%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP519-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 10:55:59 EDT 2022 % Result : Unsatisfiable 36.40s 36.50s % Output : Proof 36.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : GRP519-1 : TPTP v8.1.0. Released v2.6.0. % 0.10/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n022.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 05:52:18 EDT 2022 % 0.12/0.33 % CPUTime : % 36.40/36.50 % SZS status Unsatisfiable % 36.40/36.50 % SZS output start Proof % 36.40/36.50 The input problem is unsatisfiable because % 36.40/36.50 % 36.40/36.50 [1] the following set of Horn clauses is unsatisfiable: % 36.40/36.50 % 36.40/36.50 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C % 36.40/36.50 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 36.40/36.50 % 36.40/36.50 This holds because % 36.40/36.50 % 36.40/36.50 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 36.40/36.50 % 36.40/36.50 E: % 36.40/36.50 f1(multiply(a3, multiply(b3, c3))) = false__ % 36.40/36.50 f1(multiply(multiply(a3, b3), c3)) = true__ % 36.40/36.50 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C % 36.40/36.50 G: % 36.40/36.50 true__ = false__ % 36.40/36.50 % 36.40/36.50 This holds because % 36.40/36.50 % 36.40/36.50 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 36.40/36.50 % 36.40/36.50 multiply(X0, multiply(Y3, multiply(X3, X1))) = multiply(multiply(inverse(multiply(inverse(multiply(X0, X1)), Y1)), X3), multiply(Y3, Y1)) % 36.40/36.50 multiply(X0, multiply(multiply(inverse(X0), X1), inverse(X1))) = multiply(inverse(Y1), Y1) % 36.40/36.50 multiply(X1, Y0) = multiply(inverse(inverse(Y0)), X1) % 36.40/36.50 multiply(X1, Y2) = multiply(Y0, multiply(Y2, multiply(X1, inverse(Y0)))) % 36.40/36.50 multiply(X1, multiply(Y0, X2)) = multiply(multiply(inverse(Y2), multiply(X1, X2)), multiply(Y0, Y2)) % 36.40/36.50 multiply(X1, multiply(Y2, inverse(Y0))) = multiply(Y2, multiply(inverse(Y0), X1)) % 36.40/36.50 multiply(X1, multiply(multiply(inverse(multiply(X1, X2)), Y1), multiply(Y2, X2))) = multiply(Y2, Y1) % 36.40/36.50 multiply(X2, multiply(X0, X1)) = multiply(X0, multiply(X2, X1)) % 36.40/36.50 multiply(Y0, X1) = multiply(X1, inverse(inverse(Y0))) % 36.40/36.50 multiply(Y0, X1) = multiply(multiply(inverse(Y2), X1), multiply(Y0, Y2)) % 36.40/36.50 multiply(Y0, Y1) = multiply(Y1, Y0) % 36.40/36.50 multiply(Y0, inverse(Y0)) = multiply(Y1, inverse(Y1)) % 36.40/36.50 multiply(Y0, multiply(X2, X1)) = multiply(multiply(inverse(X0), X1), multiply(Y0, multiply(X2, X0))) % 36.40/36.50 multiply(Y0, multiply(multiply(inverse(X2), Y2), multiply(Y1, X2))) = multiply(Y1, multiply(Y0, Y2)) % 36.40/36.50 multiply(Y1, multiply(inverse(Y0), Y2)) = multiply(inverse(Y0), multiply(Y2, Y1)) % 36.40/36.50 multiply(inverse(X1), X1) = multiply(false__, multiply(multiply(inverse(false__), inverse(inverse(Y1))), inverse(inverse(inverse(Y1))))) % 