%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP523-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n024.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 17.16s 17.23s % Output : Proof 17.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : GRP523-1 : TPTP v8.1.0. Released v2.6.0. % 0.09/0.14 % Command : moca.sh %s % 0.14/0.36 % Computer : n024.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 09:58:48 EDT 2022 % 0.14/0.36 % CPUTime : % 17.16/17.23 % SZS status Unsatisfiable % 17.16/17.23 % SZS output start Proof % 17.16/17.23 The input problem is unsatisfiable because % 17.16/17.23 % 17.16/17.23 [1] the following set of Horn clauses is unsatisfiable: % 17.16/17.23 % 17.16/17.23 divide(A, divide(B, divide(C, divide(A, B)))) = C % 17.16/17.23 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 17.16/17.23 inverse(A) = divide(divide(B, B), A) % 17.16/17.23 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 17.16/17.23 % 17.16/17.23 This holds because % 17.16/17.23 % 17.16/17.23 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 17.16/17.23 % 17.16/17.23 E: % 17.16/17.23 divide(A, divide(B, divide(C, divide(A, B)))) = C % 17.16/17.23 f1(multiply(a3, multiply(b3, c3))) = false__ % 17.16/17.23 f1(multiply(multiply(a3, b3), c3)) = true__ % 17.16/17.23 inverse(A) = divide(divide(B, B), A) % 17.16/17.23 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 17.16/17.23 G: % 17.16/17.23 true__ = false__ % 17.16/17.23 % 17.16/17.23 This holds because % 17.16/17.23 % 17.16/17.23 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 17.16/17.23 % 17.16/17.23 divide(X1, X1) = divide(Y1, Y1) % 17.16/17.23 divide(X1, X1) = inverse(divide(Y0, Y0)) % 17.16/17.23 divide(X1, X1) = inverse(inverse(divide(Y0, Y0))) % 17.16/17.23 divide(X1, X1) = inverse(inverse(inverse(divide(Y0, Y0)))) % 17.16/17.23 divide(Y0, X1) = inverse(divide(X1, Y0)) % 17.16/17.23 divide(Y0, X2) = divide(X1, divide(X2, divide(Y0, X1))) % 17.16/17.23 divide(Y0, divide(X0, inverse(X1))) = inverse(divide(X0, inverse(divide(X1, Y0)))) % 17.16/17.23 divide(Y0, divide(X1, X0)) = divide(divide(X0, X1), inverse(Y0)) % 17.16/17.23 divide(Y0, divide(X2, X1)) = divide(X1, divide(X2, Y0)) % 17.16/17.23 divide(Y0, divide(Y1, inverse(divide(Y0, Y1)))) = divide(X0, X0) % 17.16/17.23 divide(Y0, divide(Y1, inverse(divide(Y0, Y2)))) = divide(Y2, Y1) % 17.16/17.23 divide(Y0, inverse(X1)) = divide(X1, inverse(Y0)) % 17.16/17.23 divide(Y0, inverse(divide(Y2, Y1))) = divide(Y2, divide(Y1, Y0)) % 17.16/17.23 divide(divide(X0, X1), divide(X0, X2)) = divide(X2, X1) % 17.16/17.23 divide(divide(X0, X1), inverse(divide(X1, X0))) = divide(Y1, Y1) % 17.16/17.23 divide(divide(Y0, Y1), X1) = divide(divide(Y0, X1), Y1) % 17.16/17.23 divide(divide(Y0, Y1), inverse(divide(Y2, Y0))) = divide(Y2, Y1) % 17.16/17.23 divide(false__, false__) = divide(Y1, Y1) % 17.16/17.23 divide(false__, false__) = inverse(divide(Y0, Y0)) % 