%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP527-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n026.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 10:56:02 EDT 2022 % Result : Unsatisfiable 8.68s 8.71s % Output : Proof 8.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : GRP527-1 : TPTP v8.1.0. Released v2.6.0. % 0.08/0.15 % Command : moca.sh %s % 0.15/0.36 % Computer : n026.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Tue Jun 14 11:51:06 EDT 2022 % 0.15/0.36 % CPUTime : % 8.68/8.71 % SZS status Unsatisfiable % 8.68/8.71 % SZS output start Proof % 8.68/8.71 The input problem is unsatisfiable because % 8.68/8.71 % 8.68/8.71 [1] the following set of Horn clauses is unsatisfiable: % 8.68/8.71 % 8.68/8.71 divide(A, divide(divide(A, B), divide(C, B))) = C % 8.68/8.71 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 8.68/8.71 inverse(A) = divide(divide(B, B), A) % 8.68/8.71 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 8.68/8.71 % 8.68/8.71 This holds because % 8.68/8.71 % 8.68/8.71 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 8.68/8.71 % 8.68/8.71 E: % 8.68/8.71 divide(A, divide(divide(A, B), divide(C, B))) = C % 8.68/8.71 f1(multiply(a3, multiply(b3, c3))) = false__ % 8.68/8.71 f1(multiply(multiply(a3, b3), c3)) = true__ % 8.68/8.71 inverse(A) = divide(divide(B, B), A) % 8.68/8.71 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 8.68/8.71 G: % 8.68/8.71 true__ = false__ % 8.68/8.71 % 8.68/8.71 This holds because % 8.68/8.71 % 8.68/8.71 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 8.68/8.71 % 8.68/8.71 divide(X0, X0) = inverse(divide(Y0, Y0)) % 8.68/8.71 divide(X0, X0) = inverse(inverse(divide(Y0, Y0))) % 8.68/8.71 divide(X1, X1) = inverse(inverse(inverse(inverse(divide(Y0, Y0))))) % 8.68/8.71 divide(X1, X1) = inverse(inverse(inverse(inverse(inverse(divide(Y0, Y0)))))) % 8.68/8.71 divide(X1, inverse(inverse(X1))) = divide(Y1, inverse(inverse(Y1))) % 8.68/8.71 divide(X1, inverse(inverse(X1))) = inverse(inverse(divide(Y0, Y0))) % 8.68/8.71 divide(X2, X2) = divide(Y2, Y2) % 8.68/8.71 divide(X2, divide(X2, X1)) = divide(Y0, divide(Y0, X1)) % 8.68/8.71 divide(Y0, X1) = divide(Y1, divide(divide(X1, X2), divide(divide(divide(Y0, Y3), divide(Y1, Y3)), X2))) % 8.68/8.71 divide(Y0, X1) = inverse(inverse(inverse(divide(X1, Y0)))) % 8.68/8.71 divide(Y0, divide(X1, inverse(divide(divide(Y0, divide(divide(X1, X2), divide(X3, X2))), X3)))) = divide(Y2, Y2) % 8.68/8.71 divide(Y0, divide(X1, inverse(inverse(divide(X1, Y0))))) = divide(Y2, Y2) % 8.68/8.71 divide(Y0, divide(X2, inverse(divide(X1, divide(X2, divide(divide(Y0, X3), divide(X1, X3))))))) = divide(Y2, Y2) % 8.68/8.71 divide(Y0, divide(Y1, divide(X0, X1))) = divide(X0, divide(X1, divide(divide(Y0, Y3), divide(Y1, Y3)))) % 8.68/8.71 divide(Y0, divide(Y1, divide(false__, false__))) = divide(divide(Y0, Y3), divide(Y1, Y3)) % 8.68/8.71 