%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP509-1 : 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 10:55:55 EDT 2022 % Result : Unsatisfiable 10.54s 10.70s % Output : Proof 10.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.10 % Problem : GRP509-1 : TPTP v8.1.0. Released v2.6.0. % 0.02/0.10 % Command : moca.sh %s % 0.08/0.30 % Computer : n005.cluster.edu % 0.08/0.30 % Model : x86_64 x86_64 % 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.30 % Memory : 8042.1875MB % 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.30 % CPULimit : 300 % 0.08/0.30 % WCLimit : 600 % 0.08/0.30 % DateTime : Tue Jun 14 08:06:24 EDT 2022 % 0.08/0.30 % CPUTime : % 10.54/10.70 % SZS status Unsatisfiable % 10.54/10.70 % SZS output start Proof % 10.54/10.70 The input problem is unsatisfiable because % 10.54/10.70 % 10.54/10.70 [1] the following set of Horn clauses is unsatisfiable: % 10.54/10.70 % 10.54/10.70 multiply(multiply(multiply(A, B), C), inverse(multiply(A, C))) = B % 10.54/10.70 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 10.54/10.70 % 10.54/10.70 This holds because % 10.54/10.70 % 10.54/10.70 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 10.54/10.70 % 10.54/10.70 E: % 10.54/10.70 f1(multiply(inverse(a1), a1)) = true__ % 10.54/10.70 f1(multiply(inverse(b1), b1)) = false__ % 10.54/10.70 multiply(multiply(multiply(A, B), C), inverse(multiply(A, C))) = B % 10.54/10.70 G: % 10.54/10.70 true__ = false__ % 10.54/10.70 % 10.54/10.70 This holds because % 10.54/10.70 % 10.54/10.70 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 10.54/10.70 % 10.54/10.70 multiply(X1, X0) = multiply(X0, X1) % 10.54/10.70 multiply(X1, inverse(inverse(X0))) = multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 10.54/10.70 multiply(Y0, inverse(Y0)) = multiply(X1, inverse(X1)) % 10.54/10.70 multiply(false__, inverse(false__)) = multiply(Y0, inverse(Y0)) % 10.54/10.70 multiply(inverse(X0), inverse(inverse(X0))) = inverse(multiply(X1, inverse(X1))) % 10.54/10.70 multiply(inverse(X0), inverse(inverse(X0))) = multiply(inverse(X1), inverse(inverse(X1))) % 10.54/10.70 multiply(inverse(false__), inverse(inverse(false__))) = multiply(X1, inverse(X1)) % 10.54/10.70 multiply(inverse(inverse(X0)), inverse(X1)) = multiply(inverse(X1), inverse(inverse(X0))) % 10.54/10.70 multiply(inverse(inverse(X0)), inverse(inverse(inverse(X1)))) = inverse(multiply(X1, inverse(X0))) % 10.54/10.70 multiply(inverse(inverse(X0)), inverse(inverse(inverse(X1)))) = multiply(inverse(X1), inverse(inverse(X0))) % 10.54/10.70 multiply(inverse(inverse(X1)), inverse(inverse(X0))) = multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 10.54/10.70 multiply(multiply(X2, Y2), inverse(multiply(Y0, Y2))) = inverse(multiply(multiply(X1, Y0), inverse(multiply(X1, X2)))) % 10.54/10.70 multiply(multiply(X2, Y2), inverse(multiply(Y0, Y2))) = multiply(multiply(X2, false__), inverse(multiply(Y0, false__))) % 10.54/10.70 multiply(multiply(Y0, multiply(X1, inverse(inverse(X0)))), inverse(Y0)) = multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 10.54/10.70 