%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP531-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n032.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 10:56:04 EDT 2022 % Result : Unsatisfiable 28.32s 28.47s % Output : Proof 28.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.09 % Problem : GRP531-1 : TPTP v8.1.0. Released v2.6.0. % 0.02/0.10 % Command : moca.sh %s % 0.10/0.28 % Computer : n032.cluster.edu % 0.10/0.28 % Model : x86_64 x86_64 % 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.28 % Memory : 8042.1875MB % 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.28 % CPULimit : 300 % 0.10/0.28 % WCLimit : 600 % 0.10/0.28 % DateTime : Tue Jun 14 09:36:42 EDT 2022 % 0.10/0.29 % CPUTime : % 28.32/28.47 % SZS status Unsatisfiable % 28.32/28.47 % SZS output start Proof % 28.32/28.47 The input problem is unsatisfiable because % 28.32/28.47 % 28.32/28.47 [1] the following set of Horn clauses is unsatisfiable: % 28.32/28.47 % 28.32/28.47 divide(divide(A, divide(B, C)), divide(A, B)) = C % 28.32/28.47 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 28.32/28.47 inverse(A) = divide(divide(B, B), A) % 28.32/28.47 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 28.32/28.47 % 28.32/28.47 This holds because % 28.32/28.47 % 28.32/28.47 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 28.32/28.47 % 28.32/28.47 E: % 28.32/28.47 divide(divide(A, divide(B, C)), divide(A, B)) = C % 28.32/28.47 f1(multiply(a3, multiply(b3, c3))) = false__ % 28.32/28.47 f1(multiply(multiply(a3, b3), c3)) = true__ % 28.32/28.47 inverse(A) = divide(divide(B, B), A) % 28.32/28.47 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 28.32/28.47 G: % 28.32/28.47 true__ = false__ % 28.32/28.47 % 28.32/28.47 This holds because % 28.32/28.47 % 28.32/28.47 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 28.32/28.47 % 28.32/28.47 divide(X1, X1) = divide(divide(Y2, Y1), inverse(divide(Y1, Y2))) % 28.32/28.47 divide(X1, X1) = inverse(divide(Y0, Y0)) % 28.32/28.47 divide(Y0, X1) = divide(X0, divide(X1, inverse(divide(X0, Y0)))) % 28.32/28.47 divide(Y0, X1) = inverse(divide(X0, inverse(divide(X1, divide(X0, inverse(Y0)))))) % 28.32/28.47 divide(Y0, Y0) = divide(X0, X0) % 28.32/28.47 divide(Y0, divide(X0, false__)) = divide(divide(false__, X0), inverse(Y0)) % 28.32/28.47 divide(Y0, divide(X0, false__)) = inverse(divide(X0, divide(false__, inverse(Y0)))) % 28.32/28.47 divide(Y0, divide(X0, inverse(X1))) = inverse(divide(X1, inverse(divide(X0, Y0)))) % 28.32/28.47 divide(Y0, divide(X1, X0)) = divide(divide(X0, X1), inverse(Y0)) % 28.32/28.47 divide(Y0, divide(X1, X0)) = inverse(divide(X1, divide(X0, inverse(Y0)))) % 28.32/28.47 divide(Y0, divide(false__, X0)) = divide(divide(X0, false__), inverse(Y0)) % 28.32/28.47 divide(Y0, divide(false__, X0)) = inverse(divide(false__, divide(X0, inverse(Y0)))) % 28.32/28.47 divide(Y0, inverse(X1)) = divide(X1, inverse(Y0)) % 