divide(Y0, divide(Y1, inverse(divide(divide(Y0, Y3), divide(Y1, Y3))))) = divide(X0, X0) % 8.68/8.71 divide(Y0, divide(Y1, inverse(divide(divide(Y0, Y3), divide(Y1, Y3))))) = inverse(divide(X0, X0)) % 8.68/8.71 divide(Y0, divide(divide(Y0, Y1), divide(X0, X1))) = divide(X0, divide(X1, Y1)) % 8.68/8.71 divide(Y0, divide(divide(Y0, Y1), inverse(Y1))) = divide(X0, X0) % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(inverse(Y2), divide(Y3, Y2))), Y3)) = divide(X0, X0) % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(inverse(Y2), divide(Y3, Y2))), Y3)) = inverse(divide(X0, X0)) % 8.68/8.71 divide(Y0, divide(false__, false__)) = divide(Y0, divide(X1, X1)) % 8.68/8.71 divide(Y0, inverse(divide(X0, X1))) = divide(X0, divide(X1, Y0)) % 8.68/8.71 divide(Y0, inverse(inverse(X0))) = inverse(divide(X0, Y0)) % 8.68/8.71 divide(Y0, inverse(inverse(Y0))) = divide(X0, X0) % 8.68/8.71 divide(Y0, inverse(inverse(Y0))) = inverse(divide(X0, X0)) % 8.68/8.71 divide(Y0, inverse(inverse(divide(divide(Y0, X1), inverse(X1))))) = divide(Y2, Y2) % 8.68/8.71 divide(divide(X0, divide(X1, Y1)), divide(divide(X0, X1), inverse(Y1))) = divide(Y2, Y2) % 8.68/8.71 divide(divide(Y0, inverse(Y2)), Y2) = divide(Y0, divide(X0, X0)) % 8.68/8.71 divide(divide(Y0, inverse(Y2)), Y2) = divide(Y0, inverse(divide(X0, X0))) % 8.68/8.71 divide(divide(inverse(inverse(divide(X0, X1))), X0), inverse(X1)) = divide(Y1, Y1) % 8.68/8.71 divide(false__, false__) = divide(X0, X0) % 8.68/8.71 divide(inverse(X0), divide(X1, divide(X0, inverse(X1)))) = divide(Y1, Y1) % 8.68/8.71 divide(inverse(X0), divide(X1, divide(X0, inverse(X1)))) = inverse(divide(Y1, Y1)) % 8.68/8.71 divide(inverse(X1), divide(X0, inverse(divide(inverse(X0), X1)))) = inverse(divide(Y1, Y1)) % 8.68/8.71 divide(inverse(X1), inverse(X0)) = inverse(inverse(divide(X0, X1))) % 8.68/8.71 divide(inverse(inverse(X1)), Y1) = inverse(divide(Y1, X1)) % 8.68/8.71 divide(inverse(inverse(inverse(X1))), inverse(Y0)) = divide(Y0, X1) % 8.68/8.71 inverse(divide(X0, X0)) = divide(false__, false__) % 8.68/8.71 inverse(divide(X0, X0)) = inverse(inverse(divide(Y0, Y0))) % 8.68/8.71 inverse(divide(X1, inverse(inverse(X1)))) = divide(Y1, Y1) % 8.68/8.71 inverse(divide(X1, inverse(inverse(X1)))) = divide(Y1, inverse(inverse(Y1))) % 8.68/8.71 inverse(divide(X1, inverse(inverse(X1)))) = divide(false__, false__) % 8.68/8.71 inverse(divide(X2, X2)) = divide(inverse(inverse(X1)), X1) % 8.68/8.71 inverse(divide(inverse(Y0), divide(X0, X1))) = divide(X0, divide(X1, Y0)) % 8.68/8.71 inverse(divide(inverse(Y0), inverse(X0))) = inverse(divide(X0, Y0)) % 8.68/8.71 inverse(divide(inverse(Y0), inverse(Y0))) = divide(X0, X0) % 8.68/8.71 inverse(divide(inverse(Y0), inverse(Y0))) = inverse(divide(X0, X0)) % 8.68/8.71 inverse(inverse(divide(X0, X0))) = divide(false__, false__) % 8.68/8.71 inverse(inverse(divide(X1, inverse(inverse(X1))))) = divide(Y1, Y1) % 