.43 divide(divide(g1, X1), divide(g1, Y0)) = divide(Y0, X1) % 3.36/3.43 divide(X1, X1) -> g1 % 3.36/3.43 divide(Y0, divide(X1, divide(Y2, divide(Y0, X1)))) -> Y2 % 3.36/3.43 divide(Y0, divide(Y0, Y1)) -> Y1 % 3.36/3.43 divide(Y0, divide(g1, divide(Y1, Y0))) -> Y1 % 3.36/3.43 divide(Y0, g1) -> Y0 % 3.36/3.43 divide(divide(X0, X1), divide(g1, divide(X1, X0))) -> g1 % 3.36/3.43 divide(divide(X1, X0), X1) -> divide(g1, X0) % 3.36/3.43 divide(divide(Y0, X1), divide(X2, X1)) -> divide(Y0, X2) % 3.36/3.43 divide(divide(Y0, divide(X2, X1)), X1) -> divide(Y0, X2) % 3.36/3.43 divide(divide(g1, X1), Y0) -> divide(g1, divide(X1, divide(g1, Y0))) % 3.36/3.43 divide(divide(g1, Y1), divide(g1, divide(Y1, X1))) -> divide(g1, X1) % 3.36/3.43 divide(divide(g1, divide(Y0, Y1)), divide(g1, Y0)) -> Y1 % 3.36/3.43 divide(divide(g1, divide(divide(g1, X1), Y1)), X1) -> Y1 % 3.36/3.43 divide(false__, multiply(divide(Y0, X1), false__)) -> divide(X1, Y0) % 3.36/3.43 divide(g1, divide(divide(g1, X1), divide(g1, Y0))) -> divide(X1, Y0) % 3.36/3.43 divide(g1, divide(divide(g1, Y0), X1)) -> divide(Y0, divide(g1, X1)) % 3.36/3.43 f1(divide(a, divide(g1, b))) -> true__ % 3.36/3.43 f1(divide(b, divide(g1, a))) -> false__ % 3.36/3.43 f1(divide(g1, divide(divide(g1, b), a))) -> true__ % 3.36/3.43 inverse(Y1) -> divide(g1, Y1) % 3.36/3.43 inverse(divide(X1, Y0)) -> divide(divide(g1, X1), divide(g1, Y0)) % 3.36/3.43 inverse(divide(inverse(inverse(divide(X1, Y1))), X1)) -> Y1 % 3.36/3.43 multiply(Y0, Y2) -> divide(Y0, divide(g1, Y2)) % 3.36/3.43 true__ -> false__ % 3.36/3.43 with the LPO induced by % 3.36/3.43 a > b > f1 > multiply > inverse > divide > g1 > true__ > false__ % 3.36/3.43 % 3.36/3.43 % SZS output end Proof % 3.36/3.43 %------------------------------------------------------------------------------