%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP592-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 15.05s 15.14s % Output : Proof 15.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : GRP592-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.13/0.14 % Command : moca.sh %s % 0.14/0.35 % Computer : n022.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Tue Jun 14 12:16:48 EDT 2022 % 0.14/0.36 % CPUTime : % 15.05/15.14 % SZS status Unsatisfiable % 15.05/15.14 % SZS output start Proof % 15.05/15.14 The input problem is unsatisfiable because % 15.05/15.14 % 15.05/15.14 [1] the following set of Horn clauses is unsatisfiable: % 15.05/15.14 % 15.05/15.14 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) = C % 15.05/15.14 multiply(A, B) = inverse(double_divide(B, A)) % 15.05/15.14 multiply(a, b) = multiply(b, a) ==> \bottom % 15.05/15.14 % 15.05/15.14 This holds because % 15.05/15.14 % 15.05/15.14 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 15.05/15.14 % 15.05/15.14 E: % 15.05/15.14 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) = C % 15.05/15.14 f1(multiply(a, b)) = true__ % 15.05/15.14 f1(multiply(b, a)) = false__ % 15.05/15.14 multiply(A, B) = inverse(double_divide(B, A)) % 15.05/15.14 G: % 15.05/15.14 true__ = false__ % 15.05/15.14 % 15.05/15.14 This holds because % 15.05/15.14 % 15.05/15.14 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 15.05/15.14 % 15.05/15.14 double_divide(X0, double_divide(X1, inverse(X1))) = inverse(X0) % 15.05/15.14 double_divide(X1, Y1) = double_divide(Y1, inverse(inverse(X1))) % 15.05/15.14 double_divide(X1, inverse(X1)) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 double_divide(Y0, Y1) = double_divide(Y1, Y0) % 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))) = double_divide(double_divide(Y2, inverse(Y0)), Y2) % 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))) = double_divide(double_divide(Y2, inverse(Y2)), Y0) % 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)) = double_divide(double_divide(Y2, inverse(Y0)), Y2) % 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)) = double_divide(double_divide(Y2, inverse(Y2)), Y0) % 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(double_divide(Y2, inverse(Y0)), Y2) % 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(double_divide(Y2, inverse(Y2)), Y0) % 15.05/15.14 double_divide(Y0, double_divide(inverse(X0), X0)) = inverse(Y0) % 15.05/15.14 double_divide(Y0, double_divide(inverse(X0), inverse(inverse(Y0)))) = double_divide(X0, double_divide(X1, inverse(X1))) % 15.05/15.14 double_divide(Y0, inverse(X0)) = double_divide(inverse(X0), Y0) % 15.05/15.14 double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))) = double_divide(double_divide(Y1, double_divide(Y2, inverse(Y2))), Y1) % 15.05/15.14 double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))) = double_divide(false__, inverse(false__)) % 15.05/15.14 double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0) = double_divide(double_divide(Y1, double_divide(Y2, inverse(Y2))), Y1) % 15.05/15.14 double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0) = double_divide(false__, inverse(false__)) % 15.05/15.14 double_divide(double_divide(X0, double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__)))), X0) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(false__, inverse(false__)) % 15.05/15.14 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(inverse(Y1), inverse(inverse(Y1))) % 15.05/15.14 double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(X0), inverse(inverse(X1)))) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 double_divide(double_divide(X1, inverse(X1)), double_divide(double_divide(Y1, double_divide(Y2, inverse(Y2))), Y1)) = double_divide(X0, inverse(X0)) % 15.05/15.14 double_divide(double_divide(Y0, X0), Y0) = double_divide(double_divide(X0, double_divide(X1, inverse(X1))), double_divide(Y2, inverse(Y2))) % 15.05/15.14 double_divide(double_divide(Y0, X0), Y0) = double_divide(double_divide(false__, inverse(false__)), double_divide(X0, double_divide(false__, inverse(false__)))) % 15.05/15.14 double_divide(double_divide(Y0, double_divide(X0, double_divide(X1, inverse(X1)))), double_divide(inverse(Y0), X0)) = double_divide(Y2, inverse(Y2)) % 15.05/15.14 double_divide(double_divide(Y0, double_divide(X1, inverse(X1))), Y0) = double_divide(double_divide(X0, inverse(X0)), double_divide(Y2, inverse(Y2))) % 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))), Y0) = double_divide(Y2, inverse(Y2)) % 