%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP558-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n019.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 10:56:15 EDT 2022 % Result : Unsatisfiable 3.13s 3.23s % Output : Proof 3.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP558-1 : TPTP v8.1.0. Released v2.6.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n019.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 : Mon Jun 13 16:36:24 EDT 2022 % 0.13/0.34 % CPUTime : % 3.13/3.23 % SZS status Unsatisfiable % 3.13/3.23 % SZS output start Proof % 3.13/3.23 The input problem is unsatisfiable because % 3.13/3.23 % 3.13/3.23 [1] the following set of Horn clauses is unsatisfiable: % 3.13/3.23 % 3.13/3.23 divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B % 3.13/3.23 multiply(A, B) = divide(A, inverse(B)) % 3.13/3.23 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 3.13/3.23 % 3.13/3.23 This holds because % 3.13/3.23 % 3.13/3.23 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.13/3.23 % 3.13/3.23 E: % 3.13/3.23 divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B % 3.13/3.23 f1(a2) = false__ % 3.13/3.23 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 3.13/3.23 multiply(A, B) = divide(A, inverse(B)) % 3.13/3.23 G: % 3.13/3.23 true__ = false__ % 3.13/3.23 % 3.13/3.23 This holds because % 3.13/3.23 % 3.13/3.23 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.13/3.23 % 3.13/3.23 divide(X1, X1) = divide(Y1, Y1) % 3.13/3.23 divide(Y0, X1) = divide(divide(divide(false__, false__), X1), divide(divide(false__, false__), Y0)) % 3.13/3.23 divide(Y0, X1) = divide(inverse(X1), inverse(Y0)) % 3.13/3.23 divide(Y0, divide(divide(false__, false__), X0)) = divide(X0, divide(divide(false__, false__), Y0)) % 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(Y1))))) = inverse(divide(X1, X1)) % 3.13/3.23 divide(divide(Y0, X1), Y0) = divide(divide(X0, X0), X1) % 3.13/3.23 divide(divide(divide(X1, X1), Y0), divide(divide(false__, false__), Y1)) = divide(Y1, Y0) % 3.13/3.23 divide(divide(divide(false__, false__), Y0), divide(divide(X1, X1), Y0)) = divide(Y1, Y1) % 3.13/3.23 divide(divide(divide(false__, false__), Y0), divide(divide(X1, X1), Y1)) = divide(Y1, Y0) % 3.13/3.23 divide(false__, false__) = divide(Y1, Y1) % 3.13/3.23 divide(inverse(X1), inverse(X1)) = divide(Y1, Y1) % 3.13/3.23 divide(inverse(X1), inverse(X1)) = divide(inverse(Y1), inverse(Y1)) % 3.13/3.23 divide(inverse(Y0), inverse(Y0)) = inverse(divide(X1, X1)) % 3.13/3.23 divide(inverse(false__), inverse(false__)) = divide(Y1, Y1) % 3.13/3.23 inverse(X1) = divide(divide(Y0, Y0), X1) % 3.13/3.23 inverse(divide(Y0, Y0)) = divide(X1, X1) % 3.13/3.23 inverse(divide(Y0, Y0)) = inverse(divide(X1, X1)) % 3.13/3.23 inverse(inverse(divide(Y0, Y0))) = divide(X1, X1) % 3.13/3.23 divide(A, inverse(divide(divide(B, C), divide(A, C)))) -> B % 3.13/3.23 divide(Y0, divide(X1, X1)) -> Y0 % 3.13/3.23 divide(Y0, divide(Y0, Y2)) -> Y2 % 3.13/3.23 divide(Y0, divide(divide(X1, X1), divide(Y1, Y0))) -> Y1 % 3.13/3.23 divide(Y0, divide(inverse(Y2), inverse(Y0))) -> Y2 % 3.13/3.23 divide(Y0, inverse(divide(X1, divide(Y0, inverse(divide(divide(X1, X2), divide(Y1, X2))))))) -> Y1 % 3.13/3.23 divide(Y0, inverse(divide(Y1, Y0))) -> Y1 % 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(X1, divide(Y3, inverse(divide(divide(X1, X2), divide(Y1, X2)))))))))) -> Y3 % 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(X3, divide(Y3, inverse(divide(X1, divide(Y1, inverse(divide(divide(X1, X2), divide(X3, X2))))))))))))) -> Y3 % 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y1, Y3)))))) -> Y3 % 