%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP593-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 10:56:30 EDT 2022 % Result : Unsatisfiable 111.43s 111.55s % Output : Proof 111.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GRP593-1 : TPTP v8.1.0. Released v2.6.0. % 0.04/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n025.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 : Tue Jun 14 10:48:24 EDT 2022 % 0.13/0.34 % CPUTime : % 111.43/111.55 % SZS status Unsatisfiable % 111.43/111.55 % SZS output start Proof % 111.43/111.55 The input problem is unsatisfiable because % 111.43/111.55 % 111.43/111.55 [1] the following set of Horn clauses is unsatisfiable: % 111.43/111.55 % 111.43/111.55 inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(C, B)))))) = C % 111.43/111.55 multiply(A, B) = inverse(double_divide(B, A)) % 111.43/111.55 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 111.43/111.55 % 111.43/111.55 This holds because % 111.43/111.55 % 111.43/111.55 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 111.43/111.55 % 111.43/111.55 E: % 111.43/111.55 f1(multiply(inverse(a1), a1)) = true__ % 111.43/111.55 f1(multiply(inverse(b1), b1)) = false__ % 111.43/111.55 inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(C, B)))))) = C % 111.43/111.55 multiply(A, B) = inverse(double_divide(B, A)) % 111.43/111.55 G: % 111.43/111.55 true__ = false__ % 111.43/111.55 % 111.43/111.55 This holds because % 111.43/111.55 % 111.43/111.55 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 111.43/111.55 % 111.43/111.55 double_divide(X0, false__) = double_divide(false__, X0) % 111.43/111.55 double_divide(X0, inverse(X0)) = double_divide(Y0, inverse(Y0)) % 111.43/111.55 double_divide(X0, inverse(double_divide(inverse(Y2), X1))) = inverse(double_divide(Y2, double_divide(X0, X1))) % 111.43/111.55 double_divide(X1, Y1) = double_divide(Y1, X1) % 111.43/111.55 double_divide(Y0, X1) = double_divide(X0, inverse(double_divide(double_divide(X0, inverse(X1)), Y0))) % 111.43/111.55 double_divide(Y0, X1) = double_divide(double_divide(X0, inverse(X1)), inverse(double_divide(X0, Y0))) % 111.43/111.55 double_divide(Y0, double_divide(X1, inverse(double_divide(inverse(inverse(Y1)), X2)))) = inverse(double_divide(Y1, double_divide(Y0, double_divide(X1, X2)))) % 111.43/111.55 double_divide(Y0, inverse(X0)) = inverse(double_divide(double_divide(double_divide(X0, inverse(double_divide(X1, Y2))), X1), double_divide(Y0, Y2))) % 111.43/111.55 double_divide(Y0, inverse(X1)) = double_divide(X0, inverse(double_divide(double_divide(X0, X1), Y0))) % 111.43/111.55 double_divide(Y0, inverse(X1)) = double_divide(double_divide(X0, X1), inverse(double_divide(X0, Y0))) % 111.43/111.55 double_divide(Y0, inverse(double_divide(X0, Y2))) = inverse(double_divide(double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(X2, X1))), X2), double_divide(Y0, Y2))) % 111.43/111.55 double_divide(Y0, inverse(double_divide(X1, X2))) = inverse(double_divide(double_divide(X0, X1), double_divide(Y0, inverse(double_divide(inverse(X0), X2))))) % 111.43/111.55 double_divide(Y0, inverse(double_divide(X1, Y2))) = inverse(double_divide(inverse(double_divide(double_divide(double_divide(X0, inverse(double_divide(false__, false__))), false__), double_divide(inverse(double_divide(double_divide(false__, inverse(X0)), inverse(double_divide(false__, X1)))), false__))), double_divide(Y0, Y2))) % 111.43/111.55 double_divide(Y0, inverse(double_divide(X2, Y2))) = inverse(double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(double_divide(X2, X1))))), double_divide(Y0, Y2))) % 111.43/111.55 double_divide(Y0, inverse(double_divide(double_divide(X1, inverse(double_divide(inverse(X0), X2))), Y2))) = inverse(double_divide(double_divide(X0, double_divide(X1, X2)), double_divide(Y0, Y2))) % 