%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP450-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n008.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 10:55:32 EDT 2022 % Result : Unsatisfiable 71.51s 71.61s % Output : Proof 71.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GRP450-1 : TPTP v8.1.0. Released v2.6.0. % 0.06/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n008.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 : Tue Jun 14 02:33:52 EDT 2022 % 0.12/0.33 % CPUTime : % 71.51/71.61 % SZS status Unsatisfiable % 71.51/71.61 % SZS output start Proof % 71.51/71.61 The input problem is unsatisfiable because % 71.51/71.61 % 71.51/71.61 [1] the following set of Horn clauses is unsatisfiable: % 71.51/71.61 % 71.51/71.61 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) = B % 71.51/71.61 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 71.51/71.61 inverse(A) = divide(divide(B, B), A) % 71.51/71.61 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 71.51/71.61 % 71.51/71.61 This holds because % 71.51/71.61 % 71.51/71.61 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 71.51/71.61 % 71.51/71.61 E: % 71.51/71.61 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) = B % 71.51/71.61 f1(multiply(a3, multiply(b3, c3))) = false__ % 71.51/71.61 f1(multiply(multiply(a3, b3), c3)) = true__ % 71.51/71.61 inverse(A) = divide(divide(B, B), A) % 71.51/71.61 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 71.51/71.61 G: % 71.51/71.61 true__ = false__ % 71.51/71.61 % 71.51/71.61 This holds because % 71.51/71.61 % 71.51/71.61 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 71.51/71.61 % 71.51/71.61 divide(X0, divide(Y2, Y1)) = divide(divide(X0, inverse(Y1)), Y2) % 71.51/71.61 divide(X0, divide(Y2, Y1)) = inverse(divide(Y2, divide(X0, inverse(Y1)))) % 71.51/71.61 divide(X1, X1) = divide(Y1, Y1) % 71.51/71.61 divide(X1, Y1) = inverse(divide(Y1, X1)) % 71.51/71.61 divide(X1, Y2) = divide(Y0, divide(Y2, inverse(divide(inverse(X1), inverse(Y0))))) % 71.51/71.61 divide(X1, divide(Y2, inverse(X0))) = divide(inverse(divide(X0, X1)), Y2) % 71.51/71.61 divide(X1, divide(Y2, inverse(X0))) = inverse(divide(Y2, inverse(divide(X0, X1)))) % 71.51/71.61 divide(X2, X2) = divide(inverse(divide(X1, X0)), divide(X0, X1)) % 71.51/71.61 divide(Y0, divide(X0, divide(inverse(Y0), inverse(X0)))) = divide(Y2, Y2) % 71.51/71.61 divide(Y0, divide(X0, divide(inverse(Y0), inverse(inverse(inverse(X0)))))) = divide(Y2, Y2) % 71.51/71.61 divide(Y0, divide(divide(X1, X0), divide(inverse(Y0), divide(X0, X1)))) = divide(Y2, Y2) % 71.51/71.61 divide(Y0, divide(inverse(Y2), divide(inverse(Y0), Y2))) = divide(X0, X0) % 71.51/71.61 divide(Y0, inverse(inverse(Y0))) = divide(X1, X1) % 71.51/71.61 divide(Y0, inverse(inverse(Y0))) = inverse(inverse(inverse(divide(X1, X1)))) % 