%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP547-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n006.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 10:56:11 EDT 2022 % Result : Unsatisfiable 146.46s 146.43s % Output : Proof 146.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GRP547-1 : TPTP v8.1.0. Released v2.6.0. % 0.04/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n006.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 : Mon Jun 13 14:58:41 EDT 2022 % 0.12/0.34 % CPUTime : % 146.46/146.43 % SZS status Unsatisfiable % 146.46/146.43 % SZS output start Proof % 146.46/146.43 The input problem is unsatisfiable because % 146.46/146.43 % 146.46/146.43 [1] the following set of Horn clauses is unsatisfiable: % 146.46/146.43 % 146.46/146.43 divide(divide(identity, divide(A, B)), divide(divide(B, C), A)) = C % 146.46/146.43 multiply(A, B) = divide(A, divide(identity, B)) % 146.46/146.43 inverse(A) = divide(identity, A) % 146.46/146.43 identity = divide(A, A) % 146.46/146.43 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 146.46/146.43 % 146.46/146.43 This holds because % 146.46/146.43 % 146.46/146.43 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 146.46/146.43 % 146.46/146.43 E: % 146.46/146.43 divide(divide(identity, divide(A, B)), divide(divide(B, C), A)) = C % 146.46/146.43 f1(multiply(a3, multiply(b3, c3))) = false__ % 146.46/146.43 f1(multiply(multiply(a3, b3), c3)) = true__ % 146.46/146.43 identity = divide(A, A) % 146.46/146.43 inverse(A) = divide(identity, A) % 146.46/146.43 multiply(A, B) = divide(A, divide(identity, B)) % 146.46/146.43 G: % 146.46/146.43 true__ = false__ % 146.46/146.43 % 146.46/146.43 This holds because % 146.46/146.43 % 146.46/146.43 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 146.46/146.43 % 146.46/146.43 divide(X0, inverse(Y1)) = divide(Y1, inverse(X0)) % 146.46/146.43 divide(X1, Y2) = divide(divide(Y0, Y2), divide(Y0, X1)) % 146.46/146.43 divide(Y0, X1) = divide(X0, divide(X1, inverse(divide(X0, Y0)))) % 146.46/146.43 divide(Y0, X1) = inverse(divide(X0, inverse(divide(X1, divide(X0, inverse(Y0)))))) % 146.46/146.43 divide(Y0, divide(X1, divide(Y1, Y0))) = divide(Y1, X1) % 146.46/146.43 divide(Y0, divide(Y1, inverse(Y2))) = inverse(divide(Y2, divide(Y0, Y1))) % 146.46/146.43 divide(divide(X0, X1), X2) = divide(divide(X0, X2), X1) % 146.46/146.43 divide(divide(X1, X0), inverse(Y1)) = divide(Y1, divide(X0, X1)) % 146.46/146.43 divide(divide(Y0, Y1), divide(X1, X0)) = divide(divide(X0, X1), divide(Y1, Y0)) % 146.46/146.43 divide(inverse(X1), Y0) = divide(inverse(Y0), X1) % 146.46/146.43 divide(inverse(X1), inverse(Y0)) = divide(Y0, X1) % 146.46/146.43 divide(inverse(Y0), divide(X1, X0)) = divide(divide(X0, X1), Y0) % 146.46/146.43 inverse(divide(X0, divide(X1, inverse(Y1)))) = divide(X1, divide(X0, Y1)) % 146.46/146.43 inverse(divide(X0, divide(X1, inverse(Y1)))) = divide(Y1, divide(X0, X1)) % 146.46/146.43 inverse(divide(X1, Y0)) = divide(Y0, X1) % 146.46/146.43 inverse(divide(X1, inverse(divide(divide(Y2, X1), Y0)))) = divide(Y0, Y2) % 146.46/146.43 inverse(divide(Y0, inverse(X1))) = divide(X0, divide(X1, inverse(divide(X0, inverse(Y0))))) % 146.46/146.43 inverse(divide(Y0, inverse(X1))) = inverse(divide(X0, inverse(divide(X1, divide(X0, Y0))))) % 