111.43/111.55 double_divide(Y0, inverse(inverse(double_divide(X1, double_divide(inverse(Y1), X2))))) = inverse(double_divide(Y1, double_divide(Y0, inverse(double_divide(inverse(X1), X2))))) % 111.43/111.55 double_divide(false__, inverse(false__)) = double_divide(X0, inverse(X0)) % 111.43/111.55 double_divide(inverse(X1), Y1) = double_divide(Y1, inverse(X1)) % 111.43/111.55 double_divide(inverse(double_divide(X0, inverse(Y2))), Y1) = inverse(double_divide(Y2, inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y1))), X1)))) % 111.43/111.55 double_divide(inverse(double_divide(Y0, Y1)), inverse(inverse(double_divide(X1, double_divide(inverse(Y0), X2))))) = double_divide(Y1, inverse(double_divide(inverse(X1), X2))) % 111.43/111.55 double_divide(inverse(double_divide(double_divide(Y0, Y1), X0)), Y1) = inverse(double_divide(double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(X2, X1))), X2), Y0)) % 111.43/111.55 double_divide(inverse(double_divide(inverse(double_divide(X2, X0)), Y1)), Y2) = inverse(double_divide(double_divide(X0, inverse(double_divide(Y1, Y2))), inverse(X2))) % 111.43/111.55 inverse(double_divide(X1, false__)) = double_divide(X0, double_divide(false__, inverse(double_divide(X1, X0)))) % 111.43/111.55 inverse(double_divide(X2, X1)) = double_divide(X0, double_divide(X1, inverse(double_divide(X2, X0)))) % 111.43/111.55 inverse(double_divide(Y0, X0)) = double_divide(inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y2))), X1)), inverse(double_divide(inverse(Y0), Y2))) % 111.43/111.55 inverse(double_divide(Y0, double_divide(Y1, inverse(X1)))) = double_divide(double_divide(Y0, X1), Y1) % 111.43/111.55 inverse(double_divide(Y0, double_divide(Y1, inverse(double_divide(Y2, Y0))))) = double_divide(Y2, Y1) % 111.43/111.55 inverse(double_divide(Y0, double_divide(Y1, inverse(double_divide(false__, Y0))))) = double_divide(false__, Y1) % 111.43/111.55 inverse(double_divide(Y0, double_divide(Y2, inverse(double_divide(Y0, Y1))))) = double_divide(Y1, Y2) % 111.43/111.55 inverse(double_divide(Y0, double_divide(false__, inverse(double_divide(Y0, Y1))))) = double_divide(Y1, false__) % 111.43/111.55 inverse(double_divide(Y0, double_divide(false__, inverse(double_divide(Y1, Y0))))) = double_divide(Y1, false__) % 111.43/111.55 inverse(double_divide(Y0, double_divide(inverse(inverse(double_divide(X1, double_divide(Y0, X2)))), Y2))) = double_divide(inverse(double_divide(inverse(X1), X2)), Y2) % 111.43/111.55 inverse(double_divide(Y0, inverse(double_divide(X1, double_divide(Y1, X2))))) = double_divide(Y1, inverse(double_divide(inverse(Y0), inverse(double_divide(inverse(X1), X2))))) % 111.43/111.55 inverse(double_divide(double_divide(X0, Y2), double_divide(double_divide(Y2, Y3), inverse(double_divide(Y1, Y3))))) = inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y1))), X1)) % 111.43/111.55 inverse(double_divide(double_divide(X0, inverse(double_divide(Y2, Y1))), Y2)) = inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y1))), X1)) % 111.43/111.55 inverse(double_divide(double_divide(Y0, X0), Y0)) = double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(Y2, X1))), Y2) % 111.43/111.55 inverse(double_divide(double_divide(Y0, X0), inverse(double_divide(Y0, Y2)))) = double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(inverse(double_divide(Y2, Y3)), X1))), Y3) % 111.43/111.55 inverse(double_divide(double_divide(Y0, Y1), inverse(double_divide(Y0, X0)))) = double_divide(double_divide(X0, X1), inverse(double_divide(Y1, X1))) % 111.43/111.55 inverse(double_divide(double_divide(Y0, Y1), inverse(double_divide(Y0, inverse(X0))))) = inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y1))), X1)) % 111.43/111.55 inverse(double_divide(double_divide(Y0, double_divide(X1, X2)), Y0)) = double_divide(Y1, double_divide(inverse(double_divide(Y1, X1)), X2)) % 