28.32/28.47 divide(Y0, inverse(divide(Y2, Y1))) = inverse(divide(Y1, divide(Y2, inverse(Y0)))) % 28.32/28.47 divide(Y0, inverse(divide(false__, Y1))) = inverse(divide(Y1, divide(false__, inverse(Y0)))) % 28.32/28.47 divide(divide(X0, false__), Y1) = inverse(divide(divide(false__, X0), inverse(Y1))) % 28.32/28.47 divide(divide(X0, false__), inverse(Y1)) = inverse(divide(divide(false__, X0), Y1)) % 28.32/28.47 divide(divide(Y0, Y1), X0) = inverse(divide(X0, inverse(divide(Y1, Y0)))) % 28.32/28.47 divide(divide(Y0, Y1), divide(X1, X0)) = divide(divide(X0, X1), divide(Y1, Y0)) % 28.32/28.47 divide(divide(Y0, false__), X0) = inverse(divide(X0, inverse(divide(false__, Y0)))) % 28.32/28.47 divide(divide(false__, X0), Y1) = inverse(divide(divide(X0, false__), inverse(Y1))) % 28.32/28.47 divide(divide(false__, X0), inverse(Y1)) = inverse(divide(divide(X0, false__), Y1)) % 28.32/28.47 divide(divide(false__, Y0), X0) = inverse(divide(X0, inverse(divide(Y0, false__)))) % 28.32/28.47 divide(divide(false__, Y0), divide(X1, X0)) = divide(divide(X0, X1), divide(Y0, false__)) % 28.32/28.47 divide(false__, false__) = inverse(divide(X1, X1)) % 28.32/28.47 inverse(divide(X0, divide(X1, Y1))) = divide(X1, divide(X0, inverse(Y1))) % 28.32/28.47 inverse(divide(X0, divide(X1, inverse(Y1)))) = divide(X1, divide(X0, Y1)) % 28.32/28.47 inverse(divide(X0, false__)) = divide(false__, X0) % 28.32/28.47 inverse(divide(X1, Y0)) = divide(Y0, X1) % 28.32/28.47 inverse(divide(X1, divide(X0, X2))) = inverse(divide(X2, divide(X0, X1))) % 28.32/28.47 inverse(divide(X1, inverse(Y0))) = inverse(divide(Y0, inverse(X1))) % 28.32/28.47 inverse(divide(Y0, divide(X0, false__))) = divide(X0, divide(false__, inverse(Y0))) % 28.32/28.47 inverse(divide(Y0, divide(X1, X0))) = divide(X1, divide(X0, inverse(Y0))) % 28.32/28.47 inverse(divide(Y0, divide(false__, X0))) = divide(false__, divide(X0, inverse(Y0))) % 28.32/28.47 inverse(divide(Y0, divide(false__, X0))) = inverse(divide(X0, inverse(divide(Y0, false__)))) % 28.32/28.47 inverse(divide(Y1, divide(Y0, X0))) = inverse(divide(X0, inverse(divide(Y1, Y0)))) % 28.32/28.47 inverse(divide(Y1, divide(Y0, divide(X1, X0)))) = inverse(divide(X1, divide(X0, divide(Y1, Y0)))) % 28.32/28.47 inverse(divide(divide(Y2, X1), divide(Y1, X1))) = divide(Y1, Y2) % 28.32/28.47 inverse(divide(divide(Y2, false__), divide(Y1, false__))) = divide(Y1, Y2) % 28.32/28.47 inverse(divide(false__, Y0)) = divide(Y0, false__) % 28.32/28.47 inverse(divide(false__, divide(X0, inverse(Y1)))) = divide(X0, divide(false__, Y1)) % 28.32/28.47 inverse(divide(false__, inverse(Y0))) = inverse(divide(Y0, inverse(false__))) % 28.32/28.47 inverse(divide(false__, inverse(divide(Y0, X0)))) = inverse(divide(Y0, divide(X0, false__))) % 28.32/28.47 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 28.32/28.47 divide(X0, divide(X1, divide(X2, X0))) -> inverse(divide(X1, X2)) % 28.32/28.47 divide(X0, divide(Y1, inverse(X0))) -> inverse(Y1) % 