%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP576-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n009.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 10:56:23 EDT 2022 % Result : Unsatisfiable 6.23s 6.24s % Output : Proof 6.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP576-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n009.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jun 13 13:23:38 EDT 2022 % 0.12/0.33 % CPUTime : % 6.23/6.24 % SZS status Unsatisfiable % 6.23/6.24 % SZS output start Proof % 6.23/6.24 The input problem is unsatisfiable because % 6.23/6.24 % 6.23/6.24 [1] the following set of Horn clauses is unsatisfiable: % 6.23/6.24 % 6.23/6.24 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) = B % 6.23/6.24 multiply(A, B) = double_divide(double_divide(B, A), identity) % 6.23/6.24 inverse(A) = double_divide(A, identity) % 6.23/6.24 identity = double_divide(A, inverse(A)) % 6.23/6.24 multiply(a, b) = multiply(b, a) ==> \bottom % 6.23/6.24 % 6.23/6.24 This holds because % 6.23/6.24 % 6.23/6.24 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.23/6.24 % 6.23/6.24 E: % 6.23/6.24 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) = B % 6.23/6.24 f1(multiply(a, b)) = true__ % 6.23/6.24 f1(multiply(b, a)) = false__ % 6.23/6.24 identity = double_divide(A, inverse(A)) % 6.23/6.24 inverse(A) = double_divide(A, identity) % 6.23/6.24 multiply(A, B) = double_divide(double_divide(B, A), identity) % 6.23/6.24 G: % 6.23/6.24 true__ = false__ % 6.23/6.24 % 6.23/6.24 This holds because % 6.23/6.24 % 6.23/6.24 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.23/6.24 % 6.23/6.24 double_divide(Y0, X0) = double_divide(X0, Y0) % 6.23/6.24 double_divide(double_divide(identity, double_divide(X1, inverse(identity))), inverse(identity)) = double_divide(X0, double_divide(double_divide(X1, double_divide(X2, X0)), inverse(X2))) % 6.23/6.24 double_divide(identity, double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 6.23/6.24 double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1))) = double_divide(inverse(identity), inverse(identity)) % 6.23/6.24 double_divide(inverse(Y2), double_divide(inverse(Y1), inverse(Y2))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 6.23/6.24 inverse(double_divide(Y0, inverse(X0))) = double_divide(X0, inverse(Y0)) % 6.23/6.24 double_divide(A, identity) -> inverse(A) % 6.23/6.24 double_divide(A, inverse(A)) -> identity % 6.23/6.24 double_divide(X0, double_divide(identity, X0)) -> identity % 6.23/6.24 double_divide(X0, double_divide(inverse(X1), X0)) -> inverse(X1) % 6.23/6.24 double_divide(X0, inverse(double_divide(X1, inverse(X0)))) -> inverse(X1) % 6.23/6.24 double_divide(X1, double_divide(X0, double_divide(inverse(X1), X0))) -> identity % 6.23/6.24 double_divide(X1, double_divide(X0, inverse(double_divide(X1, inverse(X0))))) -> identity % 6.23/6.24 double_divide(X1, double_divide(X1, Y0)) -> Y0 % 6.23/6.24 double_divide(X1, double_divide(inverse(X0), inverse(double_divide(X1, X0)))) -> identity % 6.23/6.24 double_divide(Y0, double_divide(X0, Y0)) -> X0 % 6.23/6.24 double_divide(Y0, inverse(double_divide(inverse(Y0), Y1))) -> inverse(Y1) % 6.23/6.24 double_divide(Y0, inverse(inverse(inverse(Y0)))) -> identity % 6.23/6.24 double_divide(Y1, double_divide(double_divide(identity, double_divide(Y2, Y1)), inverse(Y2))) -> double_divide(inverse(identity), inverse(identity)) % 