%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 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 10:56:20 EDT 2022 % Result : Unsatisfiable 8.11s 8.10s % Output : Proof 8.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.08/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n025.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 : Mon Jun 13 21:18:39 EDT 2022 % 0.14/0.35 % CPUTime : % 8.11/8.10 % SZS status Unsatisfiable % 8.11/8.10 % SZS output start Proof % 8.11/8.10 The input problem is unsatisfiable because % 8.11/8.10 % 8.11/8.10 [1] the following set of Horn clauses is unsatisfiable: % 8.11/8.10 % 8.11/8.10 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity, C))), double_divide(identity, identity)) = B % 8.11/8.10 multiply(A, B) = double_divide(double_divide(B, A), identity) % 8.11/8.10 inverse(A) = double_divide(A, identity) % 8.11/8.10 identity = double_divide(A, inverse(A)) % 8.11/8.10 multiply(a, b) = multiply(b, a) ==> \bottom % 8.11/8.10 % 8.11/8.10 This holds because % 8.11/8.10 % 8.11/8.10 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 8.11/8.10 % 8.11/8.10 E: % 8.11/8.10 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity, C))), double_divide(identity, identity)) = B % 8.11/8.10 f1(multiply(a, b)) = true__ % 8.11/8.10 f1(multiply(b, a)) = false__ % 8.11/8.10 identity = double_divide(A, inverse(A)) % 8.11/8.10 inverse(A) = double_divide(A, identity) % 8.11/8.10 multiply(A, B) = double_divide(double_divide(B, A), identity) % 8.11/8.10 G: % 8.11/8.10 true__ = false__ % 8.11/8.10 % 8.11/8.10 This holds because % 8.11/8.10 % 8.11/8.10 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 8.11/8.10 % 8.11/8.10 double_divide(Y0, X0) = double_divide(X0, Y0) % 8.11/8.10 double_divide(Y0, double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), inverse(Y0))) % 8.11/8.10 double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 8.11/8.10 double_divide(Y0, double_divide(inverse(Y1), double_divide(identity, inverse(Y0)))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 8.11/8.10 double_divide(Y0, inverse(double_divide(X1, X0))) = inverse(double_divide(double_divide(X0, X1), inverse(Y0))) % 8.11/8.10 double_divide(Y0, inverse(double_divide(Y1, double_divide(Y0, inverse(identity))))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 8.11/8.10 double_divide(double_divide(identity, double_divide(X1, inverse(identity))), inverse(identity)) = double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), double_divide(identity, X2))) % 8.11/8.10 double_divide(false__, inverse(double_divide(X0, double_divide(false__, inverse(identity))))) = double_divide(identity, inverse(inverse(X0))) % 8.11/8.10 inverse(double_divide(X1, inverse(Y1))) = double_divide(Y1, inverse(X1)) % 8.11/8.10 inverse(double_divide(Y0, X0)) = inverse(double_divide(X0, Y0)) % 8.11/8.10 inverse(double_divide(Y0, double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), inverse(Y0)) % 8.11/8.10 inverse(double_divide(Y0, inverse(double_divide(X1, X0)))) = double_divide(double_divide(X0, X1), inverse(Y0)) % 8.11/8.10 double_divide(A, identity) -> inverse(A) % 8.11/8.10 double_divide(A, inverse(A)) -> identity % 8.11/8.10 double_divide(X0, double_divide(X0, inverse(Y1))) -> inverse(Y1) % 8.11/8.10 double_divide(X0, double_divide(X1, X0)) -> X1 % 8.11/8.10 double_divide(X0, double_divide(X2, double_divide(X1, double_divide(X0, inverse(X2))))) -> inverse(X1) % 8.11/8.10 double_divide(X0, double_divide(identity, X0)) -> identity % 8.11/8.10 double_divide(X0, double_divide(inverse(X1), X0)) -> inverse(X1) % 8.11/8.10 double_divide(X0, inverse(double_divide(X1, inverse(X0)))) -> inverse(X1) % 8.11/8.10 double_divide(X1, double_divide(X0, double_divide(inverse(X1), X0))) -> identity % 8.11/8.10 double_divide(X1, double_divide(X1, Y0)) -> Y0 % 8.11/8.10 double_divide(X1, double_divide(inverse(X0), inverse(double_divide(X1, X0)))) -> identity % 8.11/8.10 double_divide(X1, double_divide(inverse(double_divide(X0, X1)), inverse(X0))) -> identity % 8.11/8.10 