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))), Y0) = double_divide(false__, inverse(false__)) % 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)), Y0) = double_divide(Y2, inverse(Y2)) % 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)), Y0) = double_divide(false__, inverse(false__)) % 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), Y0) = double_divide(Y2, inverse(Y2)) % 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), Y0) = double_divide(false__, inverse(false__)) % 15.05/15.14 double_divide(double_divide(Y0, double_divide(inverse(X0), inverse(X1))), Y0) = double_divide(double_divide(X0, X1), double_divide(Y2, inverse(Y2))) % 15.05/15.14 double_divide(double_divide(Y0, inverse(X0)), Y0) = double_divide(X0, double_divide(X1, inverse(X1))) % 15.05/15.14 double_divide(double_divide(Y0, inverse(Y0)), X0) = double_divide(X0, double_divide(X1, inverse(X1))) % 15.05/15.14 double_divide(double_divide(Y0, inverse(Y0)), X0) = double_divide(X0, double_divide(false__, inverse(false__))) % 15.05/15.14 double_divide(double_divide(Y0, inverse(Y0)), double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(Y2, inverse(Y2)) % 15.05/15.14 double_divide(double_divide(Y1, inverse(Y1)), Y0) = inverse(Y0) % 15.05/15.14 double_divide(double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))), Y1) = double_divide(Y1, double_divide(Y2, inverse(Y2))) % 15.05/15.14 double_divide(double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))), Y1) = double_divide(Y1, double_divide(false__, inverse(false__))) % 15.05/15.14 double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), Y1) = double_divide(Y1, double_divide(Y2, inverse(Y2))) % 15.05/15.14 double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), Y1) = double_divide(Y1, double_divide(false__, inverse(false__))) % 15.05/15.14 double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), double_divide(X2, inverse(X2))) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), Y1), double_divide(X0, inverse(Y1))) = double_divide(Y2, inverse(Y2)) % 15.05/15.14 double_divide(double_divide(double_divide(X0, inverse(X0)), Y1), Y1) = double_divide(Y2, inverse(Y2)) % 15.05/15.14 double_divide(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))), Y1) = double_divide(Y1, double_divide(Y2, inverse(Y2))) % 15.05/15.14 double_divide(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))), Y1) = double_divide(Y1, double_divide(false__, inverse(false__))) % 15.05/15.14 double_divide(double_divide(false__, inverse(false__)), X0) = double_divide(X0, double_divide(false__, inverse(false__))) % 15.05/15.14 double_divide(double_divide(false__, inverse(false__)), Y1) = inverse(Y1) % 15.05/15.14 double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__))) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 double_divide(double_divide(inverse(Y0), inverse(inverse(Y0))), double_divide(X1, inverse(X1))) = double_divide(X0, inverse(X0)) % 15.05/15.14 double_divide(false__, double_divide(inverse(X0), X0)) = inverse(false__) % 15.05/15.14 double_divide(false__, inverse(false__)) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 double_divide(inverse(X0), X0) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 double_divide(inverse(X0), X0) = double_divide(false__, inverse(false__)) % 15.05/15.14 double_divide(inverse(Y0), inverse(inverse(Y0))) = inverse(double_divide(X0, inverse(X0))) % 15.05/15.14 double_divide(inverse(double_divide(Y0, double_divide(X1, inverse(X1)))), inverse(Y0)) = double_divide(X0, inverse(X0)) % 15.05/15.14 inverse(double_divide(Y1, inverse(Y1))) = double_divide(X0, inverse(X0)) % 15.05/15.14 inverse(double_divide(Y1, inverse(Y1))) = inverse(double_divide(X0, inverse(X0))) % 15.05/15.14 inverse(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 inverse(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(Y1, inverse(Y1)) % 15.05/15.14 inverse(false__) = double_divide(false__, double_divide(Y1, inverse(Y1))) % 15.05/15.14 inverse(inverse(double_divide(Y1, inverse(Y1)))) = double_divide(X0, inverse(X0)) % 15.05/15.14 double_divide(X0, double_divide(X0, inverse(inverse(Y1)))) -> Y1 % 15.05/15.14 double_divide(X0, inverse(inverse(double_divide(Y1, X0)))) -> Y1 % 15.05/15.14 double_divide(X1, double_divide(inverse(inverse(X1)), inverse(inverse(Y0)))) -> Y0 % 15.05/15.14 double_divide(X1, double_divide(inverse(inverse(Y1)), inverse(inverse(X1)))) -> Y1 % 15.05/15.14 