%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP515-1 : 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 10:55:57 EDT 2022 % Result : Unsatisfiable 48.83s 48.97s % Output : Proof 48.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : GRP515-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n005.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jun 13 22:05:24 EDT 2022 % 0.13/0.35 % CPUTime : % 48.83/48.97 % SZS status Unsatisfiable % 48.83/48.97 % SZS output start Proof % 48.83/48.97 The input problem is unsatisfiable because % 48.83/48.97 % 48.83/48.97 [1] the following set of Horn clauses is unsatisfiable: % 48.83/48.97 % 48.83/48.97 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B % 48.83/48.97 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 48.83/48.97 % 48.83/48.97 This holds because % 48.83/48.97 % 48.83/48.97 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 48.83/48.97 % 48.83/48.97 E: % 48.83/48.97 f1(multiply(a3, multiply(b3, c3))) = false__ % 48.83/48.97 f1(multiply(multiply(a3, b3), c3)) = true__ % 48.83/48.97 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B % 48.83/48.97 G: % 48.83/48.97 true__ = false__ % 48.83/48.97 % 48.83/48.97 This holds because % 48.83/48.97 % 48.83/48.97 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 48.83/48.97 % 48.83/48.97 inverse(multiply(X0, inverse(X0))) = multiply(Y1, inverse(Y1)) % 48.83/48.97 multiply(X1, Y2) = multiply(Y0, multiply(Y2, multiply(X1, inverse(Y0)))) % 48.83/48.97 multiply(X1, Y2) = multiply(multiply(Y0, Y2), inverse(multiply(Y0, inverse(X1)))) % 48.83/48.97 multiply(X1, multiply(X0, multiply(Y1, multiply(inverse(X1), multiply(inverse(X0), Y2))))) = multiply(Y2, Y1) % 48.83/48.97 multiply(X1, multiply(Y2, inverse(Y0))) = multiply(Y2, inverse(multiply(Y0, inverse(X1)))) % 48.83/48.97 multiply(X1, multiply(Y2, inverse(Y0))) = multiply(Y2, multiply(X1, inverse(Y0))) % 48.83/48.97 multiply(X1, multiply(inverse(X0), multiply(Y1, multiply(Y2, multiply(X0, inverse(X1)))))) = multiply(Y2, Y1) % 48.83/48.97 multiply(Y0, X0) = multiply(X0, Y0) % 48.83/48.97 multiply(Y0, X0) = multiply(X0, multiply(X1, inverse(multiply(X1, inverse(Y0))))) % 48.83/48.97 multiply(Y0, X1) = multiply(Y1, multiply(X1, inverse(multiply(Y1, inverse(Y0))))) % 48.83/48.97 multiply(Y0, inverse(Y0)) = multiply(X1, inverse(X1)) % 48.83/48.97 multiply(Y0, multiply(X0, inverse(multiply(X0, X1)))) = multiply(Y0, multiply(X2, inverse(multiply(X2, X1)))) % 48.83/48.97 multiply(Y0, multiply(Y1, Y2)) = multiply(Y2, multiply(Y0, Y1)) % 48.83/48.97 multiply(Y0, multiply(Y1, Y2)) = multiply(Y2, multiply(Y1, Y0)) % 48.83/48.97 multiply(Y0, multiply(multiply(X2, X1), inverse(multiply(Y0, multiply(X2, inverse(X0)))))) = multiply(X0, X1) % 48.83/48.97 multiply(Y2, multiply(Y0, Y1)) = multiply(Y0, multiply(Y2, Y1)) % 48.83/48.97 multiply(inverse(X1), multiply(X0, multiply(Y1, multiply(Y2, multiply(X1, inverse(X0)))))) = multiply(Y2, Y1) % 48.83/48.97 multiply(inverse(X1), multiply(inverse(X0), multiply(Y1, multiply(Y2, multiply(X0, X1))))) = multiply(Y2, Y1) % 48.83/48.97 multiply(inverse(inverse(Y1)), Y0) = multiply(Y0, Y1) % 