71.51/71.61 divide(divide(X0, X1), inverse(divide(X1, X0))) = divide(Y1, Y1) % 71.51/71.61 divide(divide(X0, divide(X1, X2)), inverse(divide(inverse(divide(X2, X1)), X0))) = divide(Y1, Y1) % 71.51/71.61 divide(divide(X0, inverse(X1)), inverse(divide(inverse(X1), X0))) = divide(Y1, Y1) % 71.51/71.61 divide(divide(X0, inverse(divide(X1, X2))), inverse(divide(divide(X2, X1), X0))) = divide(Y1, Y1) % 71.51/71.61 divide(divide(X1, X0), Y1) = inverse(divide(Y1, inverse(divide(X0, X1)))) % 71.51/71.61 divide(divide(X2, divide(X1, X0)), Y1) = inverse(divide(Y1, inverse(divide(inverse(divide(X0, X1)), X2)))) % 71.51/71.61 divide(divide(X2, inverse(divide(X1, X0))), Y1) = inverse(divide(Y1, inverse(divide(divide(X0, X1), X2)))) % 71.51/71.61 divide(divide(Y0, Y1), X0) = divide(Y0, divide(X0, inverse(Y1))) % 71.51/71.61 divide(divide(Y0, Y1), X0) = inverse(divide(divide(X0, inverse(Y1)), Y0)) % 71.51/71.61 divide(divide(Y0, Y1), divide(X0, Y1)) = inverse(divide(X0, Y0)) % 71.51/71.61 divide(divide(Y0, Y1), inverse(divide(Y1, Y2))) = inverse(divide(Y2, Y0)) % 71.51/71.61 divide(divide(Y0, divide(X1, X0)), Y2) = divide(Y0, divide(Y2, divide(X0, X1))) % 71.51/71.61 divide(divide(divide(X0, X1), X2), inverse(divide(X2, inverse(divide(X1, X0))))) = divide(Y1, Y1) % 71.51/71.61 divide(divide(inverse(Y0), Y1), divide(X0, Y1)) = inverse(divide(X0, inverse(Y0))) % 71.51/71.61 divide(divide(inverse(divide(X0, X1)), X2), inverse(divide(X2, divide(X1, X0)))) = divide(Y1, Y1) % 71.51/71.61 divide(divide(inverse(divide(X2, X1)), X0), Y1) = inverse(divide(Y1, inverse(divide(X0, divide(X1, X2))))) % 71.51/71.61 divide(inverse(X0), divide(Y1, divide(X0, inverse(Y1)))) = divide(Y2, Y2) % 71.51/71.61 divide(inverse(X0), divide(inverse(Y1), divide(X0, Y1))) = divide(Y2, Y2) % 71.51/71.61 divide(inverse(X1), inverse(Y0)) = inverse(divide(inverse(Y0), inverse(X1))) % 71.51/71.61 divide(inverse(Y0), X0) = inverse(divide(X0, inverse(Y0))) % 71.51/71.61 divide(inverse(Y0), divide(X1, X0)) = inverse(divide(inverse(divide(X0, X1)), inverse(Y0))) % 71.51/71.61 divide(inverse(Y0), divide(divide(X1, X0), divide(Y0, divide(X0, X1)))) = divide(Y2, Y2) % 71.51/71.61 divide(inverse(divide(Y1, Y0)), divide(Y2, Y1)) = inverse(divide(Y2, Y0)) % 71.51/71.61 divide(inverse(divide(inverse(Y1), Y0)), Y2) = divide(Y0, divide(Y2, Y1)) % 71.51/71.61 inverse(divide(X0, X0)) = divide(Y1, Y1) % 71.51/71.61 inverse(divide(X0, X0)) = divide(false__, false__) % 71.51/71.61 inverse(divide(X0, divide(Y2, Y1))) = divide(Y2, divide(X0, inverse(Y1))) % 71.51/71.61 inverse(divide(X1, X1)) = inverse(inverse(inverse(divide(Y1, Y1)))) % 71.51/71.61 inverse(divide(X1, divide(Y2, inverse(X0)))) = divide(Y2, inverse(divide(X0, X1))) % 71.51/71.61 inverse(divide(Y0, divide(X1, X0))) = divide(inverse(divide(X0, X1)), Y0) % 71.51/71.61 