146.46/146.43 inverse(divide(Y0, inverse(divide(X1, X0)))) = divide(divide(X0, X1), Y0) % 146.46/146.43 inverse(divide(Y0, inverse(divide(X1, X0)))) = inverse(divide(X1, divide(X0, Y0))) % 146.46/146.43 inverse(divide(divide(X0, X1), inverse(X2))) = divide(divide(X1, X2), X0) % 146.46/146.43 inverse(divide(divide(X1, X0), inverse(Y1))) = divide(divide(X0, X1), Y1) % 146.46/146.43 inverse(divide(divide(X2, X1), X0)) = divide(X0, inverse(divide(X1, X2))) % 146.46/146.43 divide(A, A) -> identity % 146.46/146.43 divide(X0, divide(X1, divide(divide(X1, X0), X2))) -> inverse(X2) % 146.46/146.43 divide(X0, divide(X1, divide(divide(X1, X2), X0))) -> inverse(X2) % 146.46/146.43 divide(X0, divide(Y1, inverse(X0))) -> inverse(Y1) % 146.46/146.43 divide(X0, inverse(divide(X1, divide(X0, Y1)))) -> divide(X1, inverse(Y1)) % 146.46/146.43 divide(X0, inverse(divide(X1, divide(X0, divide(Y0, X1))))) -> Y0 % 146.46/146.43 divide(X0, inverse(divide(X1, divide(X0, inverse(divide(X1, Y1)))))) -> Y1 % 146.46/146.43 divide(X1, divide(X0, divide(Y0, divide(X1, X0)))) -> Y0 % 146.46/146.43 divide(X1, divide(divide(Y0, Y2), divide(Y0, X1))) -> Y2 % 146.46/146.43 divide(X1, inverse(divide(Y1, X1))) -> Y1 % 146.46/146.43 divide(Y0, divide(Y0, Y1)) -> Y1 % 146.46/146.43 divide(Y0, identity) -> Y0 % 146.46/146.43 divide(divide(X0, X1), X0) -> divide(inverse(X1), identity) % 146.46/146.43 divide(divide(X0, X1), X0) -> inverse(X1) % 146.46/146.43 divide(divide(Y0, Y1), divide(X1, Y1)) -> divide(Y0, X1) % 146.46/146.43 divide(divide(Y0, Y1), inverse(divide(Y1, divide(Y0, Y2)))) -> Y2 % 146.46/146.43 divide(divide(Y0, Y2), Y1) -> inverse(divide(Y2, divide(Y0, Y1))) % 146.46/146.43 divide(divide(Y1, X1), inverse(X1)) -> Y1 % 146.46/146.43 divide(divide(Y1, Y0), divide(divide(Y1, Y2), Y0)) -> Y2 % 146.46/146.43 divide(divide(identity, divide(A, B)), divide(divide(B, C), A)) -> C % 146.46/146.43 divide(false__, divide(X0, inverse(divide(false__, divide(X0, inverse(Y1)))))) -> Y1 % 146.46/146.43 divide(false__, divide(X0, inverse(divide(false__, divide(Y1, inverse(X0)))))) -> Y1 % 146.46/146.43 divide(false__, divide(X0, inverse(divide(false__, inverse(divide(X1, X0)))))) -> inverse(X1) % 146.46/146.43 divide(false__, divide(X1, inverse(divide(false__, divide(X1, X0))))) -> inverse(X0) % 146.46/146.43 divide(false__, inverse(divide(X0, divide(false__, inverse(divide(X0, Y1)))))) -> Y1 % 146.46/146.43 divide(false__, inverse(divide(Y0, divide(false__, inverse(divide(X1, inverse(Y0))))))) -> inverse(X1) % 146.46/146.43 divide(identity, A) -> inverse(A) % 146.46/146.43 divide(inverse(X0), divide(inverse(X0), Y1)) -> Y1 % 146.46/146.43 divide(inverse(X0), identity) -> inverse(X0) % 146.46/146.43 divide(inverse(X0), identity) -> inverse(divide(X0, identity)) % 146.46/146.43 divide(inverse(X1), divide(Y1, X1)) -> inverse(Y1) % 146.46/146.43 divide(inverse(X1), inverse(X0)) -> inverse(divide(X1, X0)) % 146.46/146.43 divide(inverse(X1), inverse(inverse(divide(X0, X1)))) -> inverse(X0) % 146.46/146.43 divide(inverse(Y1), Y0) -> inverse(divide(Y1, inverse(Y0))) % 146.46/146.43 divide(inverse(divide(X0, X1)), X1) -> inverse(X0) % 146.46/146.43 divide(inverse(divide(Y0, Y1)), divide(divide(Y1, Y2), Y0)) -> Y2 % 146.46/146.43 