double_divide(Y0, double_divide(Y0, false__)) -> false__ % 15.05/15.14 double_divide(Y0, double_divide(false__, Y0)) -> false__ % 15.05/15.14 double_divide(Y1, double_divide(Y0, Y1)) -> Y0 % 15.05/15.14 double_divide(Y1, double_divide(Y1, Y0)) -> Y0 % 15.05/15.14 double_divide(double_divide(X0, X1), double_divide(inverse(inverse(Y1)), double_divide(inverse(inverse(X0)), inverse(inverse(X1))))) -> Y1 % 15.05/15.14 double_divide(double_divide(X0, double_divide(X1, inverse(X1))), double_divide(inverse(inverse(Y1)), inverse(X0))) -> Y1 % 15.05/15.14 double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(X0), inverse(inverse(X1)))) -> double_divide(false__, inverse(false__)) % 15.05/15.14 double_divide(double_divide(X0, inverse(inverse(Y1))), X0) -> Y1 % 15.05/15.14 double_divide(double_divide(X1, inverse(X1)), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(double_divide(Y0, inverse(Y0)), double_divide(inverse(X0), inverse(X1))) -> double_divide(X0, X1) % 15.05/15.14 double_divide(double_divide(Y0, inverse(Y0)), double_divide(inverse(X0), inverse(inverse(X1)))) -> double_divide(X0, inverse(X1)) % 15.05/15.14 double_divide(double_divide(Y2, Y1), Y1) -> Y2 % 15.05/15.14 double_divide(double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(X0), inverse(inverse(X1)))), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(double_divide(double_divide(Y0, double_divide(Y1, inverse(Y1))), Y0), double_divide(inverse(X0), inverse(X1))) -> double_divide(X0, X1) % 15.05/15.14 double_divide(double_divide(double_divide(Y0, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))), Y0), inverse(Y2)) -> Y2 % 15.05/15.14 double_divide(double_divide(double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)), Y0), inverse(Y2)) -> Y2 % 15.05/15.14 double_divide(double_divide(double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), Y0), inverse(Y2)) -> Y2 % 15.05/15.14 double_divide(double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), double_divide(X2, inverse(X2))), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(double_divide(false__, Y1), Y1) -> false__ % 15.05/15.14 double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__))) -> double_divide(false__, inverse(false__)) % 15.05/15.14 double_divide(double_divide(inverse(X0), X0), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(Y1, inverse(Y1))) -> double_divide(X0, X1) % 15.05/15.14 double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(double_divide(Y1, double_divide(Y2, inverse(Y2))), Y1)) -> double_divide(X0, X1) % 15.05/15.14 double_divide(false__, double_divide(false__, inverse(inverse(Y1)))) -> Y1 % 15.05/15.14 double_divide(inverse(X1), double_divide(inverse(inverse(Y1)), inverse(inverse(inverse(X1))))) -> Y1 % 15.05/15.14 double_divide(inverse(X1), inverse(inverse(double_divide(Y1, inverse(X1))))) -> Y1 % 15.05/15.14 double_divide(inverse(X2), inverse(inverse(double_divide(double_divide(X0, inverse(Y1)), inverse(double_divide(X0, inverse(X2))))))) -> Y1 % 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))) -> Y0 % 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)) -> Y0 % 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) -> Y0 % 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(Y1, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))), Y1)) -> Y0 % 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(Y1, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)), Y1)) -> Y0 % 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(Y1, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), Y1)) -> Y0 % 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))), double_divide(false__, inverse(false__)))) -> Y0 % 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), double_divide(X2, inverse(X2)))) -> Y0 % 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), double_divide(false__, inverse(false__)))) -> Y0 % 15.05/15.14 double_divide(inverse(Y0), inverse(inverse(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)))) -> Y0 % 15.05/15.14 double_divide(inverse(Y0), inverse(inverse(inverse(double_divide(X1, Y0))))) -> inverse(X1) % 15.05/15.14 double_divide(inverse(Y0), inverse(inverse(inverse(inverse(double_divide(X0, inverse(X0))))))) -> Y0 % 15.05/15.14 double_divide(inverse(Y1), double_divide(X1, inverse(X1))) -> Y1 % 15.05/15.14 double_divide(inverse(Y1), double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__)))) -> Y1 % 15.05/15.14 double_divide(inverse(Y1), inverse(inverse(double_divide(X0, inverse(X0))))) -> Y1 % 15.05/15.14 double_divide(inverse(Y1), inverse(inverse(inverse(double_divide(X0, inverse(X0)))))) -> Y1 % 15.05/15.14 double_divide(inverse(double_divide(X1, inverse(Y2))), inverse(X1)) -> Y2 % 15.05/15.14 double_divide(inverse(double_divide(X2, inverse(double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(double_divide(X0, inverse(X2))))), inverse(Y2))))), Y1) -> Y2 % 15.05/15.14 double_divide(inverse(double_divide(Y0, X0)), inverse(Y0)) -> double_divide(X0, double_divide(false__, inverse(false__))) % 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(Y0))), inverse(Y3)) -> Y3 % 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(X1, inverse(Y0))), inverse(Y3))))), inverse(X1)) -> Y3 % 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(X2, inverse(double_divide(inverse(double_divide(double_divide(X0, Y2), inverse(double_divide(X0, inverse(X2))))), inverse(Y0))))), inverse(Y3))))), Y2) -> Y3 % 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(X3, inverse(double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X1, Y2), inverse(double_divide(X1, inverse(X0))))), inverse(X3))))), inverse(Y0))))), inverse(Y3))))), Y2) -> Y3 % 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(X0))), Y2), inverse(Y0))), inverse(Y3))))), Y2) -> Y3 % 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X1, inverse(Y0)), inverse(double_divide(X1, inverse(X0))))), inverse(X3))))), Y2), inverse(X3))), inverse(Y3))))), Y2) -> Y3 % 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y0)), inverse(double_divide(X0, inverse(X2))))), Y2), inverse(X2))), inverse(Y3))))), Y2) -> Y3 % 15.05/15.14 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) -> C % 15.05/15.14 double_divide(inverse(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(inverse(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(X0))), Y1), inverse(Y2))), Y1) -> Y2 % 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X1, inverse(Y2)), inverse(double_divide(X1, inverse(X0))))), inverse(X3))))), Y1), inverse(X3))), Y1) -> Y2 % 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(double_divide(Y1, inverse(Y2))), Y3), inverse(Y2))), Y3) -> Y1 % 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y2)), inverse(double_divide(X0, inverse(X2))))), Y1), inverse(X2))), Y1) -> Y2 % 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y2)), inverse(double_divide(X0, inverse(X2))))), inverse(Y1)), inverse(X2))), Y3), inverse(Y2))), Y3) -> Y1 % 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(inverse(double_divide(X0, inverse(X0)))), Y1), inverse(Y2))), Y1) -> Y2 % 15.05/15.14 double_divide(inverse(double_divide(inverse(double_divide(double_divide(Y1, Y2), inverse(double_divide(Y1, inverse(inverse(double_divide(X0, inverse(X0)))))))), inverse(Y3))), Y2) -> Y3 % 15.05/15.14 double_divide(inverse(inverse(double_divide(X0, inverse(X0)))), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(inverse(inverse(double_divide(X1, Y1))), inverse(inverse(X1))) -> Y1 % 15.05/15.14 double_divide(inverse(inverse(inverse(double_divide(X0, inverse(X0))))), inverse(Y1)) -> Y1 % 15.05/15.14 double_divide(inverse(inverse(inverse(inverse(double_divide(X0, inverse(X0)))))), inverse(Y1)) -> Y1 % 15.05/15.14 f1(double_divide(inverse(a), inverse(b))) -> false__ % 15.05/15.14 f1(double_divide(inverse(b), inverse(a))) -> true__ % 15.05/15.14 f1(inverse(double_divide(a, b))) -> false__ % 15.05/15.14 f1(inverse(double_divide(b, a))) -> true__ % 15.05/15.14 f1(multiply(a, b)) -> true__ % 15.05/15.14 f1(multiply(b, a)) -> false__ % 15.05/15.14 inverse(double_divide(X1, Y0)) -> double_divide(inverse(X1), inverse(Y0)) % 15.05/15.14 inverse(double_divide(Y0, double_divide(X1, inverse(X1)))) -> Y0 % 15.05/15.14 inverse(double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0))) -> Y0 % 15.05/15.14 inverse(double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))))) -> Y0 % 15.05/15.14 inverse(double_divide(Y0, inverse(X1))) -> double_divide(inverse(Y0), inverse(inverse(X1))) % 15.05/15.14 inverse(double_divide(Y1, inverse(double_divide(X0, inverse(X0))))) -> Y1 % 15.05/15.14 inverse(inverse(Y1)) -> Y1 % 15.05/15.14 multiply(A, B) -> inverse(double_divide(B, A)) % 15.05/15.14 true__ -> false__ % 15.05/15.14 with the LPO induced by % 15.05/15.14 a > b > f1 > multiply > inverse > double_divide > true__ > false__ % 15.05/15.14 % 15.05/15.14 % SZS output end Proof % 15.05/15.14 %------------------------------------------------------------------------------