inverse(divide(Y0, divide(X2, divide(X1, X0)))) = divide(inverse(divide(inverse(divide(X0, X1)), X2)), Y0) % 71.51/71.61 inverse(divide(Y0, divide(X2, inverse(divide(X1, X0))))) = divide(inverse(divide(divide(X0, X1), X2)), Y0) % 71.51/71.61 inverse(divide(Y0, divide(inverse(divide(X2, X1)), X0))) = divide(inverse(divide(X0, divide(X1, X2))), Y0) % 71.51/71.61 inverse(divide(divide(X1, X0), inverse(Y1))) = divide(inverse(Y1), inverse(divide(X0, X1))) % 71.51/71.61 inverse(divide(divide(X1, X0), inverse(divide(X0, X1)))) = divide(Y1, Y1) % 71.51/71.61 inverse(divide(divide(X1, X2), divide(X0, X2))) = divide(X0, X1) % 71.51/71.61 inverse(divide(divide(X2, X1), X0)) = divide(X0, inverse(divide(X1, X2))) % 71.51/71.61 inverse(divide(divide(Y0, Y1), X0)) = divide(divide(X0, inverse(Y1)), Y0) % 71.51/71.61 inverse(divide(inverse(Y1), inverse(Y1))) = divide(X0, X0) % 71.51/71.61 inverse(divide(inverse(divide(X0, X1)), divide(X1, X0))) = divide(Y1, Y1) % 71.51/71.61 inverse(divide(inverse(divide(X0, divide(X1, X2))), divide(inverse(divide(X2, X1)), X0))) = divide(Y1, Y1) % 71.51/71.61 inverse(divide(inverse(divide(X0, inverse(divide(X1, X2)))), divide(divide(X2, X1), X0))) = divide(Y1, Y1) % 71.51/71.61 inverse(divide(inverse(divide(X2, X1)), X0)) = divide(X0, divide(X1, X2)) % 71.51/71.61 inverse(divide(inverse(divide(Y1, Y0)), divide(Y2, Y1))) = divide(Y2, Y0) % 71.51/71.61 inverse(divide(inverse(divide(divide(X0, X1), X2)), divide(X2, inverse(divide(X1, X0))))) = divide(Y1, Y1) % 71.51/71.61 inverse(divide(inverse(divide(inverse(divide(X0, X1)), X2)), divide(X2, divide(X1, X0)))) = divide(Y1, Y1) % 71.51/71.61 inverse(inverse(divide(X0, X0))) = divide(false__, false__) % 71.51/71.61 inverse(inverse(divide(X1, X1))) = divide(Y1, Y1) % 71.51/71.61 inverse(inverse(divide(false__, false__))) = divide(Y1, Y1) % 71.51/71.61 inverse(inverse(inverse(divide(X0, X0)))) = divide(Y1, Y1) % 71.51/71.61 inverse(inverse(inverse(divide(X1, X1)))) = divide(inverse(X0), inverse(X0)) % 71.51/71.61 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 71.51/71.61 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) -> B % 71.51/71.61 divide(X0, inverse(divide(Y1, divide(Y2, inverse(divide(X0, inverse(Y1))))))) -> inverse(Y2) % 71.51/71.61 divide(X0, inverse(divide(Y1, divide(inverse(Y2), inverse(divide(X0, inverse(Y1))))))) -> Y2 % 71.51/71.61 divide(X1, divide(X0, inverse(X1))) -> inverse(X0) % 71.51/71.61 divide(X1, divide(inverse(Y0), inverse(X1))) -> Y0 % 71.51/71.61 divide(Y0, divide(X0, divide(inverse(Y0), Y2))) -> inverse(divide(X0, inverse(Y2))) % 71.51/71.61 divide(Y0, divide(divide(X0, Y2), divide(inverse(Y0), Y2))) -> inverse(X0) % 71.51/71.61 divide(Y0, divide(divide(Y1, Y2), inverse(divide(Y2, inverse(Y0))))) -> inverse(Y1) % 71.51/71.61 divide(Y0, divide(divide(divide(inverse(divide(X0, X0)), divide(X0, X0)), Y2), divide(inverse(Y0), Y2))) -> divide(X0, X0) % 