36.40/36.50 multiply(inverse(X1), Y0) = multiply(inverse(inverse(Y0)), inverse(X1)) % 36.40/36.50 multiply(inverse(Y0), Y0) = inverse(multiply(inverse(X1), X1)) % 36.40/36.50 multiply(inverse(Y0), Y0) = multiply(inverse(X1), X1) % 36.40/36.50 multiply(multiply(X0, Y1), multiply(Y2, inverse(X0))) = multiply(Y2, Y1) % 36.40/36.50 multiply(multiply(X1, multiply(inverse(Y0), X2)), multiply(Y2, Y0)) = multiply(Y2, multiply(X1, X2)) % 36.40/36.50 multiply(multiply(Y1, Y0), Y2) = multiply(Y0, multiply(Y2, Y1)) % 36.40/36.50 multiply(multiply(Y1, Y2), Y0) = multiply(Y1, multiply(Y0, Y2)) % 36.40/36.50 multiply(multiply(Y1, Y2), Y0) = multiply(multiply(Y0, Y2), Y1) % 36.40/36.50 multiply(multiply(inverse(X2), Y1), multiply(Y0, X2)) = multiply(multiply(inverse(Y2), Y1), multiply(Y0, Y2)) % 36.40/36.50 multiply(multiply(inverse(X2), Y3), multiply(Y0, multiply(X2, Y1))) = multiply(Y0, multiply(Y3, Y1)) % 36.40/36.50 multiply(multiply(inverse(Y0), Y1), X1) = multiply(multiply(inverse(Y0), X1), Y1) % 36.40/36.50 multiply(multiply(inverse(Y0), Y1), X1) = multiply(multiply(inverse(multiply(Y0, Y3)), X1), multiply(Y1, Y3)) % 36.40/36.50 multiply(multiply(inverse(Y0), Y1), multiply(multiply(inverse(X2), Y0), multiply(Y2, X2))) = multiply(Y2, Y1) % 36.40/36.50 multiply(multiply(inverse(false__), inverse(X1)), multiply(inverse(inverse(X1)), false__)) = multiply(inverse(Y1), Y1) % 36.40/36.50 multiply(multiply(inverse(false__), inverse(X1)), multiply(inverse(inverse(X1)), false__)) = multiply(multiply(inverse(false__), inverse(Y1)), multiply(inverse(inverse(Y1)), false__)) % 36.40/36.50 multiply(multiply(inverse(multiply(inverse(X2), Y2)), Y3), Y2) = multiply(Y0, multiply(Y3, multiply(multiply(inverse(multiply(Y0, X1)), X2), X1))) % 36.40/36.50 multiply(multiply(multiply(inverse(X2), Y1), multiply(inverse(Y0), X2)), multiply(Y2, Y0)) = multiply(Y2, Y1) % 36.40/36.50 f1(multiply(a3, multiply(b3, c3))) -> false__ % 36.40/36.50 f1(multiply(multiply(a3, b3), c3)) -> true__ % 36.40/36.50 inverse(inverse(Y1)) -> Y1 % 36.40/36.50 inverse(multiply(X1, X0)) -> multiply(inverse(X1), inverse(X0)) % 36.40/36.50 inverse(multiply(multiply(inverse(X1), X1), Y1)) -> inverse(Y1) % 36.40/36.50 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) -> C % 36.40/36.50 multiply(X0, multiply(multiply(multiply(inverse(X0), inverse(X1)), Y1), X1)) -> Y1 % 36.40/36.50 multiply(X1, inverse(inverse(Y0))) -> multiply(X1, Y0) % 36.40/36.50 multiply(X1, multiply(Y2, multiply(inverse(X0), inverse(X1)))) -> multiply(Y2, inverse(X0)) % 36.40/36.50 multiply(Y0, inverse(multiply(inverse(X1), X1))) -> Y0 % 36.40/36.50 multiply(Y0, multiply(X0, multiply(multiply(inverse(X0), X1), inverse(X1)))) -> Y0 % 36.40/36.50 multiply(Y0, multiply(X1, multiply(inverse(Y0), X2))) -> multiply(X1, X2) % 36.40/36.50 multiply(Y0, multiply(X1, multiply(multiply(inverse(multiply(X1, multiply(Y0, X2))), Y2), X2))) -> Y2 % 36.40/36.50 