double_divide(X1, double_divide(inverse(double_divide(inverse(X0), X1)), X0)) -> identity % 8.11/8.10 double_divide(Y0, double_divide(double_divide(identity, inverse(Y0)), inverse(identity))) -> identity % 8.11/8.10 double_divide(Y0, double_divide(identity, double_divide(identity, inverse(Y0)))) -> identity % 8.11/8.10 double_divide(Y0, double_divide(inverse(identity), double_divide(identity, inverse(Y0)))) -> identity % 8.11/8.10 double_divide(Y0, inverse(double_divide(double_divide(Y0, Y1), Y1))) -> identity % 8.11/8.10 double_divide(Y0, inverse(double_divide(identity, double_divide(Y0, inverse(identity))))) -> identity % 8.11/8.10 double_divide(Y0, inverse(double_divide(identity, inverse(Y0)))) -> identity % 8.11/8.10 double_divide(Y1, double_divide(double_divide(Y0, double_divide(Y1, Y2)), inverse(Y2))) -> inverse(Y0) % 8.11/8.10 double_divide(Y1, double_divide(double_divide(identity, double_divide(Y1, Y2)), double_divide(identity, Y2))) -> double_divide(inverse(identity), inverse(identity)) % 8.11/8.10 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity, C))), double_divide(identity, identity)) -> B % 8.11/8.10 double_divide(double_divide(X0, double_divide(X1, X0)), inverse(X1)) -> identity % 8.11/8.10 double_divide(double_divide(X0, double_divide(inverse(X1), X0)), X1) -> identity % 8.11/8.10 double_divide(double_divide(X0, false__), double_divide(inverse(X0), inverse(false__))) -> identity % 8.11/8.10 double_divide(double_divide(X0, inverse(false__)), double_divide(false__, inverse(X0))) -> identity % 8.11/8.10 double_divide(double_divide(X1, Y1), X1) -> Y1 % 8.11/8.10 double_divide(double_divide(X1, inverse(Y1)), X1) -> inverse(Y1) % 8.11/8.10 double_divide(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, Y2)), double_divide(identity, Y2))), inverse(identity)) -> Y1 % 8.11/8.10 double_divide(double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))), inverse(identity)) -> Y1 % 8.11/8.10 double_divide(double_divide(Y0, double_divide(inverse(Y1), double_divide(identity, inverse(Y0)))), inverse(identity)) -> Y1 % 8.11/8.10 double_divide(double_divide(Y0, inverse(double_divide(Y1, double_divide(Y0, inverse(identity))))), inverse(identity)) -> Y1 % 8.11/8.10 double_divide(double_divide(Y1, X0), X0) -> Y1 % 8.11/8.10 double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2)) -> Y1 % 8.11/8.10 double_divide(double_divide(double_divide(X0, double_divide(double_divide(X1, inverse(X0)), inverse(identity))), inverse(double_divide(Y1, X1))), inverse(identity)) -> Y1 % 8.11/8.10 double_divide(double_divide(identity, X0), X0) -> identity % 8.11/8.10 double_divide(double_divide(identity, inverse(X0)), inverse(X0)) -> identity % 8.11/8.10 double_divide(double_divide(identity, inverse(inverse(Y1))), inverse(identity)) -> Y1 % 8.11/8.10 double_divide(double_divide(inverse(X0), X0), inverse(identity)) -> identity % 8.11/8.10 double_divide(double_divide(inverse(X0), X0), inverse(inverse(identity))) -> identity % 8.11/8.10 double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(X0, X1)) -> identity % 8.11/8.10 double_divide(double_divide(inverse(X0), inverse(double_divide(X1, X0))), X1) -> identity % 8.11/8.10 double_divide(double_divide(inverse(X0), inverse(double_divide(Y1, X0))), inverse(identity)) -> Y1 % 8.11/8.10 double_divide(double_divide(inverse(X0), inverse(false__)), double_divide(X0, false__)) -> identity % 8.11/8.10 double_divide(double_divide(inverse(X1), Y1), inverse(X1)) -> Y1 % 8.11/8.10 double_divide(double_divide(inverse(double_divide(X0, X1)), inverse(X0)), X1) -> identity % 8.11/8.10 double_divide(double_divide(inverse(double_divide(inverse(X0), X1)), X0), X1) -> identity % 8.11/8.10 double_divide(double_divide(inverse(false__), X0), double_divide(false__, inverse(X0))) -> identity % 8.11/8.10 double_divide(double_divide(inverse(identity), inverse(inverse(Y1))), inverse(identity)) -> Y1 % 8.11/8.10 double_divide(double_divide(inverse(inverse(identity)), inverse(X0)), inverse(identity)) -> inverse(X0) % 8.11/8.10 