%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP514-1 : 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 10:55:57 EDT 2022 % Result : Unsatisfiable 4.73s 4.92s % Output : Proof 4.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : GRP514-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.12 % Command : moca.sh %s % 0.11/0.32 % Computer : n022.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Mon Jun 13 13:48:03 EDT 2022 % 0.11/0.32 % CPUTime : % 4.73/4.92 % SZS status Unsatisfiable % 4.73/4.92 % SZS output start Proof % 4.73/4.92 The input problem is unsatisfiable because % 4.73/4.92 % 4.73/4.92 [1] the following set of Horn clauses is unsatisfiable: % 4.73/4.92 % 4.73/4.92 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B % 4.73/4.92 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 4.73/4.92 % 4.73/4.92 This holds because % 4.73/4.92 % 4.73/4.92 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.73/4.92 % 4.73/4.92 E: % 4.73/4.92 f1(a2) = false__ % 4.73/4.92 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 4.73/4.92 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B % 4.73/4.92 G: % 4.73/4.92 true__ = false__ % 4.73/4.92 % 4.73/4.92 This holds because % 4.73/4.92 % 4.73/4.92 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.73/4.92 % 4.73/4.92 inverse(multiply(X0, inverse(X0))) = multiply(Y1, inverse(Y1)) % 4.73/4.92 multiply(X1, inverse(inverse(X0))) = multiply(X0, X1) % 4.73/4.92 multiply(X1, multiply(Y2, inverse(Y0))) = multiply(Y2, multiply(X1, inverse(Y0))) % 4.73/4.92 multiply(Y0, X0) = multiply(X0, Y0) % 4.73/4.92 multiply(Y0, X0) = multiply(X0, multiply(X1, inverse(multiply(X1, inverse(Y0))))) % 4.73/4.92 multiply(Y0, inverse(Y0)) = multiply(X1, inverse(X1)) % 4.73/4.92 multiply(Y0, multiply(X0, inverse(multiply(X0, X1)))) = multiply(Y0, multiply(X2, inverse(multiply(X2, X1)))) % 4.73/4.92 multiply(Y0, multiply(X0, inverse(multiply(Y0, Y2)))) = multiply(X0, multiply(X1, inverse(multiply(X1, Y2)))) % 4.73/4.92 multiply(Y0, multiply(multiply(X2, X1), inverse(multiply(Y0, multiply(X2, inverse(X0)))))) = multiply(X0, X1) % 4.73/4.92 multiply(Y1, multiply(Y2, inverse(multiply(X0, inverse(X0))))) = multiply(Y2, Y1) % 4.73/4.92 multiply(multiply(X0, X1), multiply(Y1, inverse(X0))) = multiply(Y1, X1) % 4.73/4.92 multiply(multiply(X2, X1), multiply(Y2, inverse(multiply(X0, X1)))) = multiply(Y2, multiply(X2, inverse(X0))) % 4.73/4.92 multiply(multiply(X2, X1), multiply(Y2, inverse(multiply(Y2, multiply(X2, inverse(X0)))))) = multiply(X0, X1) % 4.73/4.92 multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))) = multiply(multiply(Y2, Y1), multiply(Y0, inverse(Y2))) % 4.73/4.92 multiply(multiply(Y0, Y1), multiply(multiply(X2, inverse(Y0)), multiply(Y2, inverse(X2)))) = multiply(Y2, Y1) % 4.73/4.92 multiply(multiply(inverse(X0), Y1), multiply(Y2, X0)) = multiply(Y2, Y1) % 4.73/4.92 multiply(multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))), multiply(Y2, inverse(Y0))) = multiply(Y2, Y1) % 4.73/4.92 f1(a2) -> false__ % 4.73/4.92 f1(multiply(inverse(false__), multiply(false__, a2))) -> true__ % 4.73/4.92 f1(multiply(multiply(X2, a2), multiply(multiply(multiply(false__, b2), multiply(inverse(b2), inverse(false__))), inverse(X2)))) -> true__ % 4.73/4.92 f1(multiply(multiply(false__, a2), multiply(multiply(multiply(X2, b2), multiply(inverse(b2), inverse(X2))), inverse(false__)))) -> true__ % 4.73/4.92 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 4.73/4.92 inverse(inverse(Y0)) -> Y0 % 4.73/4.92 inverse(multiply(X1, inverse(Y0))) -> multiply(Y0, inverse(X1)) % 4.73/4.92 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) -> B % 4.73/4.92 multiply(X0, inverse(inverse(X1))) -> multiply(X0, X1) % 4.73/4.92 multiply(X0, inverse(multiply(X0, X1))) -> inverse(X1) % 4.73/4.92 multiply(X0, multiply(Y2, inverse(multiply(Y2, multiply(X2, inverse(multiply(X2, X1))))))) -> multiply(X0, X1) % 4.73/4.92 multiply(X1, inverse(multiply(X0, X1))) -> inverse(X0) % 4.73/4.92 multiply(X1, multiply(Y2, inverse(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y0, X2))))))) -> Y0 % 4.73/4.92 multiply(X2, multiply(Y2, inverse(multiply(Y2, multiply(X1, inverse(multiply(Y0, multiply(X1, inverse(X2))))))))) -> Y0 % 4.73/4.92 