111.43/111.55 inverse(double_divide(double_divide(Y0, inverse(X0)), inverse(double_divide(Y0, X1)))) = double_divide(double_divide(inverse(double_divide(X0, X1)), X2), X2) % 111.43/111.55 inverse(double_divide(double_divide(double_divide(X2, Y2), Y2), inverse(double_divide(X0, X1)))) = inverse(double_divide(X0, inverse(double_divide(X2, X1)))) % 111.43/111.55 inverse(double_divide(double_divide(inverse(double_divide(X2, X0)), false__), double_divide(double_divide(false__, false__), inverse(double_divide(Y1, false__))))) = inverse(double_divide(double_divide(X0, Y1), inverse(X2))) % 111.43/111.55 inverse(double_divide(false__, X1)) = double_divide(X0, double_divide(X1, inverse(double_divide(false__, X0)))) % 111.43/111.55 double_divide(X0, double_divide(X0, X1)) -> X1 % 111.43/111.55 double_divide(X0, double_divide(X0, inverse(X1))) -> inverse(X1) % 111.43/111.55 double_divide(X0, double_divide(X0, inverse(double_divide(X1, X2)))) -> inverse(double_divide(X1, X2)) % 111.43/111.55 double_divide(X0, double_divide(false__, X0)) -> false__ % 111.43/111.55 double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X0, X1), inverse(double_divide(Y1, X1)))), Y2))) -> double_divide(Y1, Y2) % 111.43/111.55 double_divide(X1, double_divide(X0, inverse(double_divide(X1, X2)))) -> inverse(double_divide(X0, X2)) % 111.43/111.55 double_divide(X1, double_divide(Y1, X1)) -> Y1 % 111.43/111.55 double_divide(X2, double_divide(double_divide(X0, X1), inverse(double_divide(X2, X1)))) -> inverse(X0) % 111.43/111.55 double_divide(Y0, double_divide(X1, inverse(X1))) -> inverse(Y0) % 111.43/111.55 double_divide(Y0, double_divide(false__, inverse(false__))) -> inverse(Y0) % 111.43/111.55 double_divide(Y0, double_divide(inverse(X1), Y0)) -> inverse(X1) % 111.43/111.55 double_divide(Y1, double_divide(false__, inverse(double_divide(Y0, Y1)))) -> inverse(double_divide(false__, Y0)) % 111.43/111.55 double_divide(Y1, inverse(double_divide(Y2, double_divide(Y0, inverse(double_divide(Y1, Y2)))))) -> Y0 % 111.43/111.55 double_divide(Y1, inverse(double_divide(Y2, double_divide(Y1, inverse(double_divide(Y2, Y0)))))) -> Y0 % 111.43/111.55 double_divide(Y2, inverse(double_divide(double_divide(Y2, inverse(Y1)), Y0))) -> double_divide(Y1, Y0) % 111.43/111.55 double_divide(double_divide(X0, X1), X0) -> X1 % 111.43/111.55 double_divide(double_divide(X0, Y2), Y2) -> X0 % 111.43/111.55 double_divide(double_divide(X0, inverse(X1)), X0) -> inverse(X1) % 111.43/111.55 double_divide(double_divide(X0, inverse(double_divide(X1, X2))), X0) -> inverse(double_divide(X1, X2)) % 111.43/111.55 double_divide(double_divide(X0, inverse(double_divide(X1, X2))), X1) -> inverse(double_divide(X0, X2)) % 111.43/111.55 double_divide(double_divide(X1, inverse(X1)), Y0) -> inverse(Y0) % 111.43/111.55 double_divide(double_divide(X1, inverse(X1)), inverse(Y0)) -> Y0 % 111.43/111.55 double_divide(double_divide(Y0, inverse(double_divide(Y2, Y1))), inverse(double_divide(Y1, Y2))) -> Y0 % 111.43/111.55 double_divide(double_divide(Y2, inverse(Y1)), inverse(double_divide(Y2, Y0))) -> double_divide(Y1, Y0) % 111.43/111.55 double_divide(double_divide(false__, X0), false__) -> X0 % 111.43/111.55 double_divide(double_divide(false__, X0), inverse(double_divide(false__, double_divide(inverse(Y1), inverse(X0))))) -> inverse(Y1) % 111.43/111.55 double_divide(double_divide(false__, X1), inverse(double_divide(false__, double_divide(inverse(X1), Y0)))) -> Y0 % 111.43/111.55 double_divide(double_divide(false__, inverse(Y0)), inverse(double_divide(false__, double_divide(inverse(Y1), Y0)))) -> inverse(Y1) % 111.43/111.55 double_divide(double_divide(false__, inverse(false__)), Y0) -> inverse(Y0) % 111.43/111.55 double_divide(double_divide(false__, inverse(false__)), inverse(Y0)) -> Y0 % 111.43/111.55 double_divide(double_divide(inverse(double_divide(Y0, X1)), X2), Y2) -> inverse(double_divide(Y0, double_divide(double_divide(X1, X2), Y2))) % 111.43/111.55 double_divide(false__, double_divide(X0, inverse(X0))) -> inverse(false__) % 111.43/111.55 double_divide(false__, inverse(double_divide(double_divide(false__, X1), double_divide(inverse(X1), Y0)))) -> Y0 % 111.43/111.55 double_divide(false__, inverse(double_divide(double_divide(false__, inverse(Y0)), double_divide(inverse(Y1), Y0)))) -> inverse(Y1) % 111.43/111.55 double_divide(false__, inverse(double_divide(double_divide(false__, inverse(Y1)), double_divide(Y1, Y0)))) -> Y0 % 111.43/111.55 double_divide(inverse(X0), inverse(double_divide(inverse(inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y1))), X1))), Y2))) -> double_divide(Y1, Y2) % 111.43/111.55 double_divide(inverse(X1), double_divide(Y0, inverse(X1))) -> Y0 % 111.43/111.55 double_divide(inverse(Y1), double_divide(X1, inverse(X1))) -> Y1 % 111.43/111.55 double_divide(inverse(Y1), double_divide(false__, inverse(false__))) -> Y1 % 111.43/111.55 double_divide(inverse(double_divide(X0, X1)), inverse(double_divide(inverse(X0), Y2))) -> double_divide(X1, Y2) % 111.43/111.55 double_divide(inverse(double_divide(X0, Y1)), Y2) -> double_divide(X0, inverse(double_divide(Y1, Y2))) % 111.43/111.55 double_divide(inverse(double_divide(double_divide(X0, inverse(double_divide(Y2, Y3))), Y2)), Y3) -> X0 % 111.43/111.55 double_divide(inverse(double_divide(double_divide(X1, X2), inverse(X0))), X2) -> inverse(double_divide(X0, X1)) % 111.43/111.55 double_divide(inverse(double_divide(double_divide(Y0, X0), double_divide(double_divide(X0, X1), inverse(double_divide(Y2, X1))))), Y2) -> Y0 % 111.43/111.55 double_divide(inverse(double_divide(double_divide(Y0, X1), double_divide(double_divide(inverse(double_divide(X0, X1)), X2), X2))), inverse(X0)) -> Y0 % 111.43/111.55 double_divide(inverse(double_divide(double_divide(Y0, X2), double_divide(X0, X1))), inverse(double_divide(X0, inverse(double_divide(X2, X1))))) -> Y0 % 111.43/111.55 double_divide(inverse(double_divide(double_divide(Y0, Y1), double_divide(double_divide(Y1, Y2), X0))), double_divide(double_divide(X0, X1), inverse(double_divide(Y2, X1)))) -> Y0 % 111.43/111.55 double_divide(inverse(double_divide(double_divide(Y0, double_divide(X1, X2)), Y1)), double_divide(inverse(double_divide(Y1, X1)), X2)) -> Y0 % 111.43/111.55 double_divide(inverse(double_divide(double_divide(Y0, double_divide(X1, X2)), double_divide(Y2, inverse(double_divide(X1, X2))))), Y2) -> Y0 % 111.43/111.55 double_divide(inverse(double_divide(double_divide(Y0, inverse(X0)), double_divide(X0, Y2))), Y2) -> Y0 % 111.43/111.55 double_divide(inverse(double_divide(double_divide(Y0, inverse(X0)), inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y2))), X1)))), Y2) -> Y0 % 111.43/111.55 double_divide(inverse(double_divide(double_divide(Y0, inverse(double_divide(X1, X2))), inverse(double_divide(X0, X1)))), inverse(double_divide(inverse(X0), X2))) -> Y0 % 111.43/111.55 double_divide(inverse(double_divide(double_divide(double_divide(X0, inverse(double_divide(X1, Y2))), X1), Y1)), inverse(X0)) -> double_divide(Y1, Y2) % 111.43/111.55 double_divide(inverse(double_divide(double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(X2, X1))), X2), Y1)), inverse(double_divide(X0, Y2))) -> double_divide(Y1, Y2) % 111.43/111.55 double_divide(inverse(double_divide(inverse(double_divide(X1, double_divide(Y0, X2))), inverse(X1))), X2) -> Y0 % 111.43/111.55 double_divide(inverse(false__), double_divide(X0, inverse(X0))) -> false__ % 111.43/111.55 double_divide(inverse(inverse(double_divide(X1, double_divide(double_divide(Y0, inverse(double_divide(inverse(double_divide(inverse(X1), X2)), Y2))), X2)))), Y2) -> Y0 % 111.43/111.55 f1(inverse(double_divide(X1, inverse(X1)))) -> false__ % 111.43/111.55 f1(inverse(double_divide(X1, inverse(X1)))) -> true__ % 111.43/111.55 f1(inverse(double_divide(a1, inverse(a1)))) -> true__ % 111.43/111.55 f1(inverse(double_divide(b1, inverse(b1)))) -> false__ % 111.43/111.55 f1(inverse(double_divide(false__, inverse(false__)))) -> false__ % 111.43/111.55 f1(inverse(double_divide(false__, inverse(false__)))) -> true__ % 111.43/111.55 f1(multiply(inverse(a1), a1)) -> true__ % 111.43/111.55 f1(multiply(inverse(b1), b1)) -> false__ % 111.43/111.55 inverse(double_divide(X0, double_divide(X0, inverse(Y1)))) -> Y1 % 111.43/111.55 inverse(double_divide(X0, inverse(double_divide(double_divide(X0, X1), inverse(double_divide(double_divide(double_divide(Y1, Y2), Y2), X1)))))) -> Y1 % 111.43/111.55 inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y1))), X1)), inverse(double_divide(Y2, Y1)))))) -> Y2 % 111.43/111.55 inverse(double_divide(X1, double_divide(Y1, X1))) -> inverse(Y1) % 111.43/111.55 inverse(double_divide(X1, double_divide(inverse(Y1), X1))) -> Y1 % 111.43/111.55 inverse(double_divide(X1, double_divide(inverse(double_divide(double_divide(Y0, inverse(inverse(double_divide(X1, double_divide(Y1, X2))))), Y1)), X2))) -> Y0 % 111.43/111.55 inverse(double_divide(Y0, double_divide(Y0, X0))) -> inverse(X0) % 111.43/111.55 inverse(double_divide(Y0, double_divide(Y1, inverse(double_divide(Y0, Y2))))) -> double_divide(Y1, Y2) % 111.43/111.55 inverse(double_divide(Y0, double_divide(false__, inverse(double_divide(Y0, Y2))))) -> double_divide(false__, Y2) % 111.43/111.55 inverse(double_divide(Y0, double_divide(inverse(double_divide(Y0, Y1)), Y2))) -> double_divide(Y1, Y2) % 111.43/111.55 inverse(double_divide(Y1, double_divide(Y0, inverse(double_divide(false__, double_divide(inverse(inverse(double_divide(Y1, double_divide(false__, X1)))), X2)))))) -> double_divide(Y0, double_divide(X1, X2)) % 111.43/111.55 inverse(double_divide(Y1, inverse(double_divide(X0, double_divide(double_divide(inverse(Y1), Y2), Y2))))) -> X0 % 111.43/111.55 inverse(double_divide(Y1, inverse(double_divide(double_divide(false__, inverse(X0)), inverse(double_divide(false__, inverse(Y1))))))) -> X0 % 111.43/111.55 inverse(double_divide(Y2, double_divide(double_divide(Y0, Y1), inverse(double_divide(Y1, Y2))))) -> Y0 % 111.43/111.55 inverse(double_divide(Y2, double_divide(double_divide(Y0, Y1), inverse(double_divide(Y2, Y1))))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(C, B)))))) -> C % 111.43/111.55 inverse(double_divide(double_divide(X0, Y1), double_divide(inverse(X0), Y2))) -> double_divide(Y1, Y2) % 111.43/111.55 inverse(double_divide(double_divide(X0, Y2), double_divide(Y1, inverse(X0)))) -> double_divide(Y2, Y1) % 111.43/111.55 inverse(double_divide(double_divide(X0, inverse(double_divide(X1, inverse(double_divide(Y1, Y2))))), X1)) -> double_divide(inverse(double_divide(X0, Y1)), Y2) % 111.43/111.55 inverse(double_divide(double_divide(X0, inverse(double_divide(Y1, Y2))), X0)) -> double_divide(Y1, Y2) % 111.43/111.55 inverse(double_divide(double_divide(X0, inverse(double_divide(Y2, Y1))), Y2)) -> double_divide(X0, Y1) % 111.43/111.55 inverse(double_divide(double_divide(Y0, X0), Y0)) -> inverse(X0) % 111.43/111.55 inverse(double_divide(double_divide(Y0, Y1), inverse(inverse(double_divide(X1, double_divide(Y0, Y1)))))) -> inverse(X1) % 111.43/111.55 inverse(double_divide(double_divide(Y0, double_divide(X1, X2)), inverse(double_divide(Y0, double_divide(X1, inverse(double_divide(inverse(Y2), X2))))))) -> Y2 % 111.43/111.55 inverse(double_divide(double_divide(Y0, inverse(X0)), Y0)) -> X0 % 111.43/111.55 inverse(double_divide(double_divide(Y0, inverse(double_divide(X0, inverse(double_divide(X2, X1))))), inverse(double_divide(Y0, X2)))) -> double_divide(X0, X1) % 