71.51/71.61 divide(Y0, divide(divide(inverse(Y1), Y2), divide(inverse(Y0), Y2))) -> Y1 % 71.51/71.61 divide(Y0, divide(divide(inverse(Y1), Y2), inverse(divide(Y2, inverse(Y0))))) -> Y1 % 71.51/71.61 divide(Y0, divide(inverse(divide(Y1, Y2)), inverse(divide(Y1, inverse(Y0))))) -> inverse(Y2) % 71.51/71.61 divide(Y0, divide(inverse(divide(Y1, inverse(Y2))), inverse(divide(Y1, inverse(Y0))))) -> Y2 % 71.51/71.61 divide(Y0, divide(inverse(divide(Y2, Y1)), divide(inverse(Y0), Y2))) -> inverse(Y1) % 71.51/71.61 divide(Y0, divide(inverse(divide(Y2, inverse(Y1))), divide(inverse(Y0), Y2))) -> Y1 % 71.51/71.61 divide(Y0, inverse(divide(divide(inverse(Y0), Y1), inverse(divide(Y1, Y2))))) -> inverse(Y2) % 71.51/71.61 divide(Y0, inverse(divide(divide(inverse(Y0), Y1), inverse(divide(Y1, inverse(Y2)))))) -> Y2 % 71.51/71.61 divide(Y0, inverse(divide(divide(inverse(Y0), Y2), divide(Y1, Y2)))) -> inverse(Y1) % 71.51/71.61 divide(Y0, inverse(divide(divide(inverse(Y0), Y2), divide(inverse(Y1), Y2)))) -> Y1 % 71.51/71.61 divide(Y0, inverse(divide(inverse(Y0), X0))) -> inverse(inverse(inverse(X0))) % 71.51/71.61 divide(Y0, inverse(divide(inverse(Y0), inverse(Y1)))) -> Y1 % 71.51/71.61 divide(Y0, inverse(divide(inverse(divide(Y1, inverse(Y0))), divide(Y2, Y1)))) -> inverse(Y2) % 71.51/71.61 divide(Y0, inverse(divide(inverse(divide(Y1, inverse(Y0))), divide(inverse(Y2), Y1)))) -> Y2 % 71.51/71.61 divide(Y0, inverse(inverse(inverse(divide(X1, X1))))) -> Y0 % 71.51/71.61 divide(Y1, divide(X1, X1)) -> Y1 % 71.51/71.61 divide(Y1, divide(false__, false__)) -> Y1 % 71.51/71.61 divide(Y1, inverse(divide(X1, X1))) -> Y1 % 71.51/71.61 divide(Y1, inverse(inverse(divide(X1, X1)))) -> Y1 % 71.51/71.61 divide(divide(B, B), A) -> inverse(A) % 71.51/71.61 divide(divide(X0, X1), divide(divide(Y1, Y2), divide(divide(X1, X0), Y2))) -> inverse(Y1) % 71.51/71.61 divide(divide(X0, X1), divide(divide(inverse(Y1), Y2), divide(divide(X1, X0), Y2))) -> Y1 % 71.51/71.61 divide(divide(X0, X1), divide(divide(inverse(Y1), inverse(X0)), X1)) -> Y1 % 71.51/71.61 divide(divide(X0, X1), inverse(X1)) -> inverse(inverse(X0)) % 71.51/71.61 divide(divide(X0, divide(X1, X2)), divide(Y1, divide(inverse(divide(X2, X1)), X0))) -> inverse(Y1) % 71.51/71.61 divide(divide(X0, divide(X1, X2)), divide(inverse(Y1), divide(inverse(divide(X2, X1)), X0))) -> Y1 % 71.51/71.61 divide(divide(X0, divide(X1, X2)), inverse(divide(divide(inverse(divide(X2, X1)), X0), inverse(Y1)))) -> Y1 % 71.51/71.61 divide(divide(X0, inverse(X1)), divide(Y1, divide(inverse(X1), X0))) -> inverse(Y1) % 71.51/71.61 divide(divide(X0, inverse(X1)), divide(inverse(Y1), divide(inverse(X1), X0))) -> Y1 % 71.51/71.61 divide(divide(X0, inverse(X1)), inverse(divide(divide(inverse(X1), X0), Y1))) -> inverse(Y1) % 71.51/71.61 