%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP580-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n016.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 10:56:25 EDT 2022 % Result : Unsatisfiable 19.41s 19.39s % Output : Proof 19.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : GRP580-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.35 % Computer : n016.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Mon Jun 13 20:33:30 EDT 2022 % 0.13/0.35 % CPUTime : % 19.41/19.39 % SZS status Unsatisfiable % 19.41/19.39 % SZS output start Proof % 19.41/19.39 The input problem is unsatisfiable because % 19.41/19.39 % 19.41/19.39 [1] the following set of Horn clauses is unsatisfiable: % 19.41/19.39 % 19.41/19.39 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) = C % 19.41/19.39 multiply(A, B) = double_divide(double_divide(B, A), identity) % 19.41/19.39 inverse(A) = double_divide(A, identity) % 19.41/19.39 identity = double_divide(A, inverse(A)) % 19.41/19.39 multiply(a, b) = multiply(b, a) ==> \bottom % 19.41/19.39 % 19.41/19.39 This holds because % 19.41/19.39 % 19.41/19.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 19.41/19.39 % 19.41/19.39 E: % 19.41/19.39 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) = C % 19.41/19.39 f1(multiply(a, b)) = true__ % 19.41/19.39 f1(multiply(b, a)) = false__ % 19.41/19.39 identity = double_divide(A, inverse(A)) % 19.41/19.39 inverse(A) = double_divide(A, identity) % 19.41/19.39 multiply(A, B) = double_divide(double_divide(B, A), identity) % 19.41/19.39 G: % 19.41/19.39 true__ = false__ % 19.41/19.39 % 19.41/19.39 This holds because % 19.41/19.39 % 19.41/19.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 19.41/19.39 % 19.41/19.39 double_divide(X0, inverse(identity)) = inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0))))) % 19.41/19.39 double_divide(X1, X0) = double_divide(X0, X1) % 19.41/19.39 inverse(double_divide(Y0, inverse(X0))) = inverse(double_divide(inverse(X0), Y0)) % 19.41/19.39 inverse(double_divide(Y0, inverse(inverse(Y1)))) = inverse(double_divide(Y1, Y0)) % 19.41/19.39 double_divide(A, identity) -> inverse(A) % 19.41/19.39 double_divide(A, inverse(A)) -> identity % 19.41/19.39 double_divide(X0, double_divide(identity, X0)) -> identity % 19.41/19.39 double_divide(X0, double_divide(identity, inverse(inverse(X0)))) -> identity % 19.41/19.39 double_divide(X0, inverse(double_divide(inverse(X0), X1))) -> inverse(X1) % 19.41/19.39 double_divide(X0, inverse(inverse(inverse(X0)))) -> identity % 19.41/19.39 double_divide(X1, double_divide(X0, inverse(double_divide(inverse(X0), X1)))) -> identity % 19.41/19.39 double_divide(X1, double_divide(inverse(X0), inverse(double_divide(X0, X1)))) -> identity % 19.41/19.39 double_divide(Y0, inverse(double_divide(Y1, inverse(Y0)))) -> inverse(Y1) % 19.41/19.39 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) -> C % 19.41/19.39 double_divide(double_divide(X0, X1), inverse(double_divide(X1, X0))) -> identity % 19.41/19.39 double_divide(double_divide(X0, inverse(double_divide(inverse(X0), X1))), X1) -> identity % 19.41/19.39 double_divide(double_divide(Y0, double_divide(double_divide(double_divide(Y1, Y0), Y2), inverse(Y1))), inverse(identity)) -> Y2 % 19.41/19.39 double_divide(double_divide(Y0, double_divide(identity, inverse(Y1))), inverse(identity)) -> inverse(double_divide(Y1, Y0)) % 19.41/19.39 double_divide(double_divide(Y0, double_divide(inverse(double_divide(Y1, Y0)), inverse(Y1))), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(Y0, inverse(double_divide(identity, double_divide(identity, Y0)))), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(Y0, inverse(inverse(double_divide(double_divide(identity, inverse(inverse(identity))), Y0)))), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(identity, X0), inverse(inverse(X0))) -> identity % 19.41/19.39 double_divide(double_divide(identity, double_divide(double_divide(inverse(Y1), Y2), inverse(Y1))), inverse(identity)) -> Y2 % 19.41/19.39 double_divide(double_divide(identity, double_divide(inverse(X0), X0)), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(identity, double_divide(inverse(double_divide(identity, Y0)), inverse(Y0))), inverse(identity)) -> inverse(identity) % 19.41/19.39 double_divide(double_divide(identity, double_divide(inverse(inverse(Y1)), inverse(Y1))), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(identity, inverse(double_divide(identity, X0))), X0) -> identity % 19.41/19.39 double_divide(double_divide(identity, inverse(inverse(X0))), X0) -> identity % 19.41/19.39 