%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP495-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n005.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 10:55:49 EDT 2022 % Result : Unsatisfiable 210.40s 210.24s % Output : Proof 210.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GRP495-1 : TPTP v8.1.0. Released v2.6.0. % 0.04/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n005.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Tue Jun 14 13:48:54 EDT 2022 % 0.14/0.35 % CPUTime : % 210.40/210.24 % SZS status Unsatisfiable % 210.40/210.24 % SZS output start Proof % 210.40/210.24 The input problem is unsatisfiable because % 210.40/210.24 % 210.40/210.24 [1] the following set of Horn clauses is unsatisfiable: % 210.40/210.24 % 210.40/210.24 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B % 210.40/210.24 multiply(A, B) = double_divide(double_divide(B, A), identity) % 210.40/210.24 inverse(A) = double_divide(A, identity) % 210.40/210.24 identity = double_divide(A, inverse(A)) % 210.40/210.24 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 210.40/210.24 % 210.40/210.24 This holds because % 210.40/210.24 % 210.40/210.24 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 210.40/210.24 % 210.40/210.24 E: % 210.40/210.24 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B % 210.40/210.24 f1(multiply(a3, multiply(b3, c3))) = false__ % 210.40/210.24 f1(multiply(multiply(a3, b3), c3)) = true__ % 210.40/210.24 identity = double_divide(A, inverse(A)) % 210.40/210.24 inverse(A) = double_divide(A, identity) % 210.40/210.24 multiply(A, B) = double_divide(double_divide(B, A), identity) % 210.40/210.24 G: % 210.40/210.24 true__ = false__ % 210.40/210.24 % 210.40/210.24 This holds because % 210.40/210.24 % 210.40/210.24 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 210.40/210.24 % 210.40/210.24 double_divide(X0, inverse(identity)) = double_divide(identity, double_divide(inverse(identity), inverse(X0))) % 210.40/210.24 double_divide(X1, inverse(X0)) = inverse(double_divide(X0, inverse(X1))) % 210.40/210.24 double_divide(Y0, double_divide(X1, X0)) = inverse(double_divide(X1, inverse(double_divide(X0, inverse(Y0))))) % 210.40/210.24 double_divide(Y0, double_divide(X1, X0)) = inverse(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y0))) % 210.40/210.24 double_divide(Y0, double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), inverse(Y0))) % 210.40/210.24 double_divide(Y0, double_divide(X2, double_divide(inverse(X1), inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, X1), inverse(X2)), inverse(Y0))) % 210.40/210.24 double_divide(Y0, double_divide(Y1, double_divide(X1, X0))) = inverse(double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y1)), inverse(Y0))) % 210.40/210.24 double_divide(Y0, double_divide(Y1, double_divide(X1, inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, inverse(X1)), inverse(Y1)), inverse(Y0))) % 210.40/210.24 double_divide(Y0, double_divide(double_divide(X2, inverse(X1)), X0)) = inverse(double_divide(double_divide(inverse(X0), double_divide(X1, inverse(X2))), inverse(Y0))) % 210.40/210.24 double_divide(Y0, double_divide(double_divide(inverse(X2), inverse(X1)), X0)) = inverse(double_divide(double_divide(inverse(X0), double_divide(X1, X2)), inverse(Y0))) % 210.40/210.24 double_divide(Y0, double_divide(inverse(X1), X0)) = inverse(double_divide(double_divide(inverse(X0), X1), inverse(Y0))) % 210.40/210.24 double_divide(double_divide(X1, X0), Y1) = inverse(double_divide(inverse(Y1), double_divide(inverse(X0), inverse(X1)))) % 210.40/210.24 double_divide(double_divide(X1, X0), inverse(Y1)) = inverse(double_divide(Y1, double_divide(inverse(X0), inverse(X1)))) % 210.40/210.24 double_divide(double_divide(X1, inverse(X0)), double_divide(Y1, Y2)) = inverse(double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(X0, inverse(X1)))) % 210.40/210.24 double_divide(double_divide(X1, inverse(X0)), inverse(Y1)) = inverse(double_divide(Y1, double_divide(X0, inverse(X1)))) % 210.40/210.24 double_divide(double_divide(X2, double_divide(inverse(X1), inverse(X0))), Y1) = inverse(double_divide(inverse(Y1), double_divide(double_divide(X0, X1), inverse(X2)))) % 210.40/210.24 double_divide(double_divide(X2, double_divide(inverse(X1), inverse(X0))), inverse(Y1)) = inverse(double_divide(Y1, double_divide(double_divide(X0, X1), inverse(X2)))) % 210.40/210.24 double_divide(double_divide(Y0, Y1), double_divide(X1, X0)) = inverse(double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(inverse(Y1), inverse(Y0)))) % 