%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP516-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n015.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 6.05s 6.17s % Output : Proof 6.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP516-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n015.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jun 13 13:17:08 EDT 2022 % 0.12/0.34 % CPUTime : % 6.05/6.17 % SZS status Unsatisfiable % 6.05/6.17 % SZS output start Proof % 6.05/6.17 The input problem is unsatisfiable because % 6.05/6.17 % 6.05/6.17 [1] the following set of Horn clauses is unsatisfiable: % 6.05/6.17 % 6.05/6.17 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B % 6.05/6.17 multiply(a, b) = multiply(b, a) ==> \bottom % 6.05/6.17 % 6.05/6.17 This holds because % 6.05/6.17 % 6.05/6.17 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.05/6.17 % 6.05/6.17 E: % 6.05/6.17 f1(multiply(a, b)) = true__ % 6.05/6.17 f1(multiply(b, a)) = false__ % 6.05/6.17 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B % 6.05/6.17 G: % 6.05/6.17 true__ = false__ % 6.05/6.17 % 6.05/6.17 This holds because % 6.05/6.17 % 6.05/6.17 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.05/6.17 % 6.05/6.17 multiply(X1, Y2) = multiply(multiply(Y0, Y2), inverse(multiply(Y0, inverse(X1)))) % 6.05/6.17 multiply(X1, multiply(Y2, inverse(Y0))) = multiply(Y2, inverse(multiply(Y0, inverse(X1)))) % 6.05/6.17 multiply(X1, multiply(Y2, inverse(Y0))) = multiply(Y2, multiply(X1, inverse(Y0))) % 6.05/6.17 multiply(Y0, X0) = multiply(X0, Y0) % 6.05/6.17 multiply(Y0, X0) = multiply(X0, multiply(X1, inverse(multiply(X1, inverse(Y0))))) % 6.05/6.17 multiply(Y0, X1) = multiply(Y1, multiply(X1, inverse(multiply(Y1, inverse(Y0))))) % 6.05/6.17 multiply(Y0, inverse(Y0)) = multiply(X1, inverse(X1)) % 6.05/6.17 multiply(Y0, multiply(X0, inverse(multiply(X0, X1)))) = multiply(Y0, multiply(X2, inverse(multiply(X2, X1)))) % 6.05/6.17 multiply(Y0, multiply(multiply(X2, X1), inverse(multiply(Y0, multiply(X2, inverse(X0)))))) = multiply(X0, X1) % 6.05/6.17 multiply(multiply(X0, X1), multiply(Y1, inverse(X0))) = multiply(Y1, X1) % 6.05/6.17 multiply(multiply(X0, Y1), X1) = multiply(multiply(Y2, Y1), multiply(multiply(X0, X1), inverse(Y2))) % 6.05/6.17 multiply(multiply(X2, X1), Y2) = multiply(multiply(multiply(X0, X1), Y2), multiply(X2, inverse(X0))) % 6.05/6.17 multiply(multiply(X2, X1), multiply(Y2, inverse(multiply(X0, X1)))) = multiply(Y2, multiply(X2, inverse(X0))) % 6.05/6.17 multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))) = multiply(multiply(Y2, Y1), multiply(Y0, inverse(Y2))) % 6.05/6.17 multiply(multiply(Y0, Y1), X0) = multiply(multiply(X0, Y0), Y1) % 6.05/6.17 multiply(multiply(Y0, Y1), multiply(multiply(X0, inverse(Y0)), X1)) = multiply(multiply(X0, X1), Y1) % 6.05/6.17 multiply(multiply(Y0, Y1), multiply(multiply(X2, inverse(Y0)), multiply(Y2, inverse(X2)))) = multiply(Y2, Y1) % 6.05/6.17 multiply(multiply(Y1, Y2), X1) = multiply(multiply(Y1, X1), Y2) % 6.05/6.17 multiply(multiply(multiply(X0, Y1), X1), multiply(Y2, inverse(multiply(X0, X1)))) = multiply(Y2, Y1) % 6.05/6.17 multiply(multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))), Y2) = multiply(multiply(Y0, Y2), Y1) % 6.05/6.17 multiply(multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))), multiply(Y2, inverse(Y0))) = multiply(Y2, Y1) % 6.05/6.17 f1(multiply(a, b)) -> true__ % 6.05/6.17 f1(multiply(b, a)) -> false__ % 6.05/6.17 f1(multiply(multiply(X2, b), multiply(a, inverse(X2)))) -> true__ % 6.05/6.17 f1(multiply(multiply(Y0, b), multiply(multiply(X2, inverse(Y0)), multiply(a, inverse(X2))))) -> true__ % 6.05/6.17 f1(multiply(multiply(multiply(X0, b), X1), multiply(a, inverse(multiply(X0, X1))))) -> true__ % 6.05/6.17 f1(multiply(multiply(multiply(X2, b), multiply(Y0, inverse(X2))), multiply(a, inverse(Y0)))) -> true__ % 6.05/6.17 f1(multiply(multiply(multiply(false__, X1), b), multiply(multiply(a, inverse(X1)), inverse(false__)))) -> true__ % 6.05/6.17 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) -> B % 6.05/6.17 multiply(X0, inverse(inverse(X1))) -> multiply(X0, X1) % 6.05/6.17 multiply(X0, multiply(Y2, inverse(multiply(X0, X1)))) -> multiply(Y2, inverse(X1)) % 6.05/6.17 multiply(X0, multiply(Y2, inverse(multiply(Y2, multiply(X2, inverse(multiply(X2, X1))))))) -> multiply(X0, X1) % 6.05/6.17 multiply(X1, inverse(inverse(multiply(Y0, inverse(X1))))) -> Y0 % 6.05/6.17 multiply(X1, multiply(Y2, inverse(multiply(Y2, multiply(X1, inverse(Y0)))))) -> Y0 % 6.05/6.17 multiply(X1, multiply(Y2, inverse(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y0, X2))))))) -> Y0 % 6.05/6.17 multiply(X2, multiply(Y2, inverse(multiply(Y2, multiply(X1, inverse(multiply(Y0, multiply(X1, inverse(X2))))))))) -> Y0 % 6.05/6.17 multiply(Y0, inverse(multiply(inverse(Y1), Y0))) -> Y1 % 6.05/6.17 multiply(Y0, inverse(multiply(multiply(X2, inverse(Y1)), multiply(Y0, inverse(X2))))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(X0, inverse(multiply(Y0, multiply(X2, inverse(multiply(X2, X1))))))) -> multiply(X0, X1) % 6.05/6.17 multiply(Y0, multiply(X1, inverse(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y1, X2))))))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(X1, inverse(multiply(Y1, multiply(X1, inverse(X2)))))) -> multiply(Y0, multiply(X2, inverse(Y1))) % 6.05/6.17 multiply(Y0, multiply(Y1, inverse(Y0))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X1, inverse(multiply(Y3, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))))))))) -> Y3 % 6.05/6.17 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X2, inverse(multiply(Y3, multiply(X1, inverse(multiply(Y1, multiply(X1, inverse(X2)))))))))))) -> Y3 % 6.05/6.17 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X3, inverse(multiply(Y3, multiply(X1, inverse(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(X3, X2))))))))))))) -> Y3 % 6.05/6.17 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y1, inverse(Y3)))))) -> Y3 % 6.05/6.17 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y2, inverse(multiply(Y3, multiply(Y2, inverse(Y1))))))))) -> Y3 % 6.05/6.17 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y2, inverse(multiply(Y3, multiply(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))), inverse(X1))))))))) -> Y3 % 6.05/6.17 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(X1, inverse(multiply(Y3, multiply(multiply(X1, X2), inverse(multiply(X3, X2))))))), inverse(X3)))))) -> Y3 % 6.05/6.17 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(Y4))), inverse(Y2)))))) -> Y4 % 6.05/6.17 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(Y3, X2)))), inverse(X1)))))) -> Y3 % 6.05/6.17 multiply(Y0, multiply(inverse(Y0), Y1)) -> Y1 % 6.05/6.17 multiply(Y0, multiply(multiply(X0, inverse(Y0)), X1)) -> multiply(X0, X1) % 6.05/6.17 multiply(Y0, multiply(multiply(X1, X2), inverse(X1))) -> multiply(Y0, X2) % 6.05/6.17 multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))) -> multiply(Y0, multiply(X1, inverse(Y1))) % 6.05/6.17 