divide(inverse(divide(Y0, Y2)), inverse(Y0)) -> Y2 % 146.46/146.43 divide(inverse(divide(divide(Y1, Y2), Y1)), identity) -> Y2 % 146.46/146.43 divide(inverse(divide(inverse(X0), Y1)), X0) -> Y1 % 146.46/146.43 divide(inverse(divide(inverse(Y1), X1)), X1) -> Y1 % 146.46/146.43 divide(inverse(divide(inverse(Y1), identity)), identity) -> Y1 % 146.46/146.43 divide(inverse(identity), divide(divide(Y1, Y2), Y1)) -> Y2 % 146.46/146.43 divide(inverse(inverse(Y1)), divide(divide(Y1, Y2), identity)) -> Y2 % 146.46/146.43 divide(inverse(inverse(Y1)), identity) -> Y1 % 146.46/146.43 f1(divide(a3, inverse(divide(b3, inverse(c3))))) -> false__ % 146.46/146.43 f1(divide(b3, inverse(divide(a3, inverse(c3))))) -> true__ % 146.46/146.43 f1(divide(divide(a3, inverse(b3)), inverse(c3))) -> true__ % 146.46/146.43 f1(multiply(a3, multiply(b3, c3))) -> false__ % 146.46/146.43 f1(multiply(multiply(a3, b3), c3)) -> true__ % 146.46/146.43 inverse(divide(X0, identity)) -> inverse(X0) % 146.46/146.43 inverse(divide(X0, inverse(divide(X1, divide(X0, Y1))))) -> inverse(divide(X1, inverse(Y1))) % 146.46/146.43 inverse(divide(X0, inverse(divide(X1, divide(X0, inverse(Y1)))))) -> inverse(divide(X1, Y1)) % 146.46/146.43 inverse(divide(X1, divide(X0, inverse(divide(Y0, divide(X0, X1)))))) -> Y0 % 146.46/146.43 inverse(divide(X1, divide(Y0, divide(divide(Y0, X1), Y2)))) -> Y2 % 146.46/146.43 inverse(divide(X1, divide(Y0, inverse(divide(X1, divide(Y0, Y2)))))) -> Y2 % 146.46/146.43 inverse(divide(X1, divide(Y1, divide(divide(Y1, Y2), X1)))) -> Y2 % 146.46/146.43 inverse(divide(X1, divide(Y2, divide(Y1, X1)))) -> divide(Y2, Y1) % 146.46/146.43 inverse(divide(X1, inverse(divide(X0, X1)))) -> inverse(X0) % 146.46/146.43 inverse(divide(X1, inverse(divide(X0, divide(X1, inverse(divide(X0, inverse(Y0)))))))) -> Y0 % 146.46/146.43 inverse(divide(divide(X0, Y1), X1)) -> divide(Y1, divide(X0, X1)) % 146.46/146.43 inverse(divide(divide(Y0, Y1), Y0)) -> Y1 % 146.46/146.43 inverse(divide(divide(Y0, Y1), inverse(divide(X1, Y0)))) -> divide(Y1, X1) % 146.46/146.43 inverse(divide(false__, divide(X0, divide(X1, divide(false__, inverse(divide(X1, divide(X0, Y1)))))))) -> Y1 % 146.46/146.43 inverse(divide(false__, inverse(divide(X1, divide(false__, divide(X0, divide(X1, inverse(divide(X0, inverse(Y1)))))))))) -> Y1 % 146.46/146.43 inverse(divide(false__, inverse(divide(X1, divide(false__, inverse(divide(X0, inverse(divide(X1, divide(X0, Y1)))))))))) -> Y1 % 146.46/146.43 inverse(divide(inverse(X1), divide(Y1, X1))) -> Y1 % 146.46/146.43 inverse(divide(inverse(Y1), X0)) -> divide(Y1, inverse(X0)) % 146.46/146.43 inverse(divide(inverse(Y1), identity)) -> Y1 % 146.46/146.43 inverse(divide(inverse(Y1), inverse(Y0))) -> divide(Y1, Y0) % 146.46/146.43 inverse(divide(inverse(divide(Y1, X1)), X1)) -> Y1 % 146.46/146.43 inverse(identity) -> identity % 146.46/146.43 inverse(inverse(Y1)) -> Y1 % 146.46/146.43 multiply(A, B) -> divide(A, divide(identity, B)) % 146.46/146.43 true__ -> false__ % 146.46/146.43 with the LPO induced by % 146.46/146.43 c3 > b3 > a3 > f1 > multiply > divide > identity > inverse > true__ > false__ % 146.46/146.43 % 146.46/146.43 % SZS output end Proof % 146.46/146.43 %------------------------------------------------------------------------------