multiply(Y0, multiply(X1, multiply(multiply(inverse(multiply(Y0, multiply(X1, X2))), Y2), X2))) -> Y2 % 36.40/36.50 multiply(Y0, multiply(Y1, inverse(Y0))) -> Y1 % 36.40/36.50 multiply(Y0, multiply(Y1, inverse(Y1))) -> Y0 % 36.40/36.50 multiply(Y0, multiply(Y1, multiply(X1, multiply(inverse(Y0), inverse(Y1))))) -> X1 % 36.40/36.50 multiply(Y0, multiply(false__, multiply(multiply(inverse(false__), multiply(inverse(X0), inverse(X1))), multiply(inverse(inverse(X0)), inverse(inverse(X1)))))) -> Y0 % 36.40/36.50 multiply(Y0, multiply(inverse(Y0), Y1)) -> Y1 % 36.40/36.50 multiply(Y0, multiply(inverse(Y0), inverse(Y1))) -> inverse(Y1) % 36.40/36.50 multiply(Y0, multiply(inverse(multiply(Y0, Y1)), X1)) -> multiply(inverse(Y1), X1) % 36.40/36.50 multiply(Y0, multiply(multiply(X0, X1), multiply(inverse(X0), inverse(X1)))) -> Y0 % 36.40/36.50 multiply(Y0, multiply(multiply(X1, multiply(inverse(multiply(Y0, Y1)), X2)), Y1)) -> multiply(X1, X2) % 36.40/36.50 multiply(Y0, multiply(multiply(inverse(X2), Y1), multiply(inverse(Y1), X2))) -> Y0 % 36.40/36.50 multiply(Y0, multiply(multiply(inverse(X2), Y2), multiply(multiply(inverse(multiply(Y0, X1)), X2), X1))) -> Y2 % 36.40/36.50 multiply(Y0, multiply(multiply(inverse(Y1), Y2), multiply(multiply(inverse(X2), Y1), multiply(multiply(inverse(multiply(Y0, X1)), X2), X1)))) -> Y2 % 36.40/36.50 multiply(Y0, multiply(multiply(inverse(false__), multiply(X1, X2)), multiply(inverse(multiply(X1, multiply(Y0, X2))), multiply(Y2, false__)))) -> Y2 % 36.40/36.50 multiply(Y1, multiply(Y0, multiply(X1, inverse(Y1)))) -> multiply(Y0, X1) % 36.40/36.50 multiply(Y1, multiply(Y0, multiply(multiply(inverse(multiply(Y1, X1)), X2), X1))) -> multiply(Y0, X2) % 36.40/36.50 multiply(Y1, multiply(inverse(Y2), Y2)) -> Y1 % 36.40/36.50 multiply(false__, multiply(X2, multiply(multiply(inverse(multiply(false__, false__)), Y0), false__))) -> multiply(X2, Y0) % 36.40/36.50 multiply(false__, multiply(Y1, multiply(multiply(inverse(false__), inverse(Y1)), X1))) -> X1 % 36.40/36.50 multiply(false__, multiply(Y1, multiply(multiply(inverse(false__), inverse(Y1)), inverse(X1)))) -> inverse(X1) % 36.40/36.50 multiply(false__, multiply(multiply(inverse(false__), inverse(Y0)), multiply(Y1, Y0))) -> Y1 % 36.40/36.50 multiply(inverse(X0), multiply(X1, multiply(multiply(inverse(X1), Y2), X0))) -> Y2 % 36.40/36.50 multiply(inverse(X0), multiply(Y0, multiply(X1, X0))) -> multiply(Y0, X1) % 36.40/36.50 multiply(inverse(X1), multiply(multiply(inverse(Y1), X1), multiply(Y2, Y1))) -> Y2 % 36.40/36.50 multiply(inverse(Y1), multiply(Y2, Y1)) -> Y2 % 36.40/36.50 multiply(inverse(inverse(X1)), inverse(multiply(Y1, X1))) -> inverse(Y1) % 36.40/36.50 multiply(inverse(inverse(Y0)), X1) -> multiply(Y0, X1) % 36.40/36.50 multiply(inverse(inverse(multiply(inverse(X1), X1))), Y1) -> Y1 % 36.40/36.50 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(Y2, X1))) -> Y2 % 36.40/36.50 