111.43/111.55 inverse(double_divide(double_divide(Y0, inverse(double_divide(Y1, X0))), inverse(double_divide(Y0, double_divide(double_divide(X0, X1), inverse(double_divide(Y3, X1))))))) -> double_divide(Y1, Y3) % 111.43/111.55 inverse(double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), X2))), inverse(double_divide(Y0, inverse(inverse(double_divide(X1, double_divide(Y2, X2)))))))) -> Y2 % 111.43/111.55 inverse(double_divide(double_divide(Y2, X1), double_divide(Y1, inverse(X1)))) -> double_divide(Y2, Y1) % 111.43/111.55 inverse(double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(Y1, X1))), double_divide(X0, Y2))) -> double_divide(Y1, Y2) % 111.43/111.55 inverse(double_divide(double_divide(double_divide(X0, Y2), Y2), inverse(double_divide(double_divide(X0, X1), inverse(double_divide(Y1, X1)))))) -> Y1 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(X0, Y2), inverse(X2)), inverse(double_divide(double_divide(double_divide(Y0, inverse(inverse(double_divide(X2, X0)))), false__), double_divide(double_divide(false__, false__), inverse(double_divide(Y2, false__))))))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(X0, false__), false__), inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(inverse(X0), X2))), false__), double_divide(double_divide(false__, false__), inverse(double_divide(X2, false__))))))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, Y1), X0), double_divide(double_divide(X0, X1), inverse(double_divide(Y1, X1))))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, Y1), X0), double_divide(inverse(X0), Y1))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, Y1), double_divide(X1, X2)), double_divide(Y1, inverse(double_divide(X1, X2))))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, Y1), inverse(X0)), double_divide(X0, Y1))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, Y1), inverse(X0)), inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y1))), X1)))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, Y1), inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y3))), X1))), double_divide(X0, inverse(double_divide(Y1, Y3))))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, Y1), inverse(inverse(double_divide(X2, X0)))), inverse(double_divide(double_divide(X0, Y1), inverse(X2))))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, double_divide(double_divide(X0, X1), inverse(double_divide(Y3, X1)))), Y2), double_divide(double_divide(Y2, Y3), X0))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, double_divide(inverse(double_divide(Y2, X1)), X2)), double_divide(X1, X2)), Y2)) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, inverse(X0)), X1), double_divide(double_divide(inverse(double_divide(X0, X1)), X2), X2))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(X0, inverse(double_divide(X2, X1))))), X2), double_divide(X0, X1))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y3))), X1))), Y2), double_divide(double_divide(Y2, Y3), inverse(X0)))) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), X2))), inverse(inverse(double_divide(X1, double_divide(Y2, X2))))), Y2)) -> Y0 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(Y2, X1), inverse(double_divide(X2, X1))), X2)) -> Y2 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(inverse(double_divide(Y2, Y1)), X1))), Y1), X0)) -> Y2 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(double_divide(inverse(double_divide(double_divide(Y2, Y1), X1)), X2), X2), Y1), X1)) -> Y2 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(inverse(X0), Y2), Y2), inverse(inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y1))), X1))))) -> Y1 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(inverse(double_divide(X0, Y2)), Y1), Y1), inverse(X0))) -> Y2 