double_divide(double_divide(identity, inverse(inverse(identity))), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(inverse(Y1), double_divide(double_divide(identity, Y2), inverse(Y1))), inverse(identity)) -> Y2 % 19.41/19.39 double_divide(double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1))), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(inverse(identity), double_divide(inverse(X1), inverse(double_divide(identity, double_divide(double_divide(inverse(X0), X1), inverse(X0)))))), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(X0, double_divide(inverse(double_divide(X1, X0)), inverse(X1)))))), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(identity, double_divide(inverse(inverse(Y1)), inverse(Y1)))))), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1)))))), inverse(identity)) -> identity % 19.41/19.39 double_divide(double_divide(inverse(identity), double_divide(inverse(inverse(double_divide(identity, X0))), inverse(inverse(X0)))), inverse(identity)) -> identity % 19.41/19.39 double_divide(identity, X0) -> inverse(X0) % 19.41/19.39 double_divide(identity, inverse(inverse(X0))) -> inverse(inverse(inverse(X0))) % 19.41/19.39 double_divide(inverse(X0), X0) -> identity % 19.41/19.39 double_divide(inverse(X0), inverse(double_divide(X0, X1))) -> inverse(X1) % 19.41/19.39 double_divide(inverse(Y0), inverse(identity)) -> inverse(double_divide(identity, Y0)) % 19.41/19.39 double_divide(inverse(double_divide(X1, inverse(identity))), inverse(X1)) -> double_divide(inverse(identity), inverse(identity)) % 19.41/19.39 double_divide(inverse(double_divide(inverse(X1), X0)), double_divide(X0, inverse(X1))) -> identity % 19.41/19.39 double_divide(inverse(inverse(X0)), double_divide(identity, X0)) -> identity % 19.41/19.39 double_divide(inverse(inverse(double_divide(identity, Y1))), inverse(identity)) -> Y1 % 19.41/19.39 double_divide(inverse(inverse(inverse(X0))), X0) -> identity % 19.41/19.39 f1(inverse(double_divide(a, b))) -> false__ % 19.41/19.39 f1(inverse(double_divide(b, a))) -> true__ % 19.41/19.39 f1(multiply(a, b)) -> true__ % 19.41/19.39 f1(multiply(b, a)) -> false__ % 19.41/19.39 inverse(double_divide(Y0, double_divide(double_divide(double_divide(Y1, Y0), Y2), inverse(Y1)))) -> Y2 % 19.41/19.39 inverse(double_divide(Y0, double_divide(inverse(double_divide(Y1, Y0)), inverse(Y1)))) -> identity % 19.41/19.39 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(Y0))))) -> Y1 % 19.41/19.39 inverse(double_divide(Y0, inverse(double_divide(identity, double_divide(identity, Y0))))) -> identity % 19.41/19.39 inverse(double_divide(Y0, inverse(double_divide(inverse(Y0), Y2)))) -> Y2 % 19.41/19.39 inverse(double_divide(identity, Y0)) -> inverse(inverse(Y0)) % 19.41/19.39 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, Y0))))) -> inverse(Y0) % 19.41/19.39 inverse(double_divide(identity, double_divide(identity, inverse(inverse(identity))))) -> identity % 19.41/19.39 inverse(double_divide(identity, double_divide(inverse(Y0), Y0))) -> identity % 19.41/19.39 inverse(double_divide(identity, double_divide(inverse(inverse(Y0)), inverse(Y0)))) -> identity % 19.41/19.39 inverse(double_divide(identity, inverse(double_divide(identity, Y0)))) -> Y0 % 19.41/19.39 inverse(double_divide(identity, inverse(inverse(identity)))) -> identity % 19.41/19.39 inverse(double_divide(inverse(X0), inverse(double_divide(X0, Y1)))) -> Y1 % 19.41/19.39 inverse(double_divide(inverse(Y0), double_divide(identity, inverse(Y0)))) -> identity % 19.41/19.39 inverse(double_divide(inverse(Y0), double_divide(inverse(Y1), inverse(Y0)))) -> Y1 % 19.41/19.39 inverse(double_divide(inverse(Y0), inverse(double_divide(Y1, Y0)))) -> Y1 % 19.41/19.39 inverse(identity) -> identity % 19.41/19.39 inverse(inverse(Y1)) -> Y1 % 19.41/19.39 inverse(inverse(double_divide(X0, inverse(inverse(inverse(X0)))))) -> identity % 19.41/19.39 inverse(inverse(double_divide(double_divide(inverse(Y0), Y1), inverse(Y0)))) -> Y1 % 19.41/19.39 inverse(inverse(double_divide(inverse(Y0), Y0))) -> identity % 19.41/19.39 inverse(inverse(double_divide(inverse(inverse(X0)), double_divide(identity, X0)))) -> identity % 19.41/19.39 inverse(inverse(inverse(double_divide(identity, Y0)))) -> Y0 % 19.41/19.39 inverse(inverse(inverse(inverse(Y0)))) -> Y0 % 19.41/19.39 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 19.41/19.39 true__ -> false__ % 19.41/19.39 with the LPO induced by % 19.41/19.39 a > b > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 19.41/19.39 % 19.41/19.39 % SZS output end Proof % 19.41/19.39 %------------------------------------------------------------------------------