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y1, inverse(divide(divide(inverse(divide(X1, X1)), Y3), divide(Y4, Y3))))))))) -> Y4 % 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y2, divide(Y3, inverse(divide(Y2, Y1))))))))) -> Y3 % 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(divide(Y1, inverse(divide(X1, divide(Y3, inverse(divide(divide(X1, X2), divide(X3, X2))))))), X3)))))) -> Y3 % 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(X1, X2), divide(Y3, X2)))), X1)))))) -> Y3 % 3.13/3.23 divide(Y0, inverse(divide(Y1, inverse(divide(divide(inverse(divide(X1, X1)), Y3), divide(Y0, Y3)))))) -> Y1 % 3.13/3.23 divide(Y0, inverse(divide(divide(Y1, inverse(divide(X1, divide(Y0, inverse(divide(divide(X1, X2), divide(X3, X2))))))), X3))) -> Y1 % 3.13/3.23 divide(Y0, inverse(divide(divide(Y1, inverse(divide(Y2, Y0))), Y2))) -> Y1 % 3.13/3.23 divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(X1, X2), divide(Y0, X2)))), X1))) -> Y1 % 3.13/3.23 divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(Y2, inverse(divide(divide(X1, X2), divide(Y0, X2)))), X1))), Y2))) -> Y1 % 3.13/3.23 divide(Y0, inverse(inverse(divide(X1, X1)))) -> Y0 % 3.13/3.23 divide(Y0, inverse(inverse(inverse(divide(X1, X1))))) -> Y0 % 3.13/3.23 divide(Y0, inverse(inverse(inverse(inverse(divide(X1, X1)))))) -> Y0 % 3.13/3.23 divide(Y3, inverse(divide(Y1, Y1))) -> Y3 % 3.13/3.23 divide(divide(X1, X1), divide(divide(Y0, Y0), Y1)) -> Y1 % 3.13/3.23 divide(divide(X1, X1), inverse(Y1)) -> Y1 % 3.13/3.23 divide(divide(X1, inverse(Y1)), X1) -> Y1 % 3.13/3.23 divide(divide(Y0, Y1), divide(divide(X1, X1), Y1)) -> Y0 % 3.13/3.23 divide(divide(Y0, divide(divide(X1, X1), Y1)), Y1) -> Y0 % 3.13/3.23 divide(divide(Y1, X1), inverse(X1)) -> Y1 % 3.13/3.23 divide(divide(Y1, inverse(X1)), X1) -> Y1 % 3.13/3.23 divide(divide(divide(X1, X1), divide(Y0, Y1)), divide(divide(false__, false__), Y0)) -> Y1 % 3.13/3.23 divide(divide(divide(divide(false__, false__), Y0), divide(divide(false__, false__), Y1)), divide(divide(X1, X1), Y0)) -> Y1 % 3.13/3.23 divide(divide(divide(false__, false__), X0), divide(X1, X0)) -> divide(divide(false__, false__), X1) % 3.13/3.23 divide(divide(false__, false__), divide(divide(X1, X1), Y1)) -> Y1 % 3.13/3.23 divide(divide(inverse(X0), inverse(X1)), X1) -> inverse(X0) % 3.13/3.23 divide(divide(inverse(Y1), inverse(Y2)), inverse(Y1)) -> Y2 % 3.13/3.23 divide(inverse(Y1), inverse(Y1)) -> divide(false__, false__) % 3.13/3.23 divide(inverse(divide(X1, X1)), inverse(Y1)) -> Y1 % 3.13/3.23 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1 % 3.13/3.23 divide(inverse(divide(divide(X1, X2), divide(Y1, X2))), inverse(X1)) -> Y1 % 3.13/3.23 divide(inverse(inverse(divide(X1, X1))), inverse(Y1)) -> Y1 % 3.13/3.23 divide(inverse(inverse(inverse(divide(X1, X1)))), inverse(Y1)) -> Y1 % 3.13/3.23 f1(a2) -> false__ % 3.13/3.23 f1(divide(divide(X1, X1), inverse(a2))) -> true__ % 3.13/3.23 f1(divide(divide(false__, false__), inverse(a2))) -> true__ % 3.13/3.23 f1(divide(divide(inverse(b2), inverse(b2)), inverse(a2))) -> true__ % 3.13/3.23 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 3.13/3.23 inverse(X1) -> divide(divide(false__, false__), X1) % 3.13/3.23 inverse(divide(X1, Y0)) -> divide(inverse(X1), inverse(Y0)) % 3.13/3.23 inverse(divide(divide(X1, X1), Y1)) -> Y1 % 3.13/3.23 multiply(A, B) -> divide(A, inverse(B)) % 3.13/3.23 true__ -> false__ % 3.13/3.23 with the LPO induced by % 3.13/3.23 b2 > a2 > f1 > multiply > inverse > divide > true__ > false__ % 3.13/3.23 % 3.13/3.23 % SZS output end Proof % 3.13/3.23 %------------------------------------------------------------------------------