48.83/48.97 multiply(multiply(X0, X1), multiply(Y1, inverse(X0))) = multiply(Y1, X1) % 48.83/48.97 multiply(multiply(X0, Y1), X1) = multiply(multiply(Y2, Y1), multiply(multiply(X0, X1), inverse(Y2))) % 48.83/48.97 multiply(multiply(X2, X1), Y2) = multiply(multiply(multiply(X0, X1), Y2), multiply(X2, inverse(X0))) % 48.83/48.97 multiply(multiply(X2, X1), multiply(Y2, inverse(multiply(X0, X1)))) = multiply(Y2, multiply(X2, inverse(X0))) % 48.83/48.97 multiply(multiply(X2, X1), multiply(Y2, inverse(multiply(Y2, multiply(X2, inverse(X0)))))) = multiply(X0, X1) % 48.83/48.97 multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))) = multiply(multiply(Y2, Y1), multiply(Y0, inverse(Y2))) % 48.83/48.97 multiply(multiply(Y0, Y1), X0) = multiply(multiply(X0, Y0), Y1) % 48.83/48.97 multiply(multiply(Y0, Y1), multiply(multiply(X0, inverse(Y0)), X1)) = multiply(multiply(X0, X1), Y1) % 48.83/48.97 multiply(multiply(Y0, Y1), multiply(multiply(X2, inverse(Y0)), multiply(Y2, inverse(X2)))) = multiply(Y2, Y1) % 48.83/48.97 multiply(multiply(Y1, Y2), X1) = multiply(multiply(Y1, X1), Y2) % 48.83/48.97 multiply(multiply(multiply(X0, Y1), X1), multiply(Y2, inverse(multiply(X0, X1)))) = multiply(Y2, Y1) % 48.83/48.97 multiply(multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))), Y2) = multiply(multiply(Y0, Y2), Y1) % 48.83/48.97 multiply(multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))), multiply(Y2, inverse(Y0))) = multiply(Y2, Y1) % 48.83/48.97 f1(multiply(a3, multiply(b3, c3))) -> false__ % 48.83/48.97 f1(multiply(multiply(a3, b3), c3)) -> true__ % 48.83/48.97 inverse(inverse(Y0)) -> Y0 % 48.83/48.97 inverse(multiply(Y0, X1)) -> multiply(inverse(X1), inverse(Y0)) % 48.83/48.97 inverse(multiply(Y0, inverse(X1))) -> multiply(X1, inverse(Y0)) % 48.83/48.97 inverse(multiply(Y0, inverse(X1))) -> multiply(inverse(Y0), X1) % 48.83/48.97 inverse(multiply(inverse(X1), Y0)) -> multiply(X1, inverse(Y0)) % 48.83/48.97 inverse(multiply(inverse(Y0), inverse(X1))) -> multiply(Y0, X1) % 48.83/48.97 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) -> B % 48.83/48.97 multiply(X0, inverse(inverse(X1))) -> multiply(X0, X1) % 48.83/48.97 multiply(X0, inverse(multiply(X0, X1))) -> inverse(X1) % 48.83/48.97 multiply(X0, multiply(X1, multiply(inverse(X0), multiply(Y0, inverse(X1))))) -> Y0 % 48.83/48.97 multiply(X0, multiply(Y2, inverse(multiply(X0, X1)))) -> multiply(Y2, inverse(X1)) % 48.83/48.97 multiply(X0, multiply(Y2, inverse(multiply(Y2, multiply(X2, inverse(multiply(X2, X1))))))) -> multiply(X0, X1) % 48.83/48.97 multiply(X1, inverse(inverse(multiply(Y0, inverse(X1))))) -> Y0 % 48.83/48.97 multiply(X1, inverse(multiply(X0, X1))) -> inverse(X0) % 48.83/48.97 multiply(X1, multiply(X0, multiply(Y0, multiply(inverse(X0), inverse(X1))))) -> Y0 % 48.83/48.97 multiply(X1, multiply(X0, multiply(Y1, multiply(inverse(X1), inverse(X0))))) -> Y1 % 48.83/48.97 multiply(X1, multiply(X0, multiply(Y2, inverse(X1)))) -> multiply(X0, Y2) % 48.83/48.97 multiply(X1, multiply(X0, multiply(inverse(X1), multiply(inverse(X0), Y1)))) -> Y1 % 48.83/48.97 