8.68/8.71 inverse(inverse(divide(X1, inverse(inverse(X1))))) = divide(false__, false__) % 8.68/8.71 inverse(inverse(divide(X1, inverse(inverse(X1))))) = inverse(divide(Y1, Y1)) % 8.68/8.71 inverse(inverse(inverse(divide(X0, X0)))) = divide(Y1, Y1) % 8.68/8.71 inverse(inverse(inverse(divide(X0, X0)))) = divide(Y1, inverse(inverse(Y1))) % 8.68/8.71 inverse(inverse(inverse(divide(X0, X0)))) = divide(false__, false__) % 8.68/8.71 inverse(inverse(inverse(divide(X0, X0)))) = inverse(divide(Y1, Y1)) % 8.68/8.71 inverse(inverse(inverse(divide(X1, X1)))) = inverse(inverse(divide(Y1, Y1))) % 8.68/8.71 inverse(inverse(inverse(inverse(divide(X0, X0))))) = divide(false__, false__) % 8.68/8.71 inverse(inverse(inverse(inverse(divide(X0, X0))))) = inverse(divide(Y1, Y1)) % 8.68/8.71 inverse(inverse(inverse(inverse(inverse(divide(X0, X0)))))) = divide(false__, false__) % 8.68/8.71 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 8.68/8.71 divide(A, divide(divide(A, B), divide(C, B))) -> C % 8.68/8.71 divide(X1, inverse(divide(inverse(X1), Y1))) -> inverse(Y1) % 8.68/8.71 divide(X2, divide(X2, divide(divide(Y0, X3), divide(Y1, X3)))) -> divide(Y0, Y1) % 8.68/8.71 divide(Y0, divide(X1, divide(Y2, inverse(divide(X1, Y0))))) -> Y2 % 8.68/8.71 divide(Y0, divide(X1, inverse(inverse(X1)))) -> Y0 % 8.68/8.71 divide(Y0, divide(X2, divide(Y2, divide(divide(Y0, X1), divide(X2, X1))))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y0, X1)) -> inverse(inverse(X1)) % 8.68/8.71 divide(Y0, divide(Y1, Y1)) -> Y0 % 8.68/8.71 divide(Y0, divide(Y1, divide(Y2, divide(X1, divide(Y1, divide(divide(Y0, divide(divide(X1, X2), divide(X3, X2))), X3)))))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y1, divide(Y2, divide(X1, divide(Y1, inverse(divide(X1, Y0))))))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y1, divide(Y2, divide(X2, divide(Y1, divide(X1, divide(X2, divide(divide(Y0, X3), divide(X1, X3))))))))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y1, divide(Y2, divide(X2, divide(Y1, divide(divide(Y0, X1), divide(X2, X1))))))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y1, divide(Y2, divide(divide(Y0, divide(X1, divide(X2, divide(divide(Y1, X3), divide(X1, X3))))), X2)))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y1, divide(Y2, divide(divide(Y0, divide(divide(Y1, X1), divide(X2, X1))), X2)))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y1, divide(Y2, divide(divide(Y0, divide(divide(Y1, X1), inverse(X1))), divide(X2, X2))))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y1, divide(Y2, divide(divide(Y0, divide(divide(Y1, divide(divide(X1, X2), divide(X3, X2))), X3)), X1)))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y1, divide(Y2, divide(divide(Y0, inverse(divide(X1, Y1))), X1)))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y1, divide(Y2, inverse(divide(Y1, divide(divide(Y0, X1), inverse(X1))))))) -> Y2 % 8.68/8.71 