17.16/17.23 divide(false__, false__) = inverse(inverse(divide(Y0, Y0))) % 17.16/17.23 divide(inverse(X0), inverse(X1)) = divide(X1, X0) % 17.16/17.23 divide(inverse(Y0), divide(X1, X0)) = divide(divide(X0, X1), Y0) % 17.16/17.23 inverse(divide(X1, inverse(divide(divide(Y2, X1), Y0)))) = divide(Y0, Y2) % 17.16/17.23 inverse(divide(X1, inverse(inverse(X1)))) = inverse(divide(Y1, inverse(inverse(Y1)))) % 17.16/17.23 inverse(divide(Y0, inverse(X0))) = divide(X1, divide(X0, inverse(divide(X1, inverse(Y0))))) % 17.16/17.23 inverse(divide(Y0, inverse(divide(X1, X0)))) = divide(X0, divide(X1, inverse(Y0))) % 17.16/17.23 inverse(divide(Y0, inverse(divide(X1, X0)))) = divide(divide(X0, X1), Y0) % 17.16/17.23 inverse(divide(Y0, inverse(inverse(Y0)))) = divide(X0, X0) % 17.16/17.23 inverse(divide(Y0, inverse(inverse(Y0)))) = inverse(divide(X0, X0)) % 17.16/17.23 inverse(divide(Y2, divide(Y0, Y1))) = divide(Y0, divide(Y2, inverse(Y1))) % 17.16/17.23 inverse(divide(divide(X0, X1), inverse(divide(X1, X0)))) = divide(Y1, Y1) % 17.16/17.23 inverse(divide(divide(X0, divide(X1, X1)), X0)) = divide(Y1, Y1) % 17.16/17.23 inverse(divide(divide(X0, divide(X1, inverse(X0))), inverse(X1))) = divide(Y1, Y1) % 17.16/17.23 inverse(divide(divide(X0, divide(false__, false__)), X0)) = divide(Y1, Y1) % 17.16/17.23 inverse(divide(divide(X0, inverse(inverse(X0))), inverse(divide(X1, X1)))) = divide(Y1, Y1) % 17.16/17.23 inverse(divide(divide(X1, X0), inverse(Y1))) = divide(divide(X0, X1), Y1) % 17.16/17.23 inverse(divide(divide(Y1, Y0), inverse(divide(Y0, Y2)))) = divide(Y2, Y1) % 17.16/17.23 inverse(inverse(divide(X0, X0))) = inverse(divide(Y1, inverse(inverse(Y1)))) % 17.16/17.23 inverse(inverse(divide(X1, inverse(inverse(X1))))) = divide(Y1, Y1) % 17.16/17.23 inverse(inverse(divide(X1, inverse(inverse(X1))))) = divide(false__, false__) % 17.16/17.23 inverse(inverse(inverse(inverse(divide(X0, X0))))) = divide(Y1, Y1) % 17.16/17.23 inverse(inverse(inverse(inverse(divide(X0, X0))))) = inverse(divide(Y1, Y1)) % 17.16/17.23 inverse(inverse(inverse(inverse(inverse(divide(X0, X0)))))) = divide(Y1, Y1) % 17.16/17.23 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 17.16/17.23 divide(A, divide(B, divide(C, divide(A, B)))) -> C % 17.16/17.23 divide(X0, divide(X1, X1)) -> X0 % 17.16/17.23 divide(X0, divide(X1, inverse(X0))) -> inverse(X1) % 17.16/17.23 divide(X0, divide(X1, inverse(divide(X0, inverse(divide(Y1, X1)))))) -> inverse(Y1) % 17.16/17.23 divide(X0, divide(X1, inverse(divide(Y1, divide(X1, X0))))) -> inverse(Y1) % 17.16/17.23 divide(X0, divide(false__, false__)) -> X0 % 17.16/17.23 divide(X1, divide(divide(X1, inverse(X0)), divide(X0, Y1))) -> inverse(Y1) % 17.16/17.23 divide(Y0, divide(Y1, divide(Y2, inverse(divide(Y1, Y0))))) -> Y2 % 17.16/17.23 divide(Y0, divide(Y1, inverse(divide(divide(Y0, Y1), Y2)))) -> Y2 % 17.16/17.23 divide(Y0, divide(divide(X2, divide(Y2, Y0)), X2)) -> Y2 % 17.16/17.23 