multiply(X1, multiply(Y2, inverse(multiply(Y2, multiply(X1, inverse(Y0)))))) -> Y0 % 48.83/48.97 multiply(X1, multiply(Y2, inverse(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y0, X2))))))) -> Y0 % 48.83/48.97 multiply(X1, multiply(inverse(X0), multiply(Y1, multiply(X0, inverse(X1))))) -> Y1 % 48.83/48.97 multiply(X1, multiply(inverse(X0), multiply(inverse(X1), multiply(X0, Y1)))) -> Y1 % 48.83/48.97 multiply(X2, multiply(Y2, inverse(multiply(Y2, multiply(X1, inverse(multiply(Y0, multiply(X1, inverse(X2))))))))) -> Y0 % 48.83/48.97 multiply(Y0, inverse(multiply(Y1, inverse(X1)))) -> multiply(Y0, multiply(X1, inverse(Y1))) % 48.83/48.97 multiply(Y0, inverse(multiply(inverse(Y1), Y0))) -> Y1 % 48.83/48.97 multiply(Y0, inverse(multiply(multiply(X2, inverse(Y1)), multiply(Y0, inverse(X2))))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(X0, inverse(multiply(Y0, multiply(X2, inverse(multiply(X2, X1))))))) -> multiply(X0, X1) % 48.83/48.97 multiply(Y0, multiply(X0, multiply(inverse(Y0), X1))) -> multiply(X0, X1) % 48.83/48.97 multiply(Y0, multiply(X1, inverse(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y1, X2))))))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(X1, inverse(multiply(Y1, multiply(X1, inverse(X2)))))) -> multiply(Y0, multiply(X2, inverse(Y1))) % 48.83/48.97 multiply(Y0, multiply(Y1, inverse(Y0))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X1, inverse(multiply(Y3, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))))))))) -> Y3 % 48.83/48.97 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X2, inverse(multiply(Y3, multiply(X1, inverse(multiply(Y1, multiply(X1, inverse(X2)))))))))))) -> Y3 % 48.83/48.97 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 % 48.83/48.97 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y1, inverse(Y3)))))) -> Y3 % 48.83/48.97 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y2, inverse(multiply(Y3, multiply(Y2, inverse(Y1))))))))) -> Y3 % 48.83/48.97 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 % 48.83/48.97 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 % 48.83/48.97 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(Y4))), inverse(Y2)))))) -> Y4 % 48.83/48.97 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(Y3, X2)))), inverse(X1)))))) -> Y3 % 48.83/48.97 multiply(Y0, multiply(inverse(Y0), Y1)) -> Y1 % 48.83/48.97 multiply(Y0, multiply(inverse(inverse(inverse(Y0))), Y1)) -> Y1 % 48.83/48.97 multiply(Y0, multiply(multiply(X0, inverse(Y0)), X1)) -> multiply(X0, X1) % 48.83/48.97 multiply(Y0, multiply(multiply(X1, X2), inverse(X1))) -> multiply(Y0, X2) % 48.83/48.97 multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))) -> multiply(Y0, multiply(X1, inverse(Y1))) % 48.83/48.97 multiply(Y0, multiply(multiply(X1, multiply(X2, inverse(Y1))), inverse(X2))) -> multiply(Y0, multiply(X1, inverse(Y1))) % 48.83/48.97 multiply(Y0, multiply(multiply(X1, multiply(Y2, inverse(Y0))), inverse(X1))) -> Y2 % 48.83/48.97 