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(double_divide(X2, X1))))), Y1)), Y2), Y2), X2)) -> Y1 % 111.43/111.55 inverse(double_divide(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(X2, X1))), X2), Y1)), Y2), Y2), X0)) -> Y1 % 111.43/111.55 inverse(double_divide(double_divide(false__, X0), false__)) -> inverse(X0) % 111.43/111.55 inverse(double_divide(double_divide(false__, inverse(Y0)), inverse(double_divide(false__, double_divide(inverse(Y1), Y0))))) -> Y1 % 111.43/111.55 inverse(double_divide(false__, double_divide(X1, inverse(X1)))) -> false__ % 111.43/111.55 inverse(double_divide(false__, double_divide(double_divide(Y0, Y1), inverse(double_divide(false__, Y1))))) -> Y0 % 111.43/111.55 inverse(double_divide(false__, inverse(double_divide(double_divide(false__, inverse(Y0)), double_divide(inverse(Y1), Y0))))) -> Y1 % 111.43/111.55 inverse(double_divide(inverse(X0), inverse(double_divide(double_divide(false__, inverse(false__)), double_divide(inverse(Y1), inverse(X0)))))) -> Y1 % 111.43/111.55 inverse(double_divide(inverse(X1), double_divide(inverse(Y1), inverse(X1)))) -> Y1 % 111.43/111.55 inverse(double_divide(inverse(double_divide(X1, double_divide(Y0, X2))), inverse(double_divide(Y0, inverse(double_divide(Y2, inverse(double_divide(inverse(X1), X2)))))))) -> Y2 % 111.43/111.55 inverse(double_divide(inverse(double_divide(X1, double_divide(double_divide(Y0, Y1), Y1))), inverse(X1))) -> Y0 % 111.43/111.55 inverse(double_divide(inverse(double_divide(double_divide(X0, inverse(double_divide(X1, Y1))), X1)), double_divide(inverse(X0), Y2))) -> double_divide(Y1, Y2) % 111.43/111.55 inverse(double_divide(inverse(double_divide(double_divide(double_divide(double_divide(X0, X1), inverse(double_divide(X2, X1))), X2), double_divide(double_divide(Y1, Y2), Y2))), X0)) -> Y1 % 111.43/111.55 inverse(double_divide(inverse(double_divide(double_divide(false__, inverse(double_divide(X0, double_divide(X1, X2)))), inverse(double_divide(false__, Y1)))), double_divide(X1, inverse(double_divide(inverse(X0), X2))))) -> Y1 % 111.43/111.55 inverse(inverse(Y1)) -> Y1 % 111.43/111.55 inverse(inverse(double_divide(X1, double_divide(double_divide(inverse(X1), Y1), inverse(double_divide(Y2, Y1)))))) -> Y2 % 111.43/111.55 inverse(inverse(double_divide(X1, double_divide(inverse(double_divide(inverse(double_divide(X1, double_divide(false__, X2))), inverse(double_divide(false__, Y1)))), X2)))) -> Y1 % 111.43/111.55 inverse(inverse(double_divide(X1, inverse(double_divide(double_divide(false__, Y0), inverse(double_divide(false__, inverse(X1)))))))) -> Y0 % 111.43/111.55 inverse(inverse(double_divide(double_divide(double_divide(X0, inverse(double_divide(false__, false__))), false__), double_divide(inverse(double_divide(double_divide(false__, inverse(X0)), inverse(double_divide(false__, Y2)))), false__)))) -> Y2 % 111.43/111.55 inverse(inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(false__, false__))), false__), double_divide(double_divide(double_divide(inverse(inverse(double_divide(X1, double_divide(Y0, X2)))), Y2), Y2), false__)))) -> inverse(double_divide(inverse(X1), X2)) % 111.43/111.55 inverse(inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(false__, false__))), false__), double_divide(inverse(double_divide(X1, double_divide(double_divide(inverse(double_divide(Y0, Y1)), inverse(double_divide(inverse(X1), X2))), X2))), false__)))) -> Y1 % 111.43/111.55 multiply(A, B) -> inverse(double_divide(B, A)) % 111.43/111.55 true__ -> false__ % 111.43/111.55 with the LPO induced by % 111.43/111.55 a1 > b1 > f1 > multiply > double_divide > inverse > true__ > false__ % 111.43/111.55 % 111.43/111.55 % SZS output end Proof % 111.43/111.55 %------------------------------------------------------------------------------