divide(Y0, divide(divide(Y0, X1), divide(Y2, X1))) -> Y2 % 17.16/17.23 divide(Y0, inverse(divide(Y1, Y1))) -> Y0 % 17.16/17.23 divide(Y0, inverse(divide(Y2, Y0))) -> Y2 % 17.16/17.23 divide(Y0, inverse(divide(Y2, divide(Y0, divide(X0, X0))))) -> Y2 % 17.16/17.23 divide(Y0, inverse(divide(divide(Y2, Y0), Y1))) -> divide(Y2, Y1) % 17.16/17.23 divide(Y1, divide(Y1, Y2)) -> Y2 % 17.16/17.23 divide(Y1, inverse(divide(X2, inverse(divide(divide(Y0, X2), Y1))))) -> Y0 % 17.16/17.23 divide(Y2, divide(Y1, divide(Y0, Y2))) -> inverse(divide(Y1, Y0)) % 17.16/17.23 divide(divide(B, B), A) -> inverse(A) % 17.16/17.23 divide(divide(X0, X1), Y1) -> divide(X0, divide(X1, inverse(Y1))) % 17.16/17.23 divide(divide(X0, X1), divide(Y1, divide(X1, X0))) -> inverse(Y1) % 17.16/17.23 divide(divide(X0, X1), inverse(Y1)) -> divide(X0, divide(X1, Y1)) % 17.16/17.23 divide(divide(X0, X1), inverse(divide(X1, X0))) -> divide(false__, false__) % 17.16/17.23 divide(divide(X1, X0), inverse(divide(divide(X0, X1), Y1))) -> inverse(Y1) % 17.16/17.23 divide(divide(Y1, X1), inverse(X1)) -> Y1 % 17.16/17.23 divide(divide(Y2, X1), divide(Y1, X1)) -> divide(Y2, Y1) % 17.16/17.23 divide(divide(false__, divide(X1, X0)), divide(false__, divide(X1, divide(X0, Y1)))) -> Y1 % 17.16/17.23 divide(divide(inverse(X0), divide(X1, X0)), divide(Y1, X1)) -> inverse(Y1) % 17.16/17.23 divide(false__, divide(X0, inverse(divide(false__, divide(X0, X1))))) -> inverse(X1) % 17.16/17.23 divide(false__, divide(X0, inverse(divide(false__, divide(Y0, inverse(X0)))))) -> Y0 % 17.16/17.23 divide(false__, divide(X0, inverse(divide(false__, inverse(divide(X1, X0)))))) -> inverse(X1) % 17.16/17.23 divide(false__, divide(X1, divide(X0, divide(false__, divide(X1, divide(X0, Y1)))))) -> Y1 % 17.16/17.23 divide(false__, divide(X1, inverse(divide(false__, divide(X1, inverse(Y0)))))) -> Y0 % 17.16/17.23 divide(false__, divide(divide(X1, X0), inverse(divide(false__, inverse(divide(divide(X0, X1), Y1)))))) -> Y1 % 17.16/17.23 divide(false__, divide(false__, divide(Y2, divide(X0, X0)))) -> Y2 % 17.16/17.23 divide(false__, inverse(divide(X1, divide(false__, inverse(divide(X1, inverse(Y0))))))) -> inverse(Y0) % 17.16/17.23 divide(false__, inverse(divide(Y0, divide(false__, divide(Y1, Y0))))) -> Y1 % 17.16/17.23 divide(false__, inverse(divide(Y0, divide(false__, inverse(divide(X1, inverse(Y0))))))) -> inverse(X1) % 17.16/17.23 divide(false__, inverse(divide(Y1, divide(false__, inverse(divide(Y1, Y0)))))) -> Y0 % 17.16/17.23 divide(inverse(X0), divide(X1, X0)) -> inverse(X1) % 17.16/17.23 divide(inverse(X0), inverse(divide(X0, X1))) -> inverse(X1) % 17.16/17.23 divide(inverse(X1), Y0) -> inverse(divide(X1, inverse(Y0))) % 17.16/17.23 divide(inverse(Y1), inverse(Y0)) -> inverse(divide(Y1, Y0)) % 17.16/17.23 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1) % 17.16/17.23 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1 % 17.16/17.23 