210.40/210.24 double_divide(double_divide(Y0, Y1), double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(Y1), inverse(Y0)))) % 210.40/210.24 double_divide(double_divide(Y0, Y1), double_divide(inverse(X1), X0)) = inverse(double_divide(double_divide(inverse(X0), X1), double_divide(inverse(Y1), inverse(Y0)))) % 210.40/210.24 double_divide(double_divide(Y0, Y1), double_divide(inverse(X1), inverse(X0))) = inverse(double_divide(double_divide(X0, X1), double_divide(inverse(Y1), inverse(Y0)))) % 210.40/210.24 double_divide(double_divide(Y0, double_divide(X1, X0)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y0)))) % 210.40/210.24 double_divide(double_divide(Y0, double_divide(X1, inverse(X0))), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(X0, inverse(X1)), inverse(Y0)))) % 210.40/210.24 double_divide(double_divide(Y0, double_divide(inverse(X1), X0)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(inverse(X0), X1), inverse(Y0)))) % 210.40/210.24 double_divide(double_divide(Y0, inverse(Y1)), double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), double_divide(Y1, inverse(Y0)))) % 210.40/210.24 double_divide(double_divide(Y0, inverse(Y1)), double_divide(inverse(X1), X0)) = inverse(double_divide(double_divide(inverse(X0), X1), double_divide(Y1, inverse(Y0)))) % 210.40/210.24 double_divide(double_divide(double_divide(X1, X0), Y1), inverse(Y2)) = inverse(double_divide(Y2, double_divide(inverse(Y1), double_divide(inverse(X0), inverse(X1))))) % 210.40/210.24 double_divide(double_divide(double_divide(X1, X0), inverse(Y1)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(Y1, double_divide(inverse(X0), inverse(X1))))) % 210.40/210.24 double_divide(double_divide(double_divide(X1, inverse(X0)), inverse(Y1)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(Y1, double_divide(X0, inverse(X1))))) % 210.40/210.24 double_divide(double_divide(double_divide(X2, inverse(X1)), X0), Y1) = inverse(double_divide(inverse(Y1), double_divide(inverse(X0), double_divide(X1, inverse(X2))))) % 210.40/210.24 double_divide(double_divide(double_divide(X2, inverse(X1)), X0), inverse(Y1)) = inverse(double_divide(Y1, double_divide(inverse(X0), double_divide(X1, inverse(X2))))) % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), X0), inverse(Y1)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(Y1, double_divide(inverse(X0), X1)))) % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(Y1, double_divide(X0, X1)))) % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X2), inverse(X1)), X0), Y1) = inverse(double_divide(inverse(Y1), double_divide(inverse(X0), double_divide(X1, X2)))) % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X2), inverse(X1)), X0), inverse(Y1)) = inverse(double_divide(Y1, double_divide(inverse(X0), double_divide(X1, X2)))) % 210.40/210.24 double_divide(double_divide(inverse(X1), X0), double_divide(Y1, Y2)) = inverse(double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(inverse(X0), X1))) % 210.40/210.24 double_divide(double_divide(inverse(X1), X0), inverse(Y1)) = inverse(double_divide(Y1, double_divide(inverse(X0), X1))) % 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X0)), double_divide(Y1, Y2)) = inverse(double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(X0, X1))) % 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)) = inverse(double_divide(Y1, double_divide(X0, X1))) % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, X0)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(inverse(X0), inverse(X1)), Y0))) % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, inverse(X0))), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(X0, inverse(X1)), Y0))) % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), X0)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(inverse(X0), X1), Y0))) % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0))), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(X0, X1), Y0))) % 210.40/210.24 double_divide(inverse(X0), inverse(double_divide(inverse(X1), inverse(Y1)))) = inverse(double_divide(Y1, double_divide(inverse(X0), inverse(X1)))) % 210.40/210.24 double_divide(inverse(X1), Y0) = inverse(double_divide(inverse(Y0), X1)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(X1, X0)) = inverse(double_divide(X1, inverse(double_divide(X0, Y0)))) % 210.40/210.24 