%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP518-1 : TPTP v8.1.0. Released v2.6.0. % 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 10:55:58 EDT 2022 % Result : Unsatisfiable 2.93s 3.14s % Output : Proof 2.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP518-1 : TPTP v8.1.0. Released v2.6.0. % 0.07/0.12 % 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 % 0.12/0.34 % DateTime : Tue Jun 14 12:43:53 EDT 2022 % 0.12/0.34 % CPUTime : % 2.93/3.14 % SZS status Unsatisfiable % 2.93/3.14 % SZS output start Proof % 2.93/3.14 The input problem is unsatisfiable because % 2.93/3.14 % 2.93/3.14 [1] the following set of Horn clauses is unsatisfiable: % 2.93/3.14 % 2.93/3.14 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C % 2.93/3.14 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 2.93/3.14 % 2.93/3.14 This holds because % 2.93/3.14 % 2.93/3.14 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.93/3.14 % 2.93/3.14 E: % 2.93/3.14 f1(a2) = false__ % 2.93/3.14 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 2.93/3.14 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C % 2.93/3.14 G: % 2.93/3.14 true__ = false__ % 2.93/3.14 % 2.93/3.14 This holds because % 2.93/3.14 % 2.93/3.14 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.93/3.14 % 2.93/3.14 multiply(Y0, X1) = multiply(multiply(inverse(Y3), multiply(inverse(Y2), X1)), multiply(Y0, multiply(Y3, Y2))) % 2.93/3.14 multiply(Y0, multiply(X2, Y1)) = multiply(multiply(inverse(X1), X2), multiply(Y0, multiply(X1, Y1))) % 2.93/3.14 f1(a2) -> false__ % 2.93/3.14 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 2.93/3.14 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) -> C % 2.93/3.14 multiply(Y0, multiply(multiply(inverse(X2), Y2), multiply(multiply(inverse(multiply(Y0, X1)), X2), X1))) -> Y2 % 2.93/3.14 multiply(multiply(inverse(Y0), Y0), Y2) -> Y2 % 2.93/3.14 multiply(multiply(inverse(Y1), X1), multiply(multiply(inverse(X1), Y2), Y1)) -> Y2 % 2.93/3.14 multiply(multiply(inverse(Y1), Y2), Y1) -> Y2 % 2.93/3.14 multiply(multiply(inverse(Y3), Y1), multiply(multiply(inverse(multiply(Y1, Y2)), X1), multiply(Y3, Y2))) -> X1 % 2.93/3.14 multiply(multiply(inverse(multiply(inverse(Y0), X1)), X2), X1) -> multiply(X2, Y0) % 2.93/3.14 multiply(multiply(inverse(multiply(inverse(multiply(Y0, Y1)), X1)), X2), X1) -> multiply(Y0, multiply(X2, Y1)) % 2.93/3.14 true__ -> false__ % 2.93/3.14 with the LPO induced by % 2.93/3.14 b2 > inverse > multiply > a2 > f1 > true__ > false__ % 2.93/3.14 % 2.93/3.14 % SZS output end Proof % 2.93/3.14 %------------------------------------------------------------------------------