%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP524-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 10:56:01 EDT 2022 % Result : Unsatisfiable 4.41s 4.49s % Output : Proof 4.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : GRP524-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.10/0.12 % Command : moca.sh %s % 0.12/0.32 % Computer : n007.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % 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 : Mon Jun 13 10:39:24 EDT 2022 % 0.12/0.33 % CPUTime : % 4.41/4.49 % SZS status Unsatisfiable % 4.41/4.49 % SZS output start Proof % 4.41/4.49 The input problem is unsatisfiable because % 4.41/4.49 % 4.41/4.49 [1] the following set of Horn clauses is unsatisfiable: % 4.41/4.49 % 4.41/4.49 divide(A, divide(B, divide(C, divide(A, B)))) = C % 4.41/4.49 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 4.41/4.49 inverse(A) = divide(divide(B, B), A) % 4.41/4.49 multiply(a, b) = multiply(b, a) ==> \bottom % 4.41/4.49 % 4.41/4.49 This holds because % 4.41/4.49 % 4.41/4.49 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.41/4.49 % 4.41/4.49 E: % 4.41/4.49 divide(A, divide(B, divide(C, divide(A, B)))) = C % 4.41/4.49 f1(multiply(a, b)) = true__ % 4.41/4.49 f1(multiply(b, a)) = false__ % 4.41/4.49 inverse(A) = divide(divide(B, B), A) % 4.41/4.49 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 4.41/4.49 G: % 4.41/4.49 true__ = false__ % 4.41/4.49 % 4.41/4.49 This holds because % 4.41/4.49 % 4.41/4.49 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.41/4.49 % 4.41/4.49 divide(X1, X1) = divide(Y1, Y1) % 4.41/4.49 divide(X1, X1) = inverse(divide(Y0, Y0)) % 4.41/4.49 divide(X1, X1) = inverse(inverse(divide(Y0, Y0))) % 4.41/4.49 divide(X1, X1) = inverse(inverse(inverse(divide(Y0, Y0)))) % 4.41/4.49 divide(Y0, X1) = inverse(divide(X1, Y0)) % 4.41/4.49 divide(Y0, divide(X1, X0)) = divide(divide(X0, X1), inverse(Y0)) % 4.41/4.49 divide(Y0, divide(Y1, inverse(divide(Y0, Y1)))) = divide(X0, X0) % 4.41/4.49 divide(Y0, inverse(X1)) = divide(X1, inverse(Y0)) % 4.41/4.49 divide(false__, false__) = divide(Y1, Y1) % 4.41/4.49 divide(false__, false__) = inverse(divide(Y0, Y0)) % 4.41/4.49 divide(false__, false__) = inverse(inverse(divide(Y0, Y0))) % 4.41/4.49 divide(inverse(X0), inverse(X1)) = divide(X1, X0) % 4.41/4.49 inverse(divide(Y0, inverse(inverse(Y0)))) = divide(X0, X0) % 4.41/4.49 inverse(divide(Y0, inverse(inverse(Y0)))) = inverse(divide(X0, X0)) % 4.41/4.49 inverse(divide(divide(X0, divide(X1, inverse(X0))), inverse(X1))) = divide(Y1, Y1) % 4.41/4.49 inverse(divide(divide(X0, inverse(inverse(X0))), inverse(divide(X1, X1)))) = divide(Y1, Y1) % 4.41/4.49 inverse(inverse(divide(X0, X0))) = inverse(divide(Y1, inverse(inverse(Y1)))) % 4.41/4.49 inverse(inverse(divide(X1, inverse(inverse(X1))))) = divide(Y1, Y1) % 4.41/4.49 inverse(inverse(divide(X1, inverse(inverse(X1))))) = divide(false__, false__) % 4.41/4.49 inverse(inverse(inverse(inverse(divide(X0, X0))))) = divide(Y1, Y1) % 4.41/4.49 inverse(inverse(inverse(inverse(divide(Y1, Y1))))) = inverse(divide(X0, X0)) % 4.41/4.49 inverse(inverse(inverse(inverse(inverse(divide(X0, X0)))))) = divide(Y1, Y1) % 4.41/4.49 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 4.41/4.49 divide(A, divide(B, divide(C, divide(A, B)))) -> C % 4.41/4.49 divide(X0, divide(X1, X1)) -> X0 % 4.41/4.49 divide(X0, divide(X1, inverse(X0))) -> inverse(X1) % 4.41/4.49 divide(X0, divide(false__, false__)) -> X0 % 4.41/4.49 divide(Y0, divide(divide(X2, divide(Y2, Y0)), X2)) -> Y2 % 4.41/4.49 divide(Y0, inverse(divide(Y1, Y1))) -> Y0 % 4.41/4.49 divide(Y0, inverse(divide(Y2, Y0))) -> Y2 % 4.41/4.49 divide(Y0, inverse(divide(Y2, divide(Y0, divide(X0, X0))))) -> Y2 % 4.41/4.49 divide(Y1, divide(Y1, Y2)) -> Y2 % 4.41/4.49 divide(divide(B, B), A) -> inverse(A) % 4.41/4.49 divide(divide(Y1, X1), inverse(X1)) -> Y1 % 4.41/4.49 divide(divide(inverse(X0), divide(X1, X0)), divide(Y1, X1)) -> inverse(Y1) % 4.41/4.49 divide(false__, divide(divide(Y1, divide(X0, X0)), Y1)) -> false__ % 4.41/4.49 divide(false__, divide(false__, divide(Y2, divide(X0, X0)))) -> Y2 % 4.41/4.49 divide(inverse(X0), divide(X1, X0)) -> inverse(X1) % 4.41/4.49 divide(inverse(X0), inverse(divide(X0, X1))) -> inverse(X1) % 4.41/4.49 divide(inverse(X1), Y0) -> inverse(divide(X1, inverse(Y0))) % 4.41/4.49 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1) % 4.41/4.49 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1 % 4.41/4.49 divide(inverse(divide(X1, inverse(inverse(X1)))), Y1) -> inverse(Y1) % 4.41/4.49 divide(inverse(divide(Y1, X1)), X1) -> inverse(Y1) % 4.41/4.49 divide(inverse(inverse(divide(X0, X0))), Y1) -> inverse(Y1) % 4.41/4.49 divide(inverse(inverse(divide(X1, inverse(inverse(X1))))), Y1) -> inverse(Y1) % 4.41/4.49 divide(inverse(inverse(inverse(divide(X0, X0)))), Y1) -> inverse(Y1) % 4.41/4.49 divide(inverse(inverse(inverse(inverse(divide(X0, X0))))), Y1) -> inverse(Y1) % 4.41/4.49 f1(divide(a, inverse(b))) -> true__ % 4.41/4.49 f1(divide(b, inverse(a))) -> false__ % 4.41/4.49 f1(inverse(divide(inverse(b), a))) -> true__ % 4.41/4.49 f1(multiply(a, b)) -> true__ % 4.41/4.49 f1(multiply(b, a)) -> false__ % 4.41/4.49 inverse(divide(X1, divide(Y1, divide(inverse(X0), divide(X1, X0))))) -> Y1 % 4.41/4.49 inverse(divide(Y0, divide(X1, X1))) -> inverse(Y0) % 4.41/4.49 inverse(divide(Y0, divide(false__, false__))) -> inverse(Y0) % 4.41/4.49 inverse(divide(Y0, inverse(divide(X1, X1)))) -> inverse(Y0) % 4.41/4.49 inverse(divide(Y0, inverse(divide(X1, inverse(inverse(X1)))))) -> inverse(Y0) % 4.41/4.49 inverse(divide(Y0, inverse(inverse(divide(X1, X1))))) -> inverse(Y0) % 4.41/4.49 inverse(divide(Y1, divide(Y2, inverse(Y1)))) -> Y2 % 4.41/4.49 inverse(divide(divide(X0, divide(X1, X1)), divide(Y1, inverse(X0)))) -> Y1 % 4.41/4.49 inverse(divide(divide(X0, divide(X1, inverse(X0))), divide(Y1, X1))) -> Y1 % 4.41/4.49 inverse(divide(divide(X0, divide(false__, false__)), divide(Y1, inverse(X0)))) -> Y1 % 4.41/4.49 inverse(divide(divide(X0, inverse(inverse(X0))), divide(Y1, divide(X1, X1)))) -> Y1 % 4.41/4.49 inverse(divide(divide(inverse(X0), divide(X1, X0)), divide(Y1, X1))) -> Y1 % 4.41/4.49 inverse(divide(inverse(X0), divide(Y1, X0))) -> Y1 % 4.41/4.49 inverse(divide(inverse(Y1), Y0)) -> divide(Y1, inverse(Y0)) % 4.41/4.49 inverse(divide(inverse(Y1), inverse(Y0))) -> divide(Y1, Y0) % 4.41/4.49 inverse(divide(inverse(divide(X1, inverse(Y1))), inverse(X1))) -> Y1 % 4.41/4.49 inverse(divide(inverse(divide(Y1, X1)), X1)) -> Y1 % 4.41/4.49 inverse(inverse(Y1)) -> Y1 % 4.41/4.49 inverse(inverse(divide(Y0, inverse(inverse(inverse(divide(X0, X0))))))) -> Y0 % 4.41/4.49 inverse(inverse(divide(Y1, inverse(divide(X0, X0))))) -> Y1 % 4.41/4.49 inverse(inverse(divide(Y1, inverse(inverse(divide(X0, X0)))))) -> Y1 % 4.41/4.49 true__ -> false__ % 4.41/4.49 with the LPO induced by % 4.41/4.49 a > b > f1 > multiply > divide > inverse > true__ > false__ % 4.41/4.49 % 4.41/4.49 % SZS output end Proof % 4.41/4.49 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