divide(divide(X0, inverse(X1)), inverse(divide(divide(inverse(X1), X0), inverse(Y1)))) -> Y1 % 71.51/71.61 divide(divide(X2, X1), divide(X0, X1)) -> divide(X2, X0) % 71.51/71.61 divide(divide(X2, inverse(divide(X1, X0))), divide(Y1, divide(divide(X0, X1), X2))) -> inverse(Y1) % 71.51/71.61 divide(divide(Y0, Y1), divide(divide(X0, inverse(Y0)), Y1)) -> inverse(X0) % 71.51/71.61 divide(divide(Y0, Y1), divide(divide(divide(X1, X0), inverse(Y0)), Y1)) -> divide(X0, X1) % 71.51/71.61 divide(divide(Y0, Y1), divide(inverse(divide(inverse(Y0), Y2)), Y1)) -> inverse(Y2) % 71.51/71.61 divide(divide(Y0, Y1), divide(inverse(divide(inverse(Y0), inverse(Y2))), Y1)) -> Y2 % 71.51/71.61 divide(divide(Y0, Y1), inverse(divide(Y1, Y2))) -> divide(Y0, Y2) % 71.51/71.61 divide(divide(Y0, Y1), inverse(divide(Y1, divide(Y2, inverse(Y0))))) -> inverse(Y2) % 71.51/71.61 divide(divide(Y0, Y1), inverse(divide(Y1, divide(inverse(Y2), inverse(Y0))))) -> Y2 % 71.51/71.61 divide(divide(Y0, Y2), Y1) -> divide(Y0, inverse(divide(inverse(Y2), Y1))) % 71.51/71.61 divide(divide(Y0, divide(X0, inverse(X1))), divide(inverse(X1), X0)) -> Y0 % 71.51/71.61 divide(divide(Y0, divide(divide(X2, X1), X0)), divide(X0, inverse(divide(X1, X2)))) -> Y0 % 71.51/71.61 divide(divide(Y0, divide(inverse(X1), X0)), divide(X0, inverse(X1))) -> Y0 % 71.51/71.61 divide(divide(Y0, inverse(X0)), X0) -> Y0 % 71.51/71.61 divide(divide(Y0, inverse(X0)), X1) -> divide(Y0, inverse(divide(X0, X1))) % 71.51/71.61 divide(divide(divide(X0, X1), X2), divide(Y1, divide(X2, inverse(divide(X1, X0))))) -> inverse(Y1) % 71.51/71.61 divide(divide(divide(X0, X1), X2), divide(inverse(Y1), divide(X2, inverse(divide(X1, X0))))) -> Y1 % 71.51/71.61 divide(divide(divide(X0, X1), Y1), divide(divide(Y2, divide(X1, X0)), Y1)) -> inverse(Y2) % 71.51/71.61 divide(divide(divide(X0, X1), Y1), divide(divide(inverse(Y2), divide(X1, X0)), Y1)) -> Y2 % 71.51/71.61 divide(divide(inverse(X0), X1), inverse(X1)) -> inverse(inverse(inverse(X0))) % 71.51/71.61 divide(divide(inverse(X0), Y1), divide(divide(Y2, X0), Y1)) -> inverse(Y2) % 71.51/71.61 divide(divide(inverse(X0), Y1), divide(divide(inverse(Y2), X0), Y1)) -> Y2 % 71.51/71.61 divide(divide(inverse(X0), inverse(X1)), X1) -> inverse(X0) % 71.51/71.61 divide(divide(inverse(X1), X0), divide(Y1, divide(X0, inverse(X1)))) -> inverse(Y1) % 71.51/71.61 divide(divide(inverse(X1), X0), inverse(divide(divide(X0, inverse(X1)), Y1))) -> inverse(Y1) % 71.51/71.61 divide(divide(inverse(X1), X0), inverse(divide(divide(X0, inverse(X1)), inverse(Y1)))) -> Y1 % 71.51/71.61 divide(divide(inverse(Y0), Y1), divide(inverse(divide(Y0, Y2)), Y1)) -> inverse(Y2) % 71.51/71.61 divide(divide(inverse(Y0), Y1), divide(inverse(divide(Y0, inverse(Y2))), Y1)) -> Y2 % 71.51/71.61 divide(divide(inverse(Y0), Y1), inverse(divide(Y1, divide(Y2, Y0)))) -> inverse(Y2) % 