double_divide(false__, inverse(double_divide(X0, double_divide(false__, inverse(identity))))) -> inverse(X0) % 8.11/8.10 double_divide(false__, inverse(double_divide(Y0, inverse(false__)))) -> inverse(Y0) % 8.11/8.10 double_divide(identity, X0) -> inverse(X0) % 8.11/8.10 double_divide(identity, inverse(X0)) -> X0 % 8.11/8.10 double_divide(identity, inverse(inverse(identity))) -> identity % 8.11/8.10 double_divide(inverse(X0), X0) -> identity % 8.11/8.10 double_divide(inverse(X0), double_divide(identity, inverse(X0))) -> identity % 8.11/8.10 double_divide(inverse(X0), false__) -> inverse(double_divide(X0, inverse(false__))) % 8.11/8.10 double_divide(inverse(X0), inverse(double_divide(X1, X0))) -> inverse(X1) % 8.11/8.10 double_divide(inverse(X0), inverse(double_divide(identity, X0))) -> identity % 8.11/8.10 double_divide(inverse(X0), inverse(false__)) -> inverse(double_divide(X0, false__)) % 8.11/8.10 double_divide(inverse(X1), double_divide(X0, double_divide(X1, X0))) -> identity % 8.11/8.10 double_divide(inverse(Y0), X1) -> inverse(double_divide(Y0, inverse(X1))) % 8.11/8.10 double_divide(inverse(Y0), inverse(X1)) -> inverse(double_divide(Y0, X1)) % 8.11/8.10 double_divide(inverse(Y0), inverse(identity)) -> Y0 % 8.11/8.10 double_divide(inverse(double_divide(X0, X1)), inverse(X0)) -> inverse(X1) % 8.11/8.10 double_divide(inverse(double_divide(X0, inverse(false__))), inverse(X0)) -> false__ % 8.11/8.10 double_divide(inverse(double_divide(inverse(X0), X1)), X0) -> inverse(X1) % 8.11/8.10 double_divide(inverse(double_divide(inverse(X0), inverse(false__))), X0) -> false__ % 8.11/8.10 double_divide(inverse(false__), X0) -> inverse(double_divide(false__, inverse(X0))) % 8.11/8.10 f1(inverse(double_divide(a, b))) -> false__ % 8.11/8.10 f1(inverse(double_divide(b, a))) -> true__ % 8.11/8.10 f1(multiply(a, b)) -> true__ % 8.11/8.10 f1(multiply(b, a)) -> false__ % 8.11/8.10 inverse(double_divide(X0, double_divide(X0, Y1))) -> inverse(Y1) % 8.11/8.10 inverse(double_divide(X0, inverse(double_divide(Y1, inverse(X0))))) -> Y1 % 8.11/8.10 inverse(double_divide(X1, double_divide(X1, inverse(Y0)))) -> Y0 % 8.11/8.10 inverse(double_divide(Y0, double_divide(X0, Y0))) -> inverse(X0) % 8.11/8.10 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, Y2)), inverse(Y2)))) -> Y1 % 8.11/8.10 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, inverse(X0))), X0))) -> Y1 % 8.11/8.10 inverse(double_divide(Y0, double_divide(inverse(Y1), Y0))) -> Y1 % 8.11/8.10 inverse(double_divide(Y0, inverse(double_divide(double_divide(Y0, Y2), Y2)))) -> identity % 8.11/8.10 inverse(double_divide(double_divide(X1, Y1), X1)) -> inverse(Y1) % 8.11/8.10 inverse(double_divide(double_divide(X1, inverse(Y1)), X1)) -> Y1 % 8.11/8.10 inverse(double_divide(identity, Y0)) -> Y0 % 8.11/8.10 inverse(double_divide(identity, inverse(Y0))) -> inverse(Y0) % 8.11/8.10 inverse(double_divide(identity, inverse(inverse(Y0)))) -> Y0 % 8.11/8.10 inverse(double_divide(inverse(X0), double_divide(inverse(Y1), inverse(X0)))) -> Y1 % 8.11/8.10 inverse(double_divide(inverse(X0), inverse(false__))) -> double_divide(X0, false__) % 8.11/8.10 inverse(double_divide(inverse(Y0), X0)) -> double_divide(Y0, inverse(X0)) % 8.11/8.10 inverse(double_divide(inverse(Y0), inverse(X1))) -> double_divide(Y0, X1) % 8.11/8.10 inverse(double_divide(inverse(Y0), inverse(double_divide(Y1, Y0)))) -> Y1 % 8.11/8.10 inverse(double_divide(inverse(double_divide(X1, Y1)), inverse(X1))) -> Y1 % 8.11/8.10 inverse(double_divide(inverse(double_divide(inverse(X0), Y1)), X0)) -> Y1 % 8.11/8.10 inverse(double_divide(inverse(false__), X1)) -> double_divide(false__, inverse(X1)) % 8.11/8.10 inverse(identity) -> identity % 8.11/8.10 inverse(inverse(Y0)) -> Y0 % 8.11/8.10 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 8.11/8.10 true__ -> false__ % 8.11/8.10 with the LPO induced by % 8.11/8.10 a > b > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 8.11/8.10 % 8.11/8.10 % SZS output end Proof % 8.11/8.10 %------------------------------------------------------------------------------