divide(inverse(divide(X1, inverse(inverse(X1)))), Y1) -> inverse(Y1) % 17.16/17.23 divide(inverse(divide(Y1, X1)), X1) -> inverse(Y1) % 17.16/17.23 divide(inverse(inverse(divide(X0, X0))), Y1) -> inverse(Y1) % 17.16/17.23 divide(inverse(inverse(divide(X1, inverse(inverse(X1))))), Y1) -> inverse(Y1) % 17.16/17.23 divide(inverse(inverse(inverse(divide(X0, X0)))), Y1) -> inverse(Y1) % 17.16/17.23 divide(inverse(inverse(inverse(inverse(divide(X0, X0))))), Y1) -> inverse(Y1) % 17.16/17.23 f1(divide(a3, inverse(divide(b3, inverse(c3))))) -> false__ % 17.16/17.23 f1(divide(divide(a3, inverse(b3)), inverse(c3))) -> true__ % 17.16/17.23 f1(multiply(a3, multiply(b3, c3))) -> false__ % 17.16/17.23 f1(multiply(multiply(a3, b3), c3)) -> true__ % 17.16/17.23 inverse(divide(X1, divide(Y1, divide(inverse(X0), divide(X1, X0))))) -> Y1 % 17.16/17.23 inverse(divide(X1, divide(divide(X1, X0), inverse(divide(X0, inverse(Y0)))))) -> Y0 % 17.16/17.23 inverse(divide(X1, divide(divide(X1, inverse(X0)), divide(X0, Y0)))) -> Y0 % 17.16/17.23 inverse(divide(Y0, divide(X1, X1))) -> inverse(Y0) % 17.16/17.23 inverse(divide(Y0, divide(false__, false__))) -> inverse(Y0) % 17.16/17.23 inverse(divide(Y0, inverse(divide(X1, X1)))) -> inverse(Y0) % 17.16/17.23 inverse(divide(Y0, inverse(divide(X1, inverse(inverse(X1)))))) -> inverse(Y0) % 17.16/17.23 inverse(divide(Y0, inverse(inverse(divide(X1, X1))))) -> inverse(Y0) % 17.16/17.23 inverse(divide(Y1, divide(Y2, inverse(Y1)))) -> Y2 % 17.16/17.23 inverse(divide(divide(X0, X1), divide(Y1, divide(X1, X0)))) -> Y1 % 17.16/17.23 inverse(divide(divide(X0, divide(X1, X1)), divide(Y1, inverse(X0)))) -> Y1 % 17.16/17.23 inverse(divide(divide(X0, divide(X1, inverse(X0))), divide(Y1, X1))) -> Y1 % 17.16/17.23 inverse(divide(divide(X0, inverse(inverse(X0))), divide(Y1, divide(X1, X1)))) -> Y1 % 17.16/17.23 inverse(divide(divide(Y0, Y2), divide(Y0, Y1))) -> divide(Y2, Y1) % 17.16/17.23 inverse(divide(divide(Y1, Y2), Y0)) -> divide(Y2, divide(Y1, Y0)) % 17.16/17.23 inverse(divide(divide(inverse(X0), divide(X1, X0)), divide(Y1, X1))) -> Y1 % 17.16/17.23 inverse(divide(inverse(X0), divide(Y1, X0))) -> Y1 % 17.16/17.23 inverse(divide(inverse(Y1), Y0)) -> divide(Y1, inverse(Y0)) % 17.16/17.23 inverse(divide(inverse(Y1), inverse(Y0))) -> divide(Y1, Y0) % 17.16/17.23 inverse(divide(inverse(divide(X1, inverse(Y1))), inverse(X1))) -> Y1 % 17.16/17.23 inverse(divide(inverse(divide(Y1, X1)), X1)) -> Y1 % 17.16/17.23 inverse(inverse(Y1)) -> Y1 % 17.16/17.23 inverse(inverse(divide(Y1, inverse(divide(X0, X0))))) -> Y1 % 17.16/17.23 inverse(inverse(divide(Y1, inverse(inverse(divide(X0, X0)))))) -> Y1 % 17.16/17.23 true__ -> false__ % 17.16/17.23 with the LPO induced by % 17.16/17.23 c3 > b3 > a3 > f1 > multiply > divide > inverse > true__ > false__ % 17.16/17.23 % 17.16/17.23 % SZS output end Proof % 17.16/17.23 %------------------------------------------------------------------------------