71.51/71.61 divide(divide(inverse(Y0), Y1), inverse(divide(Y1, divide(inverse(Y2), Y0)))) -> Y2 % 71.51/71.61 divide(divide(inverse(divide(X0, X1)), X2), divide(inverse(Y1), divide(X2, divide(X1, X0)))) -> Y1 % 71.51/71.61 divide(divide(inverse(divide(X0, X1)), X2), inverse(divide(divide(X2, divide(X1, X0)), inverse(Y1)))) -> Y1 % 71.51/71.61 divide(divide(inverse(divide(X2, X1)), X0), divide(Y1, divide(X0, divide(X1, X2)))) -> inverse(Y1) % 71.51/71.61 divide(inverse(X0), divide(divide(Y1, Y2), divide(X0, Y2))) -> inverse(Y1) % 71.51/71.61 divide(inverse(X0), divide(divide(inverse(Y1), Y2), divide(X0, Y2))) -> Y1 % 71.51/71.61 divide(inverse(X0), inverse(divide(X0, Y1))) -> inverse(Y1) % 71.51/71.61 divide(inverse(X0), inverse(divide(X0, inverse(Y1)))) -> Y1 % 71.51/71.61 divide(inverse(X1), divide(X0, X1)) -> inverse(X0) % 71.51/71.61 divide(inverse(Y0), divide(X0, divide(Y0, Y2))) -> inverse(divide(X0, inverse(Y2))) % 71.51/71.61 divide(inverse(Y0), divide(divide(Y1, Y2), inverse(divide(Y2, Y0)))) -> inverse(Y1) % 71.51/71.61 divide(inverse(Y0), divide(divide(inverse(Y1), Y2), inverse(divide(Y2, Y0)))) -> Y1 % 71.51/71.61 divide(inverse(Y0), divide(inverse(divide(Y2, Y1)), divide(Y0, Y2))) -> inverse(Y1) % 71.51/71.61 divide(inverse(Y0), divide(inverse(divide(Y2, inverse(Y1))), divide(Y0, Y2))) -> Y1 % 71.51/71.61 divide(inverse(Y0), inverse(divide(divide(Y0, Y2), divide(Y1, Y2)))) -> inverse(Y1) % 71.51/71.61 divide(inverse(Y0), inverse(divide(divide(Y0, Y2), divide(inverse(Y1), Y2)))) -> Y1 % 71.51/71.61 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1) % 71.51/71.61 divide(inverse(divide(X0, X2)), inverse(divide(X0, X1))) -> divide(X2, X1) % 71.51/71.61 divide(inverse(divide(X0, Y1)), inverse(X0)) -> Y1 % 71.51/71.61 divide(inverse(divide(X0, inverse(Y1))), inverse(X0)) -> inverse(Y1) % 71.51/71.61 divide(inverse(divide(X0, inverse(Y2))), divide(divide(Y1, Y2), X0)) -> inverse(Y1) % 71.51/71.61 divide(inverse(divide(X0, inverse(Y2))), divide(divide(inverse(Y1), Y2), X0)) -> Y1 % 71.51/71.61 divide(inverse(divide(Y1, Y0)), divide(Y2, Y1)) -> divide(Y0, Y2) % 71.51/71.61 divide(inverse(divide(Y1, Y0)), divide(divide(Y2, inverse(Y0)), Y1)) -> inverse(Y2) % 71.51/71.61 divide(inverse(divide(Y1, Y0)), divide(divide(inverse(Y2), inverse(Y0)), Y1)) -> Y2 % 71.51/71.61 divide(inverse(divide(inverse(X0), Y1)), X0) -> Y1 % 71.51/71.61 divide(inverse(divide(inverse(X0), inverse(Y1))), X0) -> inverse(Y1) % 71.51/71.61 divide(inverse(inverse(divide(X0, X0))), Y1) -> inverse(Y1) % 71.51/71.61 divide(inverse(inverse(inverse(X0))), inverse(divide(X0, inverse(Y1)))) -> Y1 % 71.51/71.61 divide(inverse(inverse(inverse(Y0))), inverse(divide(Y0, X0))) -> inverse(inverse(inverse(X0))) % 71.51/71.61 divide(inverse(inverse(inverse(divide(X0, X0)))), Y1) -> inverse(Y1) % 71.51/71.61 