%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP512-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n032.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 10:55:56 EDT 2022 % Result : Unsatisfiable 5.54s 5.70s % Output : Proof 5.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : GRP512-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.00/0.09 % Command : moca.sh %s % 0.08/0.28 % Computer : n032.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 600 % 0.08/0.28 % DateTime : Mon Jun 13 06:14:41 EDT 2022 % 0.08/0.28 % CPUTime : % 5.54/5.70 % SZS status Unsatisfiable % 5.54/5.70 % SZS output start Proof % 5.54/5.70 The input problem is unsatisfiable because % 5.54/5.70 % 5.54/5.70 [1] the following set of Horn clauses is unsatisfiable: % 5.54/5.70 % 5.54/5.70 multiply(multiply(multiply(A, B), C), inverse(multiply(A, C))) = B % 5.54/5.70 multiply(a, b) = multiply(b, a) ==> \bottom % 5.54/5.70 % 5.54/5.70 This holds because % 5.54/5.70 % 5.54/5.70 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.54/5.70 % 5.54/5.70 E: % 5.54/5.70 f1(multiply(a, b)) = true__ % 5.54/5.70 f1(multiply(b, a)) = false__ % 5.54/5.70 multiply(multiply(multiply(A, B), C), inverse(multiply(A, C))) = B % 5.54/5.70 G: % 5.54/5.70 true__ = false__ % 5.54/5.70 % 5.54/5.70 This holds because % 5.54/5.70 % 5.54/5.70 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.54/5.70 % 5.54/5.70 multiply(X1, X0) = multiply(X0, X1) % 5.54/5.70 multiply(X1, inverse(inverse(X0))) = multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 5.54/5.70 multiply(Y0, inverse(Y0)) = multiply(X1, inverse(X1)) % 5.54/5.70 multiply(inverse(X0), inverse(inverse(X0))) = inverse(multiply(X1, inverse(X1))) % 5.54/5.70 multiply(inverse(X0), inverse(inverse(X0))) = multiply(inverse(X1), inverse(inverse(X1))) % 5.54/5.70 multiply(inverse(false__), inverse(inverse(false__))) = multiply(X1, inverse(X1)) % 5.54/5.70 multiply(inverse(inverse(X0)), inverse(X1)) = multiply(inverse(X1), inverse(inverse(X0))) % 5.54/5.70 multiply(inverse(inverse(X0)), inverse(inverse(inverse(X1)))) = inverse(multiply(X1, inverse(X0))) % 5.54/5.70 multiply(inverse(inverse(X0)), inverse(inverse(inverse(X1)))) = multiply(inverse(X1), inverse(inverse(X0))) % 5.54/5.70 multiply(inverse(inverse(X1)), inverse(inverse(X0))) = multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 5.54/5.70 multiply(multiply(X2, Y2), inverse(multiply(Y0, Y2))) = inverse(multiply(multiply(X1, Y0), inverse(multiply(X1, X2)))) % 5.54/5.70 multiply(multiply(X2, Y2), inverse(multiply(Y0, Y2))) = multiply(multiply(X2, false__), inverse(multiply(Y0, false__))) % 5.54/5.70 multiply(multiply(Y0, multiply(X1, inverse(inverse(X0)))), inverse(Y0)) = multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 5.54/5.70 f1(multiply(a, b)) -> true__ % 5.54/5.70 f1(multiply(b, a)) -> false__ % 5.54/5.70 inverse(inverse(Y1)) -> Y1 % 5.54/5.70 inverse(inverse(inverse(X1))) -> inverse(X1) % 5.54/5.70 inverse(inverse(multiply(X0, X1))) -> multiply(X1, inverse(inverse(X0))) % 5.54/5.70 inverse(inverse(multiply(X0, X1))) -> multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 5.54/5.70 inverse(multiply(X0, X1)) -> multiply(inverse(X1), inverse(X0)) % 5.54/5.70 inverse(multiply(Y0, inverse(X1))) -> multiply(inverse(Y0), inverse(inverse(X1))) % 5.54/5.70 multiply(X0, multiply(Y1, inverse(Y1))) -> X0 % 5.54/5.70 multiply(X0, multiply(inverse(X0), Y1)) -> Y1 % 5.54/5.70 multiply(X1, inverse(multiply(multiply(X0, X1), inverse(multiply(X0, Y1))))) -> Y1 % 5.54/5.70 multiply(X1, inverse(multiply(multiply(Y1, X1), Y2))) -> inverse(multiply(Y1, Y2)) % 5.54/5.70 multiply(X1, inverse(multiply(multiply(multiply(Y2, multiply(multiply(X0, X1), X2)), Y3), inverse(multiply(X0, X2))))) -> inverse(multiply(Y2, Y3)) % 5.54/5.70 multiply(X2, inverse(multiply(Y0, inverse(multiply(multiply(X1, multiply(Y0, Y1)), inverse(multiply(X1, X2))))))) -> Y1 % 5.54/5.70 multiply(Y0, inverse(multiply(multiply(Y1, Y0), inverse(X2)))) -> multiply(multiply(X2, false__), inverse(multiply(Y1, false__))) % 5.54/5.70 multiply(Y0, inverse(multiply(multiply(multiply(multiply(X0, X1), X2), Y0), inverse(X1)))) -> inverse(multiply(X0, X2)) % 