divide(Y0, divide(Y3, divide(Y2, divide(divide(Y0, Y3), divide(false__, false__))))) -> Y2 % 8.68/8.71 divide(Y0, divide(divide(X0, divide(X1, Y3)), divide(Y2, divide(divide(Y0, Y3), divide(X0, X1))))) -> Y2 % 8.68/8.71 divide(Y0, divide(divide(X1, Y2), X1)) -> divide(Y0, inverse(Y2)) % 8.68/8.71 divide(Y0, divide(divide(Y0, X1), divide(divide(Y1, Y2), divide(divide(X1, X2), divide(Y2, X2))))) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, Y1), divide(false__, false__))) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(X1, divide(X2, divide(divide(Y2, X3), divide(X1, X3))))), X2)) -> Y2 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(X1, divide(Y3, inverse(divide(X1, Y1))))), Y3)) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(X2, X2)), divide(divide(Y1, inverse(X1)), X1))) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(X2, divide(Y3, divide(X1, divide(X2, divide(divide(Y1, X3), divide(X1, X3))))))), Y3)) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(divide(X0, X1), divide(Y3, Y2))), Y3)) -> divide(X0, divide(X1, Y2)) % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(divide(Y1, Y2), divide(X0, X1))), divide(X0, divide(X1, Y2)))) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(divide(Y1, Y2), divide(false__, false__))), Y2)) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(divide(Y1, Y2), inverse(Y2))), divide(X0, X0))) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(divide(Y1, Y2), inverse(Y2))), inverse(divide(X0, X0)))) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(divide(Y1, divide(X1, divide(X2, divide(divide(Y3, X3), divide(X1, X3))))), X2)), Y3)) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(divide(Y1, divide(divide(Y3, X1), divide(X2, X1))), X2)), Y3)) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(divide(Y1, divide(divide(Y3, X1), inverse(X1))), divide(X2, X2))), Y3)) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(divide(Y1, inverse(divide(X1, Y3))), X1)), Y3)) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(divide(Y2, X1), divide(X2, X1))), X2)) -> Y2 % 8.68/8.71 divide(Y0, divide(divide(Y0, divide(false__, false__)), Y3)) -> Y3 % 8.68/8.71 divide(Y0, divide(divide(Y0, false__), inverse(divide(X0, X0)))) -> false__ % 8.68/8.71 divide(Y0, divide(divide(Y0, inverse(divide(X1, Y2))), X1)) -> Y2 % 8.68/8.71 divide(Y0, divide(divide(Y0, inverse(divide(Y3, divide(divide(Y1, X1), inverse(X1))))), Y3)) -> Y1 % 8.68/8.71 divide(Y0, divide(divide(divide(Y0, Y3), divide(divide(X1, X2), divide(Y3, X2))), divide(Y2, X1))) -> Y2 % 8.68/8.71 divide(Y0, divide(divide(divide(Y0, inverse(X1)), X1), divide(Y2, divide(X2, X2)))) -> Y2 % 8.68/8.71 divide(Y0, divide(inverse(inverse(divide(X0, X0))), Y2)) -> divide(Y0, inverse(Y2)) % 8.68/8.71 divide(Y0, inverse(divide(X0, X0))) -> Y0 % 8.68/8.71 divide(Y0, inverse(divide(X1, X1))) -> inverse(inverse(inverse(inverse(Y0)))) % 