f1(divide(a3, inverse(divide(b3, inverse(c3))))) -> false__ % 71.51/71.61 f1(divide(divide(a3, inverse(b3)), inverse(c3))) -> true__ % 71.51/71.61 f1(multiply(a3, multiply(b3, c3))) -> false__ % 71.51/71.61 f1(multiply(multiply(a3, b3), c3)) -> true__ % 71.51/71.61 inverse(divide(X0, inverse(divide(X1, inverse(divide(divide(inverse(X1), X0), Y1)))))) -> Y1 % 71.51/71.61 inverse(divide(X1, inverse(divide(inverse(X0), inverse(divide(divide(X0, X1), Y1)))))) -> Y1 % 71.51/71.61 inverse(divide(X1, inverse(divide(inverse(X0), inverse(divide(divide(X0, X1), inverse(Y1))))))) -> inverse(Y1) % 71.51/71.61 inverse(divide(divide(X0, Y1), inverse(Y1))) -> inverse(inverse(inverse(X0))) % 71.51/71.61 inverse(divide(divide(X0, inverse(X1)), inverse(divide(divide(inverse(X1), X0), Y1)))) -> Y1 % 71.51/71.61 inverse(divide(divide(Y0, inverse(X0)), X0)) -> inverse(Y0) % 71.51/71.61 inverse(divide(divide(Y0, inverse(inverse(inverse(X0)))), X0)) -> inverse(inverse(inverse(Y0))) % 71.51/71.61 inverse(divide(divide(Y2, Y1), divide(Y0, Y1))) -> inverse(divide(Y2, Y0)) % 71.51/71.61 inverse(divide(divide(inverse(X1), X0), inverse(divide(divide(X0, inverse(X1)), Y1)))) -> Y1 % 71.51/71.61 inverse(divide(divide(inverse(Y0), Y1), divide(inverse(inverse(divide(X0, X0))), Y1))) -> Y0 % 71.51/71.61 inverse(divide(divide(inverse(Y0), divide(X0, X0)), divide(X1, X1))) -> Y0 % 71.51/71.61 inverse(divide(divide(inverse(Y0), inverse(X0)), X0)) -> Y0 % 71.51/71.61 inverse(divide(divide(inverse(Y0), inverse(inverse(inverse(X0)))), X0)) -> Y0 % 71.51/71.61 inverse(divide(divide(inverse(Y1), Y2), divide(inverse(divide(X0, X0)), Y2))) -> Y1 % 71.51/71.61 inverse(divide(divide(inverse(Y1), Y2), inverse(Y2))) -> Y1 % 71.51/71.61 inverse(divide(inverse(X1), inverse(divide(inverse(X0), inverse(divide(divide(X0, inverse(X1)), Y1)))))) -> Y1 % 71.51/71.61 inverse(divide(inverse(divide(X0, inverse(divide(X2, X1)))), inverse(divide(divide(X0, divide(X1, X2)), Y1)))) -> Y1 % 71.51/71.61 inverse(divide(inverse(divide(X2, divide(X0, X1))), inverse(divide(divide(X2, inverse(divide(X1, X0))), Y1)))) -> Y1 % 71.51/71.61 inverse(divide(inverse(divide(divide(X1, X0), X2)), inverse(divide(divide(inverse(divide(X0, X1)), X2), Y1)))) -> Y1 % 71.51/71.61 inverse(divide(inverse(divide(inverse(divide(X1, X0)), X2)), inverse(divide(divide(divide(X0, X1), X2), Y1)))) -> Y1 % 71.51/71.61 inverse(inverse(Y0)) -> Y0 % 71.51/71.61 inverse(inverse(divide(inverse(inverse(divide(X0, X0))), inverse(Y1)))) -> Y1 % 71.51/71.61 inverse(inverse(inverse(inverse(Y1)))) -> Y1 % 71.51/71.61 true__ -> false__ % 71.51/71.61 with the LPO induced by % 71.51/71.61 c3 > b3 > a3 > f1 > multiply > divide > inverse > true__ > false__ % 71.51/71.61 % 71.51/71.61 % SZS output end Proof % 71.51/71.61 %------------------------------------------------------------------------------