multiply(Y0, multiply(multiply(X1, multiply(X2, inverse(Y1))), inverse(X2))) -> multiply(Y0, multiply(X1, inverse(Y1))) % 6.05/6.17 multiply(Y0, multiply(multiply(X1, multiply(Y2, inverse(Y0))), inverse(X1))) -> Y2 % 6.05/6.17 multiply(Y0, multiply(multiply(X2, inverse(Y0)), multiply(Y1, inverse(X2)))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(multiply(X2, inverse(multiply(Y0, Y2))), multiply(multiply(Y1, Y2), inverse(X2)))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(multiply(Y1, inverse(Y1)), Y2)) -> multiply(Y0, Y2) % 6.05/6.17 multiply(Y0, multiply(multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(X1, inverse(X2)))))), inverse(X2))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(X3, X2))))))), inverse(X3))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(multiply(Y1, multiply(X3, inverse(multiply(Y0, multiply(X1, inverse(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(X3, X2)))))))))), inverse(Y2))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(Y0))), inverse(Y2))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(Y0, X2)))), inverse(X1))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, multiply(X2, inverse(Y0))), inverse(X2))), inverse(X1))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(multiply(Y1, multiply(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y0, X2)))), inverse(X1))), inverse(Y2))) -> Y1 % 6.05/6.17 multiply(Y0, multiply(multiply(multiply(X0, Y2), X1), inverse(multiply(Y0, Y2)))) -> multiply(X0, X1) % 6.05/6.17 multiply(Y1, inverse(multiply(Y1, inverse(Y0)))) -> Y0 % 6.05/6.17 multiply(Y3, multiply(Y1, inverse(Y1))) -> Y3 % 6.05/6.17 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1 % 6.05/6.17 multiply(inverse(Y1), multiply(Y0, Y1)) -> Y0 % 6.05/6.17 multiply(multiply(X0, X1), inverse(multiply(multiply(X0, inverse(Y1)), X1))) -> Y1 % 6.05/6.17 multiply(multiply(X0, X1), multiply(multiply(Y1, multiply(X2, inverse(X0))), inverse(multiply(X2, X1)))) -> Y1 % 6.05/6.17 multiply(multiply(X0, X1), multiply(multiply(Y1, multiply(X2, inverse(multiply(X2, X1)))), inverse(X0))) -> Y1 % 6.05/6.17 multiply(multiply(X0, Y1), inverse(X0)) -> Y1 % 6.05/6.17 multiply(multiply(Y0, multiply(X1, inverse(multiply(Y2, multiply(X1, inverse(X2)))))), multiply(Y2, inverse(X2))) -> Y0 % 6.05/6.17 multiply(multiply(Y0, multiply(X2, inverse(multiply(X2, X1)))), X1) -> Y0 % 6.05/6.17 multiply(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y2, X2)))), multiply(Y2, inverse(X1))) -> Y0 % 6.05/6.17 multiply(multiply(Y1, X1), inverse(X1)) -> Y1 % 6.05/6.17 multiply(multiply(Y1, inverse(Y1)), Y0) -> Y0 % 6.05/6.17 multiply(multiply(Y1, multiply(Y2, inverse(X2))), multiply(X2, inverse(Y2))) -> Y1 % 6.05/6.17 multiply(multiply(Y2, multiply(X2, inverse(X0))), multiply(multiply(X0, X1), inverse(Y2))) -> multiply(X2, X1) % 6.05/6.17 multiply(multiply(Y3, Y2), multiply(Y1, inverse(multiply(Y1, Y2)))) -> Y3 % 6.05/6.17 multiply(multiply(multiply(X0, X1), Y2), inverse(X1)) -> multiply(X0, Y2) % 6.05/6.17 multiply(multiply(multiply(X0, Y1), X1), multiply(Y2, inverse(multiply(Y2, Y1)))) -> multiply(X0, X1) % 6.05/6.17 multiply(multiply(multiply(X0, multiply(Y1, inverse(multiply(Y1, Y2)))), X1), Y2) -> multiply(X0, X1) % 6.05/6.17 multiply(multiply(multiply(Y2, inverse(X1)), Y1), X1) -> multiply(Y2, Y1) % 6.05/6.17 true__ -> false__ % 6.05/6.17 with the LPO induced by % 6.05/6.17 a > b > f1 > inverse > multiply > true__ > false__ % 6.05/6.17 % 6.05/6.17 % SZS output end Proof % 6.05/6.17 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