8.68/8.71 divide(Y0, inverse(divide(X1, inverse(inverse(X1))))) -> Y0 % 8.68/8.71 divide(Y0, inverse(divide(Y2, divide(divide(Y0, Y3), inverse(Y3))))) -> Y2 % 8.68/8.71 divide(Y0, inverse(divide(false__, false__))) -> Y0 % 8.68/8.71 divide(Y0, inverse(inverse(X1))) -> divide(Y0, X1) % 8.68/8.71 divide(Y0, inverse(inverse(X1))) -> inverse(inverse(divide(Y0, X1))) % 8.68/8.71 divide(Y0, inverse(inverse(divide(X0, X0)))) -> Y0 % 8.68/8.71 divide(Y0, inverse(inverse(divide(X1, X1)))) -> inverse(inverse(Y0)) % 8.68/8.71 divide(Y0, inverse(inverse(false__))) -> divide(Y0, false__) % 8.68/8.71 divide(Y0, inverse(inverse(inverse(divide(X0, X0))))) -> Y0 % 8.68/8.71 divide(Y0, inverse(inverse(inverse(inverse(divide(X0, X0)))))) -> Y0 % 8.68/8.71 divide(Y1, divide(X1, inverse(inverse(X1)))) -> inverse(inverse(Y1)) % 8.68/8.71 divide(Y1, divide(Y1, divide(Y2, divide(false__, false__)))) -> Y2 % 8.68/8.71 divide(Y1, inverse(divide(Y2, Y1))) -> Y2 % 8.68/8.71 divide(Y2, divide(false__, false__)) -> Y2 % 8.68/8.71 divide(divide(B, B), A) -> inverse(A) % 8.68/8.71 divide(divide(X0, divide(X1, Y1)), divide(divide(X0, X1), divide(Y2, Y1))) -> Y2 % 8.68/8.71 divide(divide(X0, divide(X1, Y3)), divide(Y1, divide(Y2, divide(divide(X0, X1), divide(Y1, Y3))))) -> Y2 % 8.68/8.71 divide(divide(X0, divide(X1, divide(Y1, Y2))), Y1) -> divide(divide(X0, X1), Y2) % 8.68/8.71 divide(divide(X0, divide(X1, divide(divide(Y1, Y2), divide(Y3, Y2)))), divide(divide(X0, X1), Y3)) -> Y1 % 8.68/8.71 divide(divide(X1, X0), X1) -> inverse(X0) % 8.68/8.71 divide(divide(X1, divide(X2, divide(divide(Y1, X3), divide(X1, X3)))), inverse(X2)) -> Y1 % 8.68/8.71 divide(divide(X1, inverse(inverse(X1))), Y1) -> inverse(Y1) % 8.68/8.71 divide(divide(X1, inverse(inverse(X1))), inverse(Y1)) -> Y1 % 8.68/8.71 divide(divide(Y0, X1), divide(divide(Y1, divide(divide(X1, X2), divide(X3, X2))), X3)) -> divide(Y0, Y1) % 8.68/8.71 divide(divide(Y0, X1), inverse(divide(X1, Y1))) -> divide(Y0, Y1) % 8.68/8.71 divide(divide(Y0, X2), divide(X1, divide(X2, divide(divide(Y1, X3), divide(X1, X3))))) -> divide(Y0, Y1) % 8.68/8.71 divide(divide(Y0, X2), divide(divide(Y1, X1), divide(X2, X1))) -> divide(Y0, Y1) % 8.68/8.71 divide(divide(Y0, divide(X0, X1)), Y2) -> divide(Y0, divide(X0, divide(X1, Y2))) % 8.68/8.71 divide(divide(Y0, divide(X2, X1)), X1) -> divide(Y0, X2) % 8.68/8.71 divide(divide(Y0, divide(X2, X2)), divide(divide(Y1, X1), inverse(X1))) -> divide(Y0, Y1) % 8.68/8.71 divide(divide(Y0, divide(false__, false__)), Y2) -> divide(Y0, Y2) % 8.68/8.71 divide(divide(Y0, inverse(divide(X0, X0))), false__) -> divide(Y0, false__) % 8.68/8.71 divide(divide(Y1, X1), inverse(X1)) -> inverse(inverse(Y1)) % 8.68/8.71 divide(divide(Y1, X1), inverse(inverse(inverse(X1)))) -> Y1 % 8.68/8.71 divide(divide(divide(Y1, X1), divide(X2, X1)), inverse(X2)) -> Y1 % 8.68/8.71 divide(divide(divide(Y1, X1), inverse(X1)), inverse(divide(X2, X2))) -> Y1 % 8.68/8.71 divide(divide(divide(Y1, divide(divide(X1, X2), divide(X3, X2))), X3), inverse(X1)) -> Y1 % 8.68/8.71 divide(false__, inverse(divide(X0, X0))) -> false__ % 8.68/8.71 divide(false__, inverse(divide(X0, X0))) -> inverse(inverse(false__)) % 8.68/8.71 divide(false__, inverse(divide(inverse(false__), inverse(Y2)))) -> Y2 % 8.68/8.71 divide(false__, inverse(inverse(divide(X0, X0)))) -> false__ % 8.68/8.71 divide(false__, inverse(inverse(divide(X0, X0)))) -> inverse(inverse(false__)) % 8.68/8.71 divide(false__, inverse(inverse(inverse(divide(X0, X0))))) -> false__ % 8.68/8.71 divide(inverse(X1), inverse(Y0)) -> inverse(divide(X1, Y0)) % 8.68/8.71 divide(inverse(X1), inverse(divide(X1, Y0))) -> inverse(Y0) % 8.68/8.71 divide(inverse(X1), inverse(inverse(divide(X0, X1)))) -> inverse(X0) % 8.68/8.71 divide(inverse(Y0), divide(divide(X1, X2), divide(Y0, X2))) -> inverse(X1) % 8.68/8.71 divide(inverse(Y1), inverse(divide(X0, X0))) -> inverse(Y1) % 8.68/8.71 divide(inverse(Y1), inverse(inverse(divide(X0, X0)))) -> inverse(Y1) % 8.68/8.71 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1) % 8.68/8.71 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1 % 8.68/8.71 divide(inverse(divide(X1, inverse(inverse(X1)))), Y1) -> inverse(Y1) % 8.68/8.71 divide(inverse(divide(X1, inverse(inverse(X1)))), inverse(Y1)) -> Y1 % 8.68/8.71 divide(inverse(divide(Y1, Y2)), Y2) -> inverse(Y1) % 8.68/8.71 divide(inverse(divide(inverse(X0), Y1)), X0) -> Y1 % 8.68/8.71 divide(inverse(divide(inverse(X0), divide(X1, divide(X0, Y1)))), X1) -> Y1 % 8.68/8.71 divide(inverse(divide(inverse(X0), inverse(inverse(Y1)))), X0) -> Y1 % 8.68/8.71 divide(inverse(inverse(X0)), Y1) -> inverse(inverse(divide(X0, Y1))) % 8.68/8.71 divide(inverse(inverse(X0)), inverse(inverse(divide(X0, Y1)))) -> Y1 % 8.68/8.71 divide(inverse(inverse(X1)), inverse(divide(Y1, X1))) -> Y1 % 8.68/8.71 divide(inverse(inverse(Y1)), divide(X1, inverse(inverse(X1)))) -> Y1 % 8.68/8.71 divide(inverse(inverse(Y1)), inverse(divide(X1, X1))) -> Y1 % 8.68/8.71 divide(inverse(inverse(Y1)), inverse(inverse(divide(X1, X1)))) -> Y1 % 8.68/8.71 divide(inverse(inverse(divide(X0, X0))), Y1) -> inverse(Y1) % 8.68/8.71 divide(inverse(inverse(divide(X1, inverse(inverse(X1))))), Y1) -> inverse(Y1) % 8.68/8.71 divide(inverse(inverse(inverse(divide(X0, X0)))), Y1) -> inverse(Y1) % 8.68/8.71 divide(inverse(inverse(inverse(inverse(divide(X0, X0))))), Y1) -> inverse(Y1) % 8.68/8.71 f1(divide(a3, inverse(divide(b3, inverse(c3))))) -> false__ % 8.68/8.71 f1(divide(divide(a3, inverse(b3)), inverse(c3))) -> true__ % 8.68/8.71 f1(multiply(a3, multiply(b3, c3))) -> false__ % 8.68/8.71 f1(multiply(multiply(a3, b3), c3)) -> true__ % 8.68/8.71 inverse(divide(X0, divide(Y1, inverse(X0)))) -> Y1 % 8.68/8.71 inverse(divide(X1, divide(Y1, divide(inverse(X0), divide(X1, X0))))) -> Y1 % 8.68/8.71 