multiply(Y0, inverse(multiply(X0, inverse(X0)))) -> Y0 % 4.73/4.92 multiply(Y0, inverse(multiply(Y0, inverse(Y1)))) -> Y1 % 4.73/4.92 multiply(Y0, multiply(X0, inverse(multiply(Y0, multiply(X2, inverse(multiply(X2, X1))))))) -> multiply(X0, X1) % 4.73/4.92 multiply(Y0, multiply(X1, inverse(multiply(X1, inverse(Y1))))) -> multiply(Y0, Y1) % 4.73/4.92 multiply(Y0, multiply(X1, inverse(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y1, X2))))))) -> Y1 % 4.73/4.92 multiply(Y0, multiply(Y1, inverse(Y0))) -> Y1 % 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X1, inverse(multiply(Y3, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))))))))) -> Y3 % 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X2, inverse(multiply(Y3, multiply(X1, inverse(multiply(Y1, multiply(X1, inverse(X2)))))))))))) -> Y3 % 4.73/4.92 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 % 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y1, inverse(Y3)))))) -> Y3 % 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y2, inverse(multiply(Y3, multiply(Y2, inverse(Y1))))))))) -> Y3 % 4.73/4.92 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 % 4.73/4.92 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 % 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(Y4))), inverse(Y2)))))) -> Y4 % 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(Y3, X2)))), inverse(X1)))))) -> Y3 % 4.73/4.92 multiply(Y0, multiply(inverse(Y0), Y1)) -> Y1 % 4.73/4.92 multiply(Y0, multiply(multiply(X1, X2), inverse(X1))) -> multiply(Y0, X2) % 4.73/4.92 multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))) -> multiply(Y0, multiply(X1, inverse(Y1))) % 4.73/4.92 multiply(Y0, multiply(multiply(X1, multiply(Y2, inverse(Y0))), inverse(X1))) -> Y2 % 4.73/4.92 multiply(Y0, multiply(multiply(X2, inverse(Y0)), multiply(Y1, inverse(X2)))) -> Y1 % 4.73/4.92 multiply(Y0, multiply(multiply(X2, inverse(multiply(Y0, Y2))), multiply(multiply(Y1, Y2), inverse(X2)))) -> Y1 % 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(X3, X2))))))), inverse(X3))) -> Y1 % 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(Y0))), inverse(Y2))) -> Y1 % 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(multiply(Y0, multiply(Y2, inverse(Y4)))))), inverse(Y4))) -> Y1 % 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(Y0, X2)))), inverse(X1))) -> Y1 % 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(multiply(Y2, multiply(X1, inverse(Y0))), inverse(X1))), inverse(Y2))) -> Y1 % 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y0, X2)))), inverse(X1))), inverse(Y2))) -> Y1 % 4.73/4.92 multiply(Y2, multiply(Y1, inverse(multiply(Y1, multiply(Y2, inverse(Y3)))))) -> Y3 % 4.73/4.92 multiply(Y3, multiply(Y1, inverse(Y1))) -> Y3 % 4.73/4.92 multiply(inverse(X0), multiply(Y1, X0)) -> Y1 % 4.73/4.92 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1 % 4.73/4.92 multiply(inverse(multiply(X0, inverse(X0))), Y1) -> Y1 % 4.73/4.92 multiply(multiply(X0, X1), multiply(multiply(Y1, multiply(X2, inverse(X0))), inverse(multiply(X2, X1)))) -> Y1 % 4.73/4.92 multiply(multiply(X0, X1), multiply(multiply(Y1, multiply(X2, inverse(multiply(X2, X1)))), inverse(X0))) -> Y1 % 4.73/4.92 multiply(multiply(X0, multiply(X1, inverse(multiply(X1, Y2)))), multiply(multiply(Y1, Y2), inverse(X0))) -> Y1 % 4.73/4.92 multiply(multiply(X1, inverse(X1)), Y0) -> Y0 % 4.73/4.92 multiply(multiply(Y0, Y1), inverse(Y0)) -> Y1 % 4.73/4.92 multiply(multiply(Y0, multiply(X2, inverse(multiply(X2, X1)))), X1) -> Y0 % 4.73/4.92 multiply(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y2, X2)))), multiply(Y2, inverse(X1))) -> Y0 % 4.73/4.92 multiply(multiply(Y1, Y2), inverse(Y2)) -> Y1 % 4.73/4.92 multiply(multiply(Y2, multiply(X2, inverse(X0))), multiply(multiply(X0, X1), inverse(Y2))) -> multiply(X2, X1) % 4.73/4.92 multiply(multiply(Y3, Y2), multiply(Y1, inverse(multiply(Y1, Y2)))) -> Y3 % 4.73/4.92 multiply(multiply(Y3, multiply(Y2, inverse(Y1))), multiply(Y1, inverse(Y2))) -> Y3 % 4.73/4.92 true__ -> false__ % 4.73/4.92 with the LPO induced by % 4.73/4.92 b2 > a2 > f1 > inverse > multiply > true__ > false__ % 4.73/4.92 % 4.73/4.92 % SZS output end Proof % 4.73/4.92 %------------------------------------------------------------------------------