5.54/5.70 multiply(Y0, multiply(Y1, inverse(Y0))) -> Y1 % 5.54/5.70 multiply(inverse(X0), inverse(inverse(multiply(X0, Y2)))) -> Y2 % 5.54/5.70 multiply(inverse(X0), multiply(inverse(Y1), inverse(inverse(X0)))) -> inverse(Y1) % 5.54/5.70 multiply(inverse(X0), multiply(inverse(inverse(X0)), inverse(inverse(Y1)))) -> Y1 % 5.54/5.70 multiply(inverse(X1), inverse(multiply(Y0, inverse(Y0)))) -> inverse(X1) % 5.54/5.70 multiply(inverse(X1), inverse(multiply(Y1, inverse(X1)))) -> inverse(Y1) % 5.54/5.70 multiply(inverse(Y0), multiply(X0, inverse(X0))) -> inverse(Y0) % 5.54/5.70 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1 % 5.54/5.70 multiply(inverse(Y0), multiply(Y1, Y0)) -> Y1 % 5.54/5.70 multiply(inverse(Y0), multiply(inverse(X0), X0)) -> inverse(Y0) % 5.54/5.70 multiply(inverse(inverse(X0)), multiply(inverse(X0), inverse(inverse(X1)))) -> inverse(inverse(X1)) % 5.54/5.70 multiply(inverse(inverse(multiply(X0, X1))), inverse(X1)) -> inverse(inverse(X0)) % 5.54/5.70 multiply(inverse(multiply(X0, X2)), inverse(multiply(X1, inverse(multiply(multiply(multiply(X0, X1), X2), Y2))))) -> Y2 % 5.54/5.70 multiply(inverse(multiply(X0, inverse(X1))), inverse(inverse(inverse(X1)))) -> inverse(X0) % 5.54/5.70 multiply(inverse(multiply(X1, X2)), inverse(multiply(Y0, inverse(Y0)))) -> inverse(multiply(X1, X2)) % 5.54/5.70 multiply(multiply(X1, Y2), inverse(multiply(multiply(multiply(X0, X1), X2), Y2))) -> inverse(multiply(X0, X2)) % 5.54/5.70 multiply(multiply(X2, false__), inverse(multiply(Y0, false__))) -> multiply(X2, inverse(Y0)) % 5.54/5.70 multiply(multiply(Y0, X0), inverse(Y0)) -> X0 % 5.54/5.70 multiply(multiply(Y0, inverse(X1)), inverse(Y0)) -> inverse(X1) % 5.54/5.70 multiply(multiply(Y0, inverse(multiply(Y2, Y3))), inverse(Y0)) -> inverse(multiply(Y2, Y3)) % 5.54/5.70 multiply(multiply(Y0, multiply(inverse(X1), inverse(X0))), inverse(Y0)) -> multiply(inverse(X1), inverse(X0)) % 5.54/5.70 multiply(multiply(Y1, Y0), inverse(Y0)) -> Y1 % 5.54/5.70 multiply(multiply(Y1, inverse(Y1)), Y0) -> Y0 % 5.54/5.70 multiply(multiply(false__, multiply(multiply(inverse(X1), inverse(X0)), inverse(inverse(X0)))), inverse(false__)) -> inverse(X1) % 5.54/5.70 multiply(multiply(inverse(X0), inverse(Y1)), X0) -> inverse(Y1) % 5.54/5.70 multiply(multiply(inverse(X1), Y2), inverse(multiply(multiply(X0, inverse(X1)), Y2))) -> inverse(X0) % 5.54/5.70 multiply(multiply(inverse(X1), false__), inverse(multiply(multiply(X0, inverse(X1)), false__))) -> inverse(X0) % 5.54/5.70 multiply(multiply(inverse(X1), inverse(X0)), multiply(multiply(inverse(inverse(X0)), inverse(inverse(X1))), inverse(inverse(Y1)))) -> Y1 % 5.54/5.70 multiply(multiply(inverse(X1), inverse(inverse(X1))), inverse(inverse(X0))) -> inverse(inverse(X0)) % 5.54/5.70 multiply(multiply(inverse(Y1), Y0), inverse(Y0)) -> inverse(Y1) % 5.54/5.70 multiply(multiply(inverse(inverse(X0)), inverse(Y1)), inverse(X0)) -> inverse(Y1) % 5.54/5.70 multiply(multiply(inverse(multiply(X0, X1)), inverse(Y1)), multiply(X1, inverse(inverse(X0)))) -> inverse(Y1) % 5.54/5.70 multiply(multiply(inverse(multiply(X1, X2)), Y2), inverse(multiply(multiply(X0, inverse(multiply(X1, X2))), Y2))) -> inverse(X0) % 5.54/5.70 multiply(multiply(multiply(A, B), C), inverse(multiply(A, C))) -> B % 5.54/5.70 multiply(multiply(multiply(X0, X1), inverse(Y1)), multiply(inverse(X1), inverse(X0))) -> inverse(Y1) % 5.54/5.70 multiply(multiply(multiply(X2, false__), inverse(multiply(Y1, false__))), inverse(multiply(X2, inverse(multiply(Y1, Y2))))) -> Y2 % 5.54/5.70 multiply(multiply(multiply(Y0, Y1), inverse(multiply(multiply(X1, Y0), inverse(multiply(X1, X2))))), inverse(X2)) -> Y1 % 5.54/5.70 multiply(multiply(multiply(multiply(X0, inverse(X1)), Y1), inverse(X0)), inverse(inverse(X1))) -> Y1 % 5.54/5.70 multiply(multiply(multiply(multiply(multiply(X0, X1), X2), Y1), inverse(multiply(X0, X2))), inverse(X1)) -> Y1 % 5.54/5.70 true__ -> false__ % 5.54/5.70 with the LPO induced by % 5.54/5.70 a > b > f1 > inverse > multiply > true__ > false__ % 5.54/5.70 % 5.54/5.70 % SZS output end Proof % 5.54/5.70 %------------------------------------------------------------------------------