28.32/28.47 divide(X0, inverse(divide(X1, divide(X0, Y1)))) -> divide(X1, inverse(Y1)) % 28.32/28.47 divide(X1, inverse(divide(Y0, Y0))) -> X1 % 28.32/28.47 divide(X1, inverse(divide(Y1, X1))) -> Y1 % 28.32/28.47 divide(X2, divide(divide(Y1, divide(Y2, X2)), Y1)) -> Y2 % 28.32/28.47 divide(Y0, divide(X2, divide(Y1, inverse(divide(X2, Y0))))) -> Y1 % 28.32/28.47 divide(Y0, divide(X2, divide(false__, inverse(divide(X2, Y0))))) -> false__ % 28.32/28.47 divide(Y0, divide(Y0, Y2)) -> Y2 % 28.32/28.47 divide(Y0, divide(Y0, false__)) -> false__ % 28.32/28.47 divide(Y1, divide(X0, X0)) -> Y1 % 28.32/28.47 divide(divide(A, divide(B, C)), divide(A, B)) -> C % 28.32/28.47 divide(divide(B, B), A) -> inverse(A) % 28.32/28.47 divide(divide(X0, X1), X0) -> inverse(X1) % 28.32/28.47 divide(divide(X0, false__), divide(Y1, divide(false__, X0))) -> inverse(Y1) % 28.32/28.47 divide(divide(Y0, X1), divide(Y0, Y1)) -> inverse(divide(X1, Y1)) % 28.32/28.47 divide(divide(Y0, Y1), X1) -> inverse(divide(Y1, divide(Y0, X1))) % 28.32/28.47 divide(divide(Y0, divide(X0, false__)), divide(false__, X0)) -> Y0 % 28.32/28.47 divide(divide(Y0, divide(Y1, Y2)), inverse(divide(Y1, Y0))) -> Y2 % 28.32/28.47 divide(divide(Y0, divide(false__, X0)), divide(X0, false__)) -> Y0 % 28.32/28.47 divide(divide(Y0, divide(false__, Y2)), inverse(divide(false__, Y0))) -> Y2 % 28.32/28.47 divide(divide(Y0, inverse(Y2)), divide(Y0, divide(X0, X0))) -> Y2 % 28.32/28.47 divide(divide(Y1, X1), inverse(X1)) -> Y1 % 28.32/28.47 divide(divide(Y1, Y0), divide(divide(Y1, Y2), Y0)) -> Y2 % 28.32/28.47 divide(divide(Y1, false__), inverse(false__)) -> Y1 % 28.32/28.47 divide(divide(false__, X0), divide(Y1, divide(X0, false__))) -> inverse(Y1) % 28.32/28.47 divide(divide(false__, X0), inverse(X0)) -> false__ % 28.32/28.47 divide(false__, divide(X2, divide(Y0, inverse(divide(X2, false__))))) -> Y0 % 28.32/28.47 divide(false__, divide(false__, Y2)) -> Y2 % 28.32/28.47 divide(inverse(X0), divide(X1, X1)) -> inverse(X0) % 28.32/28.47 divide(inverse(X1), Y0) -> inverse(divide(X1, inverse(Y0))) % 28.32/28.47 divide(inverse(X1), divide(Y1, X1)) -> inverse(Y1) % 28.32/28.47 divide(inverse(X1), inverse(Y0)) -> inverse(divide(X1, Y0)) % 28.32/28.47 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1) % 28.32/28.47 divide(inverse(divide(Y1, Y2)), inverse(Y1)) -> Y2 % 28.32/28.47 divide(inverse(divide(divide(divide(X0, X1), X0), Y1)), X1) -> Y1 % 28.32/28.47 divide(inverse(divide(inverse(X0), Y1)), X0) -> Y1 % 28.32/28.47 divide(inverse(inverse(Y1)), inverse(divide(X0, X0))) -> Y1 % 28.32/28.47 divide(inverse(inverse(divide(X0, X0))), Y1) -> inverse(Y1) % 28.32/28.47 f1(divide(a3, inverse(divide(b3, inverse(c3))))) -> false__ % 28.32/28.47 f1(divide(b3, inverse(divide(a3, inverse(c3))))) -> true__ % 28.32/28.47 f1(divide(divide(a3, inverse(b3)), inverse(c3))) -> true__ % 28.32/28.47 f1(multiply(a3, multiply(b3, c3))) -> false__ % 28.32/28.47 f1(multiply(multiply(a3, b3), c3)) -> true__ % 28.32/28.47 inverse(divide(X0, divide(Y1, Y1))) -> inverse(X0) % 28.32/28.47 inverse(divide(X0, divide(Y1, inverse(X0)))) -> Y1 % 28.32/28.47 inverse(divide(X1, divide(Y0, divide(divide(Y0, X1), Y2)))) -> Y2 % 28.32/28.47 inverse(divide(X1, inverse(divide(X0, divide(Y0, inverse(divide(X0, inverse(X1)))))))) -> Y0 % 28.32/28.47 inverse(divide(X1, inverse(divide(X0, divide(Y0, inverse(divide(X1, inverse(X0)))))))) -> Y0 % 28.32/28.47 inverse(divide(X2, divide(X0, divide(X1, X2)))) -> divide(X0, X1) % 28.32/28.47 inverse(divide(X2, divide(Y1, inverse(divide(X2, Y0))))) -> divide(Y1, Y0) % 28.32/28.47 inverse(divide(divide(X0, X1), inverse(X1))) -> inverse(X0) % 28.32/28.47 inverse(divide(divide(X0, false__), divide(Y1, divide(false__, X0)))) -> Y1 % 28.32/28.47 inverse(divide(divide(X0, false__), inverse(divide(divide(false__, X0), Y1)))) -> Y1 % 28.32/28.47 inverse(divide(divide(Y0, X1), Y2)) -> divide(X1, divide(Y0, Y2)) % 28.32/28.47 inverse(divide(divide(Y1, Y2), Y1)) -> Y2 % 28.32/28.47 inverse(divide(divide(divide(Y1, Y2), Y0), inverse(divide(Y0, Y1)))) -> Y2 % 28.32/28.47 inverse(divide(divide(false__, X0), divide(Y1, divide(X0, false__)))) -> Y1 % 28.32/28.47 inverse(divide(divide(false__, X0), inverse(divide(divide(X0, false__), Y1)))) -> Y1 % 28.32/28.47 inverse(divide(false__, divide(X0, divide(X1, divide(false__, inverse(divide(X1, divide(X0, Y1)))))))) -> Y1 % 28.32/28.47 inverse(divide(false__, divide(Y0, divide(divide(Y0, false__), Y2)))) -> Y2 % 28.32/28.47 inverse(divide(false__, inverse(divide(X0, divide(false__, inverse(divide(X0, inverse(Y1)))))))) -> Y1 % 28.32/28.47 inverse(divide(false__, inverse(divide(X1, divide(false__, divide(X0, divide(X1, inverse(divide(X0, inverse(Y1)))))))))) -> Y1 % 28.32/28.47 inverse(divide(false__, inverse(divide(X1, divide(false__, inverse(divide(X0, inverse(divide(X1, divide(X0, Y1)))))))))) -> Y1 % 28.32/28.47 inverse(divide(false__, inverse(divide(X1, divide(false__, inverse(divide(X1, Y1))))))) -> inverse(Y1) % 28.32/28.47 inverse(divide(false__, inverse(divide(Y0, divide(false__, inverse(divide(Y1, inverse(Y0)))))))) -> Y1 % 28.32/28.47 inverse(divide(false__, inverse(divide(Y0, divide(false__, inverse(divide(false__, inverse(Y0)))))))) -> false__ % 28.32/28.47 inverse(divide(inverse(X1), divide(Y1, X1))) -> Y1 % 28.32/28.47 inverse(divide(inverse(Y0), X1)) -> divide(Y0, inverse(X1)) % 28.32/28.47 inverse(divide(inverse(Y1), divide(X0, X0))) -> Y1 % 28.32/28.47 inverse(divide(inverse(Y1), inverse(divide(X0, X0)))) -> Y1 % 28.32/28.47 inverse(inverse(Y1)) -> Y1 % 28.32/28.47 true__ -> false__ % 28.32/28.47 with the LPO induced by % 28.32/28.47 c3 > b3 > a3 > f1 > multiply > divide > inverse > true__ > false__ % 28.32/28.47 % 28.32/28.47 % SZS output end Proof % 28.32/28.47 %------------------------------------------------------------------------------