inverse(divide(divide(X1, inverse(inverse(X1))), Y1)) -> Y1 % 8.68/8.71 inverse(divide(false__, divide(divide(false__, Y1), divide(inverse(Y1), Y2)))) -> Y2 % 8.68/8.71 inverse(divide(inverse(X1), divide(inverse(inverse(inverse(X1))), Y0))) -> inverse(Y0) % 8.68/8.71 inverse(divide(inverse(Y0), divide(X1, inverse(inverse(X1))))) -> Y0 % 8.68/8.71 inverse(divide(inverse(Y0), divide(false__, false__))) -> Y0 % 8.68/8.71 inverse(divide(inverse(Y0), inverse(X1))) -> divide(Y0, X1) % 8.68/8.71 inverse(divide(inverse(Y0), inverse(divide(X0, X0)))) -> Y0 % 8.68/8.71 inverse(divide(inverse(Y0), inverse(divide(X1, X1)))) -> inverse(inverse(Y0)) % 8.68/8.71 inverse(divide(inverse(Y0), inverse(inverse(divide(X0, X0))))) -> Y0 % 8.68/8.71 inverse(divide(inverse(Y1), divide(Y2, Y1))) -> Y2 % 8.68/8.71 inverse(divide(inverse(divide(X1, divide(X2, divide(divide(Y1, X3), divide(X1, X3))))), X2)) -> Y1 % 8.68/8.71 inverse(divide(inverse(divide(Y1, X1)), inverse(inverse(X1)))) -> Y1 % 8.68/8.71 inverse(divide(inverse(divide(divide(Y1, X1), inverse(X1))), divide(X2, X2))) -> Y1 % 8.68/8.71 inverse(divide(inverse(divide(divide(Y1, Y2), divide(Y3, Y2))), Y3)) -> Y1 % 8.68/8.71 inverse(divide(inverse(divide(divide(Y1, divide(divide(X1, X2), divide(X3, X2))), X3)), X1)) -> Y1 % 8.68/8.71 inverse(divide(inverse(false__), inverse(divide(X0, X0)))) -> false__ % 8.68/8.71 inverse(divide(inverse(false__), inverse(inverse(divide(X0, X0))))) -> false__ % 8.68/8.71 inverse(divide(inverse(inverse(X0)), X1)) -> inverse(divide(X0, X1)) % 8.68/8.71 inverse(divide(inverse(inverse(divide(X1, Y1))), X1)) -> Y1 % 8.68/8.71 inverse(divide(inverse(inverse(divide(X1, inverse(inverse(X1))))), Y1)) -> Y1 % 8.68/8.71 inverse(divide(inverse(inverse(inverse(Y1))), inverse(divide(X1, X1)))) -> Y1 % 8.68/8.71 inverse(inverse(Y1)) -> Y1 % 8.68/8.71 inverse(inverse(divide(X1, Y0))) -> divide(X1, Y0) % 8.68/8.71 inverse(inverse(divide(X1, inverse(divide(Y0, Y0))))) -> X1 % 8.68/8.71 inverse(inverse(divide(Y0, divide(X1, inverse(inverse(X1)))))) -> Y0 % 8.68/8.71 inverse(inverse(divide(Y0, inverse(divide(X1, inverse(inverse(X1))))))) -> Y0 % 8.68/8.71 inverse(inverse(divide(Y0, inverse(inverse(divide(X0, X0)))))) -> Y0 % 8.68/8.71 inverse(inverse(divide(Y0, inverse(inverse(inverse(divide(X0, X0))))))) -> Y0 % 8.68/8.71 inverse(inverse(divide(Y1, divide(X0, X0)))) -> Y1 % 8.68/8.71 inverse(inverse(divide(inverse(X1), divide(inverse(inverse(inverse(X1))), Y1)))) -> Y1 % 8.68/8.71 inverse(inverse(false__)) -> false__ % 8.68/8.71 inverse(inverse(inverse(Y0))) -> inverse(Y0) % 8.68/8.71 inverse(inverse(inverse(inverse(Y1)))) -> Y1 % 8.68/8.71 true__ -> false__ % 8.68/8.71 with the LPO induced by % 8.68/8.71 c3 > b3 > a3 > f1 > multiply > divide > inverse > true__ > false__ % 8.68/8.71 % 8.68/8.71 % SZS output end Proof % 8.68/8.71 %------------------------------------------------------------------------------