f1(multiply(false__, inverse(false__))) -> false__ % 10.54/10.70 f1(multiply(false__, inverse(false__))) -> true__ % 10.54/10.71 f1(multiply(inverse(a1), a1)) -> true__ % 10.54/10.71 f1(multiply(inverse(b1), b1)) -> false__ % 10.54/10.71 inverse(inverse(Y1)) -> Y1 % 10.54/10.71 inverse(inverse(inverse(X1))) -> inverse(X1) % 10.54/10.71 inverse(inverse(multiply(X0, X1))) -> multiply(X1, inverse(inverse(X0))) % 10.54/10.71 inverse(inverse(multiply(X0, X1))) -> multiply(inverse(inverse(X0)), inverse(inverse(X1))) % 10.54/10.71 inverse(multiply(X0, X1)) -> multiply(inverse(X1), inverse(X0)) % 10.54/10.71 inverse(multiply(Y0, inverse(X1))) -> multiply(inverse(Y0), inverse(inverse(X1))) % 10.54/10.71 multiply(X0, multiply(Y1, inverse(Y1))) -> X0 % 10.54/10.71 multiply(X0, multiply(inverse(X0), Y1)) -> Y1 % 10.54/10.71 multiply(X1, inverse(multiply(multiply(X0, X1), inverse(multiply(X0, Y1))))) -> Y1 % 10.54/10.71 multiply(X1, inverse(multiply(multiply(Y1, X1), Y2))) -> inverse(multiply(Y1, Y2)) % 10.54/10.71 multiply(X1, inverse(multiply(multiply(multiply(Y2, multiply(multiply(X0, X1), X2)), Y3), inverse(multiply(X0, X2))))) -> inverse(multiply(Y2, Y3)) % 10.54/10.71 multiply(X2, inverse(multiply(Y0, inverse(multiply(multiply(X1, multiply(Y0, Y1)), inverse(multiply(X1, X2))))))) -> Y1 % 10.54/10.71 multiply(Y0, inverse(multiply(multiply(Y1, Y0), inverse(X2)))) -> multiply(multiply(X2, false__), inverse(multiply(Y1, false__))) % 10.54/10.71 multiply(Y0, inverse(multiply(multiply(multiply(multiply(X0, X1), X2), Y0), inverse(X1)))) -> inverse(multiply(X0, X2)) % 10.54/10.71 multiply(Y0, multiply(Y1, inverse(Y0))) -> Y1 % 10.54/10.71 multiply(Y0, multiply(multiply(X0, X1), multiply(inverse(X1), inverse(X0)))) -> Y0 % 10.54/10.71 multiply(inverse(X0), inverse(inverse(multiply(X0, Y2)))) -> Y2 % 10.54/10.71 multiply(inverse(X0), multiply(inverse(Y1), inverse(inverse(X0)))) -> inverse(Y1) % 10.54/10.71 multiply(inverse(X0), multiply(inverse(inverse(X0)), inverse(inverse(Y1)))) -> Y1 % 10.54/10.71 multiply(inverse(X1), inverse(multiply(Y0, inverse(Y0)))) -> inverse(X1) % 10.54/10.71 multiply(inverse(X1), inverse(multiply(Y1, inverse(X1)))) -> inverse(Y1) % 10.54/10.71 multiply(inverse(Y0), multiply(X0, inverse(X0))) -> inverse(Y0) % 10.54/10.71 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1 % 10.54/10.71 multiply(inverse(Y0), multiply(Y1, Y0)) -> Y1 % 10.54/10.71 multiply(inverse(Y0), multiply(inverse(X0), X0)) -> inverse(Y0) % 10.54/10.71 multiply(inverse(inverse(X0)), multiply(inverse(X0), inverse(inverse(X1)))) -> inverse(inverse(X1)) % 10.54/10.71 multiply(inverse(inverse(multiply(X0, X1))), inverse(X1)) -> inverse(inverse(X0)) % 10.54/10.71 multiply(inverse(multiply(X0, X2)), inverse(multiply(X1, inverse(multiply(multiply(multiply(X0, X1), X2), Y2))))) -> Y2 % 10.54/10.71 multiply(inverse(multiply(X0, inverse(X1))), inverse(inverse(inverse(X1)))) -> inverse(X0) % 10.54/10.71 multiply(inverse(multiply(X1, X2)), inverse(multiply(Y0, inverse(Y0)))) -> inverse(multiply(X1, X2)) % 10.54/10.71 multiply(multiply(X0, X1), multiply(multiply(inverse(X1), inverse(X0)), Y1)) -> Y1 % 10.54/10.71 multiply(multiply(X1, Y2), inverse(multiply(multiply(multiply(X0, X1), X2), Y2))) -> inverse(multiply(X0, X2)) % 10.54/10.71 multiply(multiply(X2, false__), inverse(multiply(Y0, false__))) -> multiply(X2, inverse(Y0)) % 10.54/10.71 multiply(multiply(Y0, X0), inverse(Y0)) -> X0 % 10.54/10.71 multiply(multiply(Y0, inverse(X1)), inverse(Y0)) -> inverse(X1) % 10.54/10.71 multiply(multiply(Y0, inverse(multiply(Y2, Y3))), inverse(Y0)) -> inverse(multiply(Y2, Y3)) % 10.54/10.71 multiply(multiply(Y0, multiply(inverse(X1), inverse(X0))), inverse(Y0)) -> multiply(inverse(X1), inverse(X0)) % 10.54/10.71 multiply(multiply(Y1, Y0), inverse(Y0)) -> Y1 % 10.54/10.71 multiply(multiply(Y1, inverse(Y1)), Y0) -> Y0 % 10.54/10.71 multiply(multiply(false__, multiply(multiply(inverse(X1), inverse(X0)), inverse(inverse(X0)))), inverse(false__)) -> inverse(X1) % 10.54/10.71 multiply(multiply(inverse(X0), inverse(Y1)), X0) -> inverse(Y1) % 10.54/10.71 multiply(multiply(inverse(X1), Y2), inverse(multiply(multiply(X0, inverse(X1)), Y2))) -> inverse(X0) % 10.54/10.71 multiply(multiply(inverse(X1), false__), inverse(multiply(multiply(X0, inverse(X1)), false__))) -> inverse(X0) % 10.54/10.71 multiply(multiply(inverse(X1), inverse(X0)), multiply(multiply(X0, X1), Y1)) -> Y1 % 10.54/10.71 multiply(multiply(inverse(X1), inverse(X0)), multiply(multiply(inverse(inverse(X0)), inverse(inverse(X1))), inverse(inverse(Y1)))) -> Y1 % 10.54/10.71 multiply(multiply(inverse(X1), inverse(inverse(X1))), inverse(inverse(X0))) -> inverse(inverse(X0)) % 10.54/10.71 multiply(multiply(inverse(Y1), Y0), inverse(Y0)) -> inverse(Y1) % 10.54/10.71 multiply(multiply(inverse(inverse(X0)), inverse(Y1)), inverse(X0)) -> inverse(Y1) % 10.54/10.71 multiply(multiply(inverse(multiply(X0, X1)), inverse(Y1)), multiply(X1, inverse(inverse(X0)))) -> inverse(Y1) % 10.54/10.71 multiply(multiply(inverse(multiply(X1, X2)), Y2), inverse(multiply(multiply(X0, inverse(multiply(X1, X2))), Y2))) -> inverse(X0) % 10.54/10.71 multiply(multiply(multiply(A, B), C), inverse(multiply(A, C))) -> B % 10.54/10.71 multiply(multiply(multiply(X0, X1), Y1), multiply(inverse(X1), inverse(X0))) -> Y1 % 10.54/10.71 multiply(multiply(multiply(X0, X1), inverse(Y1)), multiply(inverse(X1), inverse(X0))) -> inverse(Y1) % 10.54/10.71 multiply(multiply(multiply(X2, false__), inverse(multiply(Y1, false__))), inverse(multiply(X2, inverse(multiply(Y1, Y2))))) -> Y2 % 10.54/10.71 multiply(multiply(multiply(Y0, Y1), inverse(multiply(multiply(X1, Y0), inverse(multiply(X1, X2))))), inverse(X2)) -> Y1 % 10.54/10.71 multiply(multiply(multiply(multiply(X0, inverse(X1)), Y1), inverse(X0)), inverse(inverse(X1))) -> Y1 % 10.54/10.71 multiply(multiply(multiply(multiply(multiply(X0, X1), X2), Y1), inverse(multiply(X0, X2))), inverse(X1)) -> Y1 % 10.54/10.71 true__ -> false__ % 10.54/10.71 with the LPO induced by % 10.54/10.71 a1 > b1 > f1 > inverse > multiply > true__ > false__ % 10.54/10.71 % 10.54/10.71 % SZS output end Proof % 10.54/10.71 %------------------------------------------------------------------------------