6.23/6.24 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) -> B % 6.23/6.24 double_divide(double_divide(X0, double_divide(inverse(X1), X0)), X1) -> identity % 6.23/6.24 double_divide(double_divide(X0, inverse(double_divide(X1, inverse(X0)))), X1) -> identity % 6.23/6.24 double_divide(double_divide(X1, Y1), X1) -> Y1 % 6.23/6.24 double_divide(double_divide(X1, inverse(Y1)), X1) -> inverse(Y1) % 6.23/6.24 double_divide(double_divide(Y0, X0), X0) -> Y0 % 6.23/6.24 double_divide(double_divide(Y0, double_divide(X0, Y0)), inverse(X0)) -> identity % 6.23/6.24 double_divide(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y2, Y0)), inverse(Y2))), inverse(identity)) -> Y1 % 6.23/6.24 double_divide(double_divide(Y0, inverse(Y1)), inverse(Y1)) -> Y0 % 6.23/6.24 double_divide(double_divide(identity, X0), inverse(inverse(X0))) -> identity % 6.23/6.24 double_divide(double_divide(identity, double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2))), inverse(identity)) -> Y1 % 6.23/6.24 double_divide(double_divide(identity, double_divide(identity, inverse(X0))), X0) -> identity % 6.23/6.24 double_divide(double_divide(identity, double_divide(identity, inverse(Y1))), inverse(identity)) -> Y1 % 6.23/6.24 double_divide(double_divide(inverse(X0), double_divide(inverse(X1), inverse(X0))), X1) -> identity % 6.23/6.24 double_divide(double_divide(inverse(X0), inverse(double_divide(X1, X0))), X1) -> identity % 6.23/6.24 double_divide(double_divide(inverse(X1), Y1), inverse(X1)) -> Y1 % 6.23/6.24 double_divide(double_divide(inverse(Y2), double_divide(inverse(Y1), inverse(Y2))), inverse(identity)) -> Y1 % 6.23/6.24 double_divide(double_divide(inverse(identity), X0), inverse(identity)) -> inverse(inverse(X0)) % 6.23/6.24 double_divide(double_divide(inverse(identity), double_divide(double_divide(Y0, Y1), inverse(double_divide(identity, double_divide(double_divide(Y1, inverse(Y3)), inverse(Y3)))))), inverse(identity)) -> Y0 % 6.23/6.24 double_divide(double_divide(inverse(identity), double_divide(double_divide(Y1, X0), inverse(inverse(inverse(inverse(X0)))))), inverse(identity)) -> Y1 % 6.23/6.24 double_divide(double_divide(inverse(identity), double_divide(double_divide(Y1, X1), inverse(double_divide(X0, double_divide(double_divide(X1, double_divide(X2, X0)), inverse(X2)))))), inverse(identity)) -> Y1 % 6.23/6.24 double_divide(double_divide(inverse(identity), double_divide(inverse(Y0), inverse(double_divide(Y2, double_divide(double_divide(identity, double_divide(Y3, Y2)), inverse(Y3)))))), inverse(identity)) -> Y0 % 6.23/6.24 double_divide(identity, X0) -> inverse(X0) % 6.23/6.24 double_divide(identity, double_divide(double_divide(X0, inverse(false__)), inverse(false__))) -> inverse(inverse(inverse(X0))) % 6.23/6.24 double_divide(identity, double_divide(double_divide(Y1, inverse(false__)), inverse(false__))) -> double_divide(identity, double_divide(identity, inverse(Y1))) % 6.23/6.24 double_divide(identity, double_divide(double_divide(identity, inverse(Y1)), inverse(Y1))) -> double_divide(inverse(identity), inverse(identity)) % 6.23/6.24 double_divide(identity, double_divide(identity, inverse(X0))) -> inverse(inverse(inverse(X0))) % 6.23/6.24 double_divide(identity, double_divide(identity, inverse(false__))) -> inverse(inverse(inverse(false__))) % 6.23/6.24 double_divide(identity, double_divide(identity, inverse(inverse(Y1)))) -> Y1 % 6.23/6.24 double_divide(inverse(X0), X0) -> identity % 6.23/6.24 double_divide(inverse(X0), double_divide(Y1, double_divide(X0, Y1))) -> identity % 6.23/6.24 double_divide(inverse(X0), double_divide(inverse(X1), inverse(X0))) -> inverse(inverse(inverse(X1))) % 6.23/6.24 double_divide(inverse(X0), inverse(double_divide(X1, X0))) -> inverse(X1) % 6.23/6.24 double_divide(inverse(X1), double_divide(inverse(X1), Y0)) -> Y0 % 6.23/6.24 double_divide(inverse(Y0), X1) -> inverse(double_divide(Y0, inverse(X1))) % 6.23/6.24 double_divide(inverse(Y0), double_divide(identity, inverse(Y0))) -> identity % 6.23/6.24 double_divide(inverse(Y0), inverse(double_divide(Y0, Y1))) -> inverse(Y1) % 6.23/6.24 double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1))) -> identity % 6.23/6.24 double_divide(inverse(identity), inverse(identity)) -> identity % 6.23/6.24 double_divide(inverse(inverse(X0)), inverse(X0)) -> identity % 6.23/6.24 double_divide(inverse(inverse(identity)), inverse(identity)) -> inverse(inverse(identity)) % 6.23/6.24 double_divide(inverse(inverse(inverse(X0))), X0) -> identity % 6.23/6.24 double_divide(inverse(inverse(inverse(X0))), inverse(inverse(X0))) -> identity % 6.23/6.24 double_divide(inverse(inverse(inverse(Y1))), inverse(identity)) -> Y1 % 6.23/6.24 f1(inverse(double_divide(a, b))) -> false__ % 6.23/6.24 f1(inverse(double_divide(b, a))) -> true__ % 6.23/6.24 f1(multiply(a, b)) -> true__ % 6.23/6.24 f1(multiply(b, a)) -> false__ % 6.23/6.24 inverse(double_divide(X0, double_divide(inverse(Y1), X0))) -> Y1 % 6.23/6.24 inverse(double_divide(Y0, double_divide(X0, Y0))) -> inverse(inverse(inverse(X0))) % 6.23/6.24 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y2, Y0)), inverse(Y2)))) -> Y1 % 6.23/6.24 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(inverse(X0), Y0)), X0))) -> Y1 % 6.23/6.24 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(Y0))))) -> Y1 % 6.23/6.24 inverse(double_divide(Y0, inverse(double_divide(inverse(Y0), Y1)))) -> Y1 % 6.23/6.24 inverse(double_divide(double_divide(X1, inverse(Y1)), X1)) -> Y1 % 6.23/6.24 inverse(double_divide(identity, Y0)) -> inverse(inverse(Y0)) % 6.23/6.24 inverse(double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0 % 6.23/6.24 inverse(double_divide(inverse(X0), inverse(double_divide(Y1, X0)))) -> Y1 % 6.23/6.24 inverse(double_divide(inverse(Y0), double_divide(X0, inverse(Y0)))) -> inverse(inverse(inverse(X0))) % 6.23/6.24 inverse(double_divide(inverse(Y0), double_divide(identity, inverse(Y0)))) -> identity % 6.23/6.24 inverse(double_divide(inverse(Y0), double_divide(inverse(Y1), inverse(Y0)))) -> Y1 % 6.23/6.24 inverse(double_divide(inverse(Y0), inverse(double_divide(Y0, Y1)))) -> Y1 % 6.23/6.24 inverse(identity) -> identity % 6.23/6.24 inverse(inverse(Y0)) -> Y0 % 6.23/6.24 inverse(inverse(double_divide(double_divide(Y0, inverse(Y1)), inverse(Y1)))) -> Y0 % 6.23/6.24 inverse(inverse(identity)) -> identity % 6.23/6.24 inverse(inverse(inverse(identity))) -> identity % 6.23/6.24 inverse(inverse(inverse(inverse(Y0)))) -> Y0 % 6.23/6.24 inverse(inverse(inverse(inverse(identity)))) -> identity % 6.23/6.24 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 6.23/6.24 true__ -> false__ % 6.23/6.24 with the LPO induced by % 6.23/6.24 a > b > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 6.23/6.24 % 6.23/6.24 % SZS output end Proof % 6.23/6.24 %------------------------------------------------------------------------------