double_divide(inverse(Y0), double_divide(X1, X0)) = inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(X2, double_divide(inverse(X1), inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, X1), inverse(X2)), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(Y1, double_divide(X1, X0))) = inverse(double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y1)), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(Y1, double_divide(X1, inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, inverse(X1)), inverse(Y1)), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(X1, X0), Y2)) = inverse(double_divide(double_divide(inverse(Y2), double_divide(inverse(X0), inverse(X1))), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(X1, X0), inverse(Y2))) = inverse(double_divide(double_divide(Y2, double_divide(inverse(X0), inverse(X1))), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(X1, inverse(X0)), inverse(Y2))) = inverse(double_divide(double_divide(Y2, double_divide(X0, inverse(X1))), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(X2, inverse(X1)), X0)) = inverse(double_divide(double_divide(inverse(X0), double_divide(X1, inverse(X2))), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(inverse(X1), X0), inverse(Y2))) = inverse(double_divide(double_divide(Y2, double_divide(inverse(X0), X1)), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y2))) = inverse(double_divide(double_divide(Y2, double_divide(X0, X1)), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(inverse(X2), inverse(X1)), X0)) = inverse(double_divide(double_divide(inverse(X0), double_divide(X1, X2)), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(X1), X0)) = inverse(double_divide(double_divide(inverse(X0), X1), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0))) = inverse(double_divide(double_divide(X0, X1), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(Y1), double_divide(X1, X0))) = inverse(double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), Y1), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(Y1), double_divide(X1, inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, inverse(X1)), Y1), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(Y1), double_divide(inverse(X1), X0))) = inverse(double_divide(double_divide(double_divide(inverse(X0), X1), Y1), Y0)) % 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, X1), Y1), Y0)) % 210.40/210.24 double_divide(inverse(Y0), inverse(X1)) = inverse(double_divide(X1, Y0)) % 210.40/210.24 double_divide(inverse(double_divide(X0, X1)), inverse(X2)) = inverse(double_divide(X2, inverse(double_divide(inverse(X1), inverse(X0))))) % 210.40/210.24 double_divide(inverse(double_divide(inverse(X0), inverse(X1))), inverse(X2)) = inverse(double_divide(X2, inverse(double_divide(X1, X0)))) % 210.40/210.24 inverse(double_divide(double_divide(X1, X0), inverse(Y1))) = double_divide(Y1, double_divide(inverse(X0), inverse(X1))) % 210.40/210.24 inverse(double_divide(double_divide(X1, inverse(X0)), double_divide(Y1, Y2))) = double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(X0, inverse(X1))) % 210.40/210.24 inverse(double_divide(double_divide(X2, double_divide(inverse(X1), inverse(X0))), inverse(Y1))) = double_divide(Y1, double_divide(double_divide(X0, X1), inverse(X2))) % 210.40/210.24 inverse(double_divide(double_divide(Y0, Y1), double_divide(X1, X0))) = double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(inverse(Y1), inverse(Y0))) % 210.40/210.24 inverse(double_divide(double_divide(Y0, Y1), double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(Y1), inverse(Y0))) % 210.40/210.24 inverse(double_divide(double_divide(Y0, Y1), double_divide(inverse(X1), X0))) = double_divide(double_divide(inverse(X0), X1), double_divide(inverse(Y1), inverse(Y0))) % 210.40/210.24 inverse(double_divide(double_divide(double_divide(X2, inverse(X1)), X0), inverse(Y1))) = double_divide(Y1, double_divide(inverse(X0), double_divide(X1, inverse(X2)))) % 210.40/210.24 inverse(double_divide(double_divide(double_divide(inverse(X2), inverse(X1)), X0), inverse(Y1))) = double_divide(Y1, double_divide(inverse(X0), double_divide(X1, X2))) % 210.40/210.24 inverse(double_divide(double_divide(inverse(X1), X0), double_divide(Y1, Y2))) = double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(inverse(X0), X1)) % 210.40/210.24 inverse(double_divide(inverse(X1), inverse(Y1))) = double_divide(Y1, X1) % 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(X1, X0))) = double_divide(double_divide(inverse(X0), inverse(X1)), Y0) % 