multiply(inverse(multiply(X1, X0)), X1) -> inverse(X0) % 36.40/36.50 multiply(inverse(multiply(Y0, Y1)), multiply(Y0, X1)) -> multiply(inverse(Y1), X1) % 36.40/36.50 multiply(inverse(multiply(inverse(Y1), Y1)), Y2) -> Y2 % 36.40/36.50 multiply(inverse(multiply(multiply(inverse(multiply(Y2, Y1)), X1), Y1)), X1) -> Y2 % 36.40/36.50 multiply(multiply(X0, X1), multiply(Y1, multiply(inverse(X0), inverse(X1)))) -> Y1 % 36.40/36.50 multiply(multiply(X0, X1), multiply(multiply(inverse(X0), inverse(X1)), Y1)) -> Y1 % 36.40/36.50 multiply(multiply(X0, multiply(multiply(inverse(X0), X1), inverse(X1))), Y1) -> Y1 % 36.40/36.50 multiply(multiply(X1, multiply(inverse(Y0), X2)), Y0) -> multiply(X1, X2) % 36.40/36.50 multiply(multiply(Y0, Y2), Y1) -> multiply(Y0, multiply(Y2, Y1)) % 36.40/36.50 multiply(multiply(Y0, inverse(Y0)), Y1) -> Y1 % 36.40/36.50 multiply(multiply(Y1, Y0), inverse(Y0)) -> Y1 % 36.40/36.50 multiply(multiply(Y1, Y0), inverse(Y1)) -> Y0 % 36.40/36.50 multiply(multiply(false__, multiply(multiply(inverse(false__), multiply(inverse(X0), inverse(X1))), multiply(inverse(inverse(X0)), inverse(inverse(X1))))), Y1) -> Y1 % 36.40/36.50 multiply(multiply(inverse(X0), inverse(X1)), multiply(Y1, multiply(X0, X1))) -> Y1 % 36.40/36.50 multiply(multiply(inverse(X1), X1), Y1) -> Y1 % 36.40/36.50 multiply(multiply(inverse(X1), Y1), multiply(multiply(inverse(X0), X0), X1)) -> Y1 % 36.40/36.50 multiply(multiply(inverse(X2), multiply(Y2, Y0)), multiply(multiply(inverse(Y0), Y1), X2)) -> multiply(Y2, Y1) % 36.40/36.50 multiply(multiply(inverse(Y1), X1), multiply(Y2, Y1)) -> multiply(X1, Y2) % 36.40/36.50 multiply(multiply(inverse(Y1), X1), multiply(multiply(inverse(X1), Y2), Y1)) -> Y2 % 36.40/36.50 multiply(multiply(inverse(Y1), Y2), Y1) -> Y2 % 36.40/36.50 multiply(multiply(inverse(Y2), multiply(X1, X0)), multiply(inverse(X0), Y2)) -> X1 % 36.40/36.50 multiply(multiply(inverse(false__), multiply(X1, X2)), multiply(Y0, multiply(multiply(inverse(multiply(X1, multiply(Y0, X2))), Y2), false__))) -> Y2 % 36.40/36.50 multiply(multiply(inverse(false__), multiply(Y0, Y1)), multiply(inverse(multiply(Y0, Y1)), multiply(Y2, false__))) -> Y2 % 36.40/36.50 multiply(multiply(inverse(multiply(X1, X0)), Y1), X1) -> multiply(inverse(X0), Y1) % 36.40/36.50 multiply(multiply(inverse(multiply(inverse(multiply(X0, X1)), Y1)), X3), multiply(multiply(inverse(multiply(X0, multiply(X3, X1))), Y2), Y1)) -> Y2 % 36.40/36.50 multiply(multiply(inverse(multiply(inverse(multiply(Y0, Y1)), X1)), X2), X1) -> multiply(Y0, multiply(X2, Y1)) % 36.40/36.50 multiply(multiply(multiply(X0, X1), multiply(inverse(X0), inverse(X1))), Y1) -> Y1 % 36.40/36.50 true__ -> false__ % 36.40/36.50 with the LPO induced by % 36.40/36.50 c3 > b3 > a3 > f1 > inverse > multiply > true__ > false__ % 36.40/36.50 % 36.40/36.50 % SZS output end Proof % 36.40/36.50 %------------------------------------------------------------------------------