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), Y0) % 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(X2, double_divide(inverse(X1), inverse(X0))))) = double_divide(double_divide(double_divide(X0, X1), inverse(X2)), Y0) % 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(Y1, double_divide(X1, X0)))) = double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y1)), Y0) % 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(double_divide(X2, inverse(X1)), X0))) = double_divide(double_divide(inverse(X0), double_divide(X1, inverse(X2))), Y0) % 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(double_divide(inverse(X2), inverse(X1)), X0))) = double_divide(double_divide(inverse(X0), double_divide(X1, X2)), Y0) % 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(inverse(X1), X0))) = double_divide(double_divide(inverse(X0), X1), Y0) % 210.40/210.24 double_divide(A, identity) -> inverse(A) % 210.40/210.24 double_divide(A, inverse(A)) -> identity % 210.40/210.24 double_divide(X0, double_divide(Y1, X0)) -> Y1 % 210.40/210.24 double_divide(X0, double_divide(double_divide(inverse(Y1), inverse(Y2)), double_divide(inverse(X0), Y1))) -> Y2 % 210.40/210.24 double_divide(X0, double_divide(inverse(double_divide(X0, inverse(X1))), X1)) -> identity % 210.40/210.24 double_divide(X0, inverse(double_divide(X1, double_divide(Y1, inverse(double_divide(X0, X1)))))) -> Y1 % 210.40/210.24 double_divide(X0, inverse(double_divide(inverse(X0), Y1))) -> inverse(Y1) % 210.40/210.24 double_divide(X0, inverse(double_divide(inverse(X0), inverse(Y1)))) -> Y1 % 210.40/210.24 double_divide(X0, inverse(double_divide(inverse(X1), double_divide(Y1, inverse(double_divide(X0, inverse(X1))))))) -> Y1 % 210.40/210.24 double_divide(X0, inverse(double_divide(inverse(Y1), double_divide(Y2, double_divide(Y1, inverse(X0)))))) -> Y2 % 210.40/210.24 double_divide(Y0, double_divide(X1, double_divide(inverse(Y0), Y1))) -> inverse(double_divide(X1, inverse(Y1))) % 210.40/210.24 double_divide(Y0, double_divide(double_divide(X0, inverse(Y2)), double_divide(inverse(Y0), inverse(X0)))) -> Y2 % 210.40/210.24 double_divide(Y0, double_divide(double_divide(Y1, X0), double_divide(inverse(Y0), inverse(Y1)))) -> inverse(X0) % 210.40/210.24 double_divide(Y0, double_divide(double_divide(inverse(Y1), X0), double_divide(inverse(Y0), Y1))) -> inverse(X0) % 210.40/210.24 double_divide(Y0, inverse(double_divide(X0, double_divide(Y2, double_divide(inverse(X0), inverse(Y0)))))) -> Y2 % 210.40/210.24 double_divide(double_divide(X0, X1), double_divide(inverse(X1), inverse(X0))) -> identity % 210.40/210.24 double_divide(double_divide(X0, inverse(Y1)), double_divide(Y2, inverse(X0))) -> double_divide(Y1, inverse(Y2)) % 210.40/210.24 double_divide(double_divide(X1, X0), double_divide(Y1, inverse(double_divide(inverse(X0), inverse(X1))))) -> Y1 % 210.40/210.24 double_divide(double_divide(X1, X0), inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y1))) -> inverse(Y1) % 210.40/210.24 double_divide(double_divide(X1, X0), inverse(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y1)))) -> Y1 % 210.40/210.24 double_divide(double_divide(X1, Y1), X1) -> Y1 % 210.40/210.24 double_divide(double_divide(X1, inverse(X0)), X1) -> inverse(X0) % 210.40/210.24 double_divide(double_divide(Y0, X0), double_divide(Y2, inverse(Y0))) -> double_divide(inverse(X0), inverse(Y2)) % 210.40/210.24 double_divide(double_divide(Y0, double_divide(X0, X1)), double_divide(Y2, inverse(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y0))))) -> Y2 % 210.40/210.24 double_divide(double_divide(Y0, double_divide(X0, X1)), double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y0))) -> identity % 210.40/210.24 double_divide(double_divide(Y0, double_divide(X0, inverse(X1))), double_divide(Y2, inverse(double_divide(double_divide(X1, inverse(X0)), inverse(Y0))))) -> Y2 % 210.40/210.24 double_divide(double_divide(Y0, double_divide(X0, inverse(X1))), double_divide(double_divide(X1, inverse(X0)), inverse(Y0))) -> identity % 210.40/210.24 double_divide(double_divide(Y0, double_divide(inverse(X0), X1)), double_divide(Y2, inverse(double_divide(double_divide(inverse(X1), X0), inverse(Y0))))) -> Y2 % 210.40/210.24 double_divide(double_divide(Y0, double_divide(inverse(X0), X1)), double_divide(double_divide(inverse(X1), X0), inverse(Y0))) -> identity % 210.40/210.24 double_divide(double_divide(Y0, double_divide(inverse(X0), inverse(X1))), double_divide(Y2, inverse(double_divide(double_divide(X1, X0), inverse(Y0))))) -> Y2 % 210.40/210.24 double_divide(double_divide(Y0, double_divide(inverse(X0), inverse(X1))), double_divide(double_divide(X1, X0), inverse(Y0))) -> identity % 210.40/210.24 double_divide(double_divide(Y1, Y0), X1) -> double_divide(inverse(Y0), inverse(double_divide(inverse(Y1), X1))) % 210.40/210.24 double_divide(double_divide(double_divide(X0, X1), Y1), double_divide(Y2, inverse(double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0)))))) -> Y2 % 210.40/210.24 double_divide(double_divide(double_divide(X0, X1), Y1), double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0)))) -> identity % 210.40/210.24 double_divide(double_divide(double_divide(X0, X1), inverse(X2)), double_divide(X2, double_divide(inverse(X1), inverse(X0)))) -> identity % 210.40/210.24 double_divide(double_divide(double_divide(X0, inverse(X1)), Y1), double_divide(Y2, inverse(double_divide(inverse(Y1), double_divide(X1, inverse(X0)))))) -> Y2 % 210.40/210.24 double_divide(double_divide(double_divide(X0, inverse(X1)), Y1), double_divide(inverse(Y1), double_divide(X1, inverse(X0)))) -> identity % 210.40/210.24 double_divide(double_divide(double_divide(X1, X0), inverse(Y1)), double_divide(Y2, inverse(double_divide(Y1, double_divide(inverse(X0), inverse(X1)))))) -> Y2 % 210.40/210.24 double_divide(double_divide(double_divide(X1, inverse(X0)), inverse(Y1)), double_divide(Y1, double_divide(X0, inverse(X1)))) -> identity % 210.40/210.24 double_divide(double_divide(double_divide(X1, inverse(X0)), inverse(Y1)), double_divide(Y2, inverse(double_divide(Y1, double_divide(X0, inverse(X1)))))) -> Y2 % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X0), X1), Y1), double_divide(Y2, inverse(double_divide(inverse(Y1), double_divide(inverse(X1), X0))))) -> Y2 % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X0), X1), Y1), double_divide(inverse(Y1), double_divide(inverse(X1), X0))) -> identity % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), Y1), double_divide(Y2, inverse(double_divide(inverse(Y1), double_divide(X1, X0))))) -> Y2 % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), Y1), double_divide(inverse(Y1), double_divide(X1, X0))) -> identity % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), X0), inverse(Y1)), double_divide(Y1, double_divide(inverse(X0), X1))) -> identity % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), X0), inverse(Y1)), double_divide(Y2, inverse(double_divide(Y1, double_divide(inverse(X0), X1))))) -> Y2 % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)), double_divide(Y1, double_divide(X0, X1))) -> identity % 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)), double_divide(Y2, inverse(double_divide(Y1, double_divide(X0, X1))))) -> Y2 % 210.40/210.24 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) -> B % 210.40/210.24 double_divide(double_divide(identity, X0), X0) -> identity % 210.40/210.24 double_divide(double_divide(identity, Y0), double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(Y0, Y2))) -> Y1 % 210.40/210.24 double_divide(double_divide(identity, Y0), double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(Y0))) -> Y1 % 210.40/210.24 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, inverse(Y1)))) -> Y1 % 210.40/210.24 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(Y0))) -> identity % 210.40/210.24 double_divide(double_divide(identity, Y0), inverse(double_divide(double_divide(Y1, inverse(Y0)), inverse(identity)))) -> Y1 % 210.40/210.24 double_divide(double_divide(identity, Y1), inverse(identity)) -> Y1 % 210.40/210.24 double_divide(double_divide(identity, double_divide(identity, X0)), double_divide(identity, X0)) -> identity % 210.40/210.24 double_divide(double_divide(identity, inverse(X0)), double_divide(identity, X0)) -> identity % 210.40/210.24 double_divide(double_divide(identity, inverse(inverse(X0))), X0) -> identity % 210.40/210.24 double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(X1, X0)) -> identity % 210.40/210.24 double_divide(double_divide(inverse(X0), inverse(X2)), X1) -> double_divide(X2, inverse(double_divide(X0, X1))) % 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X0)), double_divide(Y1, inverse(double_divide(X0, X1)))) -> Y1 % 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X0)), inverse(double_divide(double_divide(X0, X1), Y1))) -> inverse(Y1) % 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X0)), inverse(double_divide(double_divide(X0, X1), inverse(Y1)))) -> Y1 % 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X2)), double_divide(X0, X1)) -> double_divide(X2, inverse(X0)) % 210.40/210.24 double_divide(double_divide(inverse(Y0), X0), double_divide(Y2, Y0)) -> double_divide(inverse(X0), inverse(Y2)) % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, X0)), double_divide(Y2, inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y0)))) -> Y2 % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, X0)), double_divide(double_divide(inverse(X0), inverse(X1)), Y0)) -> identity % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, inverse(X0))), double_divide(Y2, inverse(double_divide(double_divide(X0, inverse(X1)), Y0)))) -> Y2 % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, inverse(X0))), double_divide(double_divide(X0, inverse(X1)), Y0)) -> identity % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), X0)), double_divide(Y2, inverse(double_divide(double_divide(inverse(X0), X1), Y0)))) -> Y2 % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), X0)), double_divide(double_divide(inverse(X0), X1), Y0)) -> identity % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0))), double_divide(Y2, inverse(double_divide(double_divide(X0, X1), Y0)))) -> Y2 % 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0))), double_divide(double_divide(X0, X1), Y0)) -> identity % 210.40/210.24 double_divide(double_divide(inverse(double_divide(X0, X1)), inverse(X1)), X0) -> identity % 210.40/210.24 double_divide(double_divide(inverse(double_divide(X0, inverse(X1))), X1), X0) -> identity % 210.40/210.24 double_divide(identity, X0) -> inverse(X0) % 210.40/210.24 double_divide(identity, double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(inverse(identity), Y2))) -> Y1 % 210.40/210.24 double_divide(identity, double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(inverse(identity)))) -> Y1 % 210.40/210.24 double_divide(identity, double_divide(identity, X0)) -> X0 % 210.40/210.24 double_divide(identity, double_divide(identity, X0)) -> double_divide(identity, inverse(X0)) % 210.40/210.24 double_divide(identity, double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0 % 210.40/210.24 double_divide(identity, double_divide(identity, double_divide(inverse(identity), inverse(Y1)))) -> Y1 % 210.40/210.24 double_divide(identity, double_divide(identity, inverse(Y0))) -> inverse(Y0) % 210.40/210.24 double_divide(identity, inverse(X0)) -> inverse(inverse(X0)) % 210.40/210.24 double_divide(identity, inverse(double_divide(double_divide(Y1, inverse(inverse(identity))), inverse(identity)))) -> Y1 % 210.40/210.24 double_divide(identity, inverse(inverse(Y0))) -> double_divide(identity, Y0) % 210.40/210.24 double_divide(inverse(X0), X0) -> identity % 210.40/210.24 double_divide(inverse(X0), inverse(double_divide(inverse(X1), double_divide(Y1, inverse(double_divide(inverse(X0), inverse(X1))))))) -> Y1 % 210.40/210.24 double_divide(inverse(Y0), double_divide(X1, double_divide(Y0, Y1))) -> inverse(double_divide(X1, inverse(Y1))) % 210.40/210.24 double_divide(inverse(Y0), double_divide(X1, double_divide(Y0, inverse(double_divide(inverse(Y2), X1))))) -> Y2 % 210.40/210.24 double_divide(inverse(Y0), double_divide(Y1, inverse(Y0))) -> Y1 % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(X0, inverse(Y2)), double_divide(Y0, inverse(X0)))) -> Y2 % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(Y1, X0), double_divide(Y0, inverse(Y1)))) -> inverse(X0) % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(inverse(Y1), X0), double_divide(Y0, Y1))) -> inverse(X0) % 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(Y0, Y2))) -> Y1 % 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(X0), inverse(Y0))) -> inverse(X0) % 210.40/210.24 double_divide(inverse(Y0), inverse(double_divide(X0, double_divide(Y2, double_divide(inverse(X0), Y0))))) -> Y2 % 210.40/210.24 double_divide(inverse(Y0), inverse(double_divide(Y0, X0))) -> inverse(X0) % 210.40/210.24 double_divide(inverse(Y0), inverse(double_divide(Y0, inverse(Y1)))) -> Y1 % 210.40/210.24 double_divide(inverse(Y0), inverse(double_divide(inverse(X1), double_divide(Y2, double_divide(X1, Y0))))) -> Y2 % 210.40/210.24 double_divide(inverse(Y0), inverse(double_divide(inverse(double_divide(Y0, X1)), double_divide(Y2, X1)))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(X0, X1)), double_divide(Y1, double_divide(inverse(X1), inverse(X0)))) -> Y1 % 210.40/210.24 double_divide(inverse(double_divide(X0, X1)), inverse(X1)) -> inverse(X0) % 210.40/210.24 double_divide(inverse(double_divide(X0, X1)), inverse(double_divide(inverse(double_divide(inverse(X1), inverse(X0))), inverse(Y1)))) -> Y1 % 210.40/210.24 double_divide(inverse(double_divide(X0, inverse(X1))), X1) -> inverse(X0) % 210.40/210.24 double_divide(inverse(double_divide(X1, Y1)), inverse(double_divide(inverse(Y1), double_divide(Y2, X1)))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(X2, inverse(double_divide(X1, X0)))), inverse(double_divide(inverse(X0), inverse(X1)))) -> inverse(X2) % 210.40/210.24 double_divide(inverse(double_divide(X2, inverse(double_divide(inverse(X1), inverse(X0))))), inverse(double_divide(X0, X1))) -> inverse(X2) % 210.40/210.24 double_divide(inverse(double_divide(Y0, Y1)), double_divide(double_divide(inverse(Y0), X0), Y1)) -> inverse(X0) % 210.40/210.24 double_divide(inverse(double_divide(Y0, Y1)), inverse(double_divide(inverse(Y1), inverse(Y0)))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(Y0, Y1)), inverse(double_divide(inverse(double_divide(inverse(Y1), inverse(Y0))), X0))) -> inverse(X0) % 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(X0, X1))), double_divide(Y2, double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y0)))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(X0, X1))), inverse(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y0)))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(X0, inverse(X1)))), double_divide(Y2, double_divide(double_divide(X1, inverse(X0)), inverse(Y0)))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(X0, inverse(X1)))), inverse(double_divide(double_divide(X1, inverse(X0)), inverse(Y0)))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(inverse(X0), X1))), double_divide(Y2, double_divide(double_divide(inverse(X1), X0), inverse(Y0)))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(inverse(X0), X1))), inverse(double_divide(double_divide(inverse(X1), X0), inverse(Y0)))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(inverse(X0), inverse(X1)))), double_divide(Y2, double_divide(double_divide(X1, X0), inverse(Y0)))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(inverse(X0), inverse(X1)))), inverse(double_divide(double_divide(X1, X0), inverse(Y0)))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(Y1, X1)), double_divide(double_divide(inverse(Y1), inverse(Y2)), X1)) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(double_divide(X0, X1), Y1)), double_divide(Y2, double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0))))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(double_divide(X0, X1), Y1)), inverse(double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0))))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(double_divide(X0, inverse(X1)), Y1)), double_divide(Y2, double_divide(inverse(Y1), double_divide(X1, inverse(X0))))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(double_divide(X0, inverse(X1)), Y1)), inverse(double_divide(inverse(Y1), double_divide(X1, inverse(X0))))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(double_divide(X1, X0), inverse(Y1))), double_divide(Y2, double_divide(Y1, double_divide(inverse(X0), inverse(X1))))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(double_divide(X1, X0), inverse(Y1))), inverse(double_divide(Y1, double_divide(inverse(X0), inverse(X1))))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(double_divide(X1, inverse(X0)), inverse(Y1))), double_divide(Y2, double_divide(Y1, double_divide(X0, inverse(X1))))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(double_divide(X1, inverse(X0)), inverse(Y1))), inverse(double_divide(Y1, double_divide(X0, inverse(X1))))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X0), X1), Y1)), double_divide(Y2, double_divide(inverse(Y1), double_divide(inverse(X1), X0)))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X0), X1), Y1)), inverse(double_divide(inverse(Y1), double_divide(inverse(X1), X0)))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y1)), double_divide(Y2, double_divide(inverse(Y1), double_divide(X1, X0)))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y1)), inverse(double_divide(inverse(Y1), double_divide(X1, X0)))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X1), X0), inverse(Y1))), double_divide(Y2, double_divide(Y1, double_divide(inverse(X0), X1)))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X1), X0), inverse(Y1))), inverse(double_divide(Y1, double_divide(inverse(X0), X1)))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1))), double_divide(Y2, double_divide(Y1, double_divide(X0, X1)))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1))), inverse(double_divide(Y1, double_divide(X0, X1)))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(inverse(X0), Y1)), double_divide(double_divide(X0, inverse(Y2)), Y1)) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(inverse(X0), inverse(X1))), double_divide(Y1, double_divide(X1, X0))) -> Y1 % 210.40/210.24 double_divide(inverse(double_divide(inverse(X0), inverse(X1))), inverse(double_divide(inverse(double_divide(X1, X0)), inverse(Y1)))) -> Y1 % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), Y1)), double_divide(double_divide(Y0, X0), Y1)) -> inverse(X0) % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(X1, X0))), double_divide(Y2, double_divide(double_divide(inverse(X0), inverse(X1)), Y0))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(X1, X0))), inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y0))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(X1, inverse(X0)))), double_divide(Y2, double_divide(double_divide(X0, inverse(X1)), Y0))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(X1, inverse(X0)))), inverse(double_divide(double_divide(X0, inverse(X1)), Y0))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(inverse(X1), X0))), double_divide(Y2, double_divide(double_divide(inverse(X0), X1), Y0))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(inverse(X1), X0))), inverse(double_divide(double_divide(inverse(X0), X1), Y0))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0)))), double_divide(Y2, double_divide(double_divide(X0, X1), Y0))) -> Y2 % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0)))), inverse(double_divide(double_divide(X0, X1), Y0))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), inverse(Y1))), inverse(double_divide(Y1, Y0))) -> identity % 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), inverse(Y1))), inverse(double_divide(inverse(double_divide(Y1, Y0)), X0))) -> inverse(X0) % 210.40/210.24 double_divide(inverse(identity), double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(identity, Y2))) -> Y1 % 210.40/210.24 double_divide(inverse(identity), double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(identity))) -> Y1 % 210.40/210.24 double_divide(inverse(identity), double_divide(identity, double_divide(identity, inverse(Y1)))) -> Y1 % 210.40/210.24 double_divide(inverse(identity), inverse(double_divide(X0, inverse(identity)))) -> double_divide(identity, X0) % 210.40/210.24 double_divide(inverse(identity), inverse(double_divide(double_divide(Y1, inverse(identity)), inverse(identity)))) -> Y1 % 210.40/210.24 double_divide(inverse(identity), inverse(identity)) -> identity % 210.40/210.24 f1(double_divide(inverse(a3), inverse(double_divide(inverse(b3), inverse(c3))))) -> false__ % 210.40/210.24 f1(double_divide(inverse(double_divide(inverse(a3), inverse(b3))), inverse(c3))) -> true__ % 210.40/210.24 f1(inverse(double_divide(c3, inverse(double_divide(b3, a3))))) -> true__ % 210.40/210.24 f1(inverse(double_divide(inverse(double_divide(c3, b3)), a3))) -> false__ % 210.40/210.24 f1(multiply(a3, multiply(b3, c3))) -> false__ % 210.40/210.24 f1(multiply(multiply(a3, b3), c3)) -> true__ % 210.40/210.24 inverse(double_divide(X2, double_divide(inverse(double_divide(X0, X1)), double_divide(inverse(X2), X1)))) -> inverse(X0) % 210.40/210.24 inverse(double_divide(identity, Y0)) -> Y0 % 210.40/210.24 inverse(double_divide(identity, double_divide(inverse(Y1), inverse(identity)))) -> Y1 % 210.40/210.24 inverse(double_divide(identity, inverse(inverse(Y0)))) -> Y0 % 210.40/210.24 inverse(double_divide(inverse(X2), double_divide(inverse(double_divide(X0, X1)), double_divide(X2, X1)))) -> inverse(X0) % 210.40/210.24 inverse(double_divide(inverse(double_divide(Y0, Y1)), inverse(Y1))) -> Y0 % 210.40/210.24 inverse(double_divide(inverse(double_divide(Y0, inverse(X0))), X0)) -> Y0 % 210.40/210.24 inverse(identity) -> identity % 210.40/210.24 inverse(inverse(Y0)) -> Y0 % 210.40/210.24 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 210.40/210.24 true__ -> false__ % 210.40/210.24 with the LPO induced by % 210.40/210.24 c3 > b3 > a3 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 210.40/210.24 % 210.40/210.24 % SZS output end Proof % 210.40/210.24 %------------------------------------------------------------------------------