multiply(Y0, multiply(multiply(X2, inverse(Y0)), multiply(Y1, inverse(X2)))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(multiply(X2, inverse(multiply(Y0, Y2))), multiply(multiply(Y1, Y2), inverse(X2)))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(multiply(Y1, Y2), inverse(multiply(multiply(X2, Y2), multiply(Y0, inverse(X2)))))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(multiply(Y1, inverse(Y1)), Y2)) -> multiply(Y0, Y2) % 48.83/48.97 multiply(Y0, multiply(multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(X1, inverse(X2)))))), inverse(X2))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(X3, X2))))))), inverse(X3))) -> Y1 % 48.83/48.97 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 % 48.83/48.97 multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(Y0))), inverse(Y2))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(Y0, X2)))), inverse(X1))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, multiply(X2, inverse(Y0))), inverse(X2))), inverse(X1))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(multiply(Y1, multiply(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y0, X2)))), inverse(X1))), inverse(Y2))) -> Y1 % 48.83/48.97 multiply(Y0, multiply(multiply(multiply(X0, Y2), X1), inverse(multiply(Y0, Y2)))) -> multiply(X0, X1) % 48.83/48.97 multiply(Y0, multiply(multiply(multiply(X2, Y2), multiply(Y1, inverse(X2))), inverse(multiply(Y0, Y2)))) -> Y1 % 48.83/48.97 multiply(Y1, inverse(multiply(Y1, inverse(Y0)))) -> Y0 % 48.83/48.97 multiply(Y3, multiply(Y1, inverse(Y1))) -> Y3 % 48.83/48.97 multiply(inverse(X1), multiply(X0, multiply(Y1, multiply(X1, inverse(X0))))) -> Y1 % 48.83/48.97 multiply(inverse(X1), multiply(X0, multiply(Y1, multiply(inverse(X0), X1)))) -> Y1 % 48.83/48.97 multiply(inverse(X1), multiply(inverse(X0), multiply(Y1, multiply(X0, X1)))) -> Y1 % 48.83/48.97 multiply(inverse(Y0), multiply(X1, multiply(Y0, inverse(X2)))) -> multiply(X1, inverse(X2)) % 48.83/48.97 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1 % 48.83/48.97 multiply(inverse(Y1), multiply(Y0, Y1)) -> Y0 % 48.83/48.97 multiply(inverse(inverse(Y1)), Y0) -> multiply(Y1, Y0) % 48.83/48.97 multiply(inverse(inverse(multiply(X1, inverse(X1)))), Y0) -> Y0 % 48.83/48.97 multiply(inverse(multiply(X1, inverse(X1))), Y1) -> Y1 % 48.83/48.97 multiply(multiply(X0, X1), inverse(multiply(multiply(X0, inverse(Y1)), X1))) -> Y1 % 48.83/48.97 multiply(multiply(X0, X1), multiply(multiply(Y1, multiply(X2, inverse(X0))), inverse(multiply(X2, X1)))) -> Y1 % 48.83/48.97 multiply(multiply(X0, X1), multiply(multiply(Y1, multiply(X2, inverse(multiply(X2, X1)))), inverse(X0))) -> Y1 % 48.83/48.97 multiply(multiply(X0, Y1), inverse(X0)) -> Y1 % 48.83/48.97 multiply(multiply(Y0, Y2), Y1) -> multiply(Y2, multiply(Y0, Y1)) % 48.83/48.97 multiply(multiply(Y0, multiply(X1, inverse(multiply(Y2, multiply(X1, inverse(X2)))))), multiply(Y2, inverse(X2))) -> Y0 % 48.83/48.97 multiply(multiply(Y0, multiply(X2, inverse(multiply(X2, X1)))), X1) -> Y0 % 48.83/48.97 multiply(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y2, X2)))), multiply(Y2, inverse(X1))) -> Y0 % 48.83/48.97 multiply(multiply(Y1, X1), inverse(X1)) -> Y1 % 48.83/48.97 multiply(multiply(Y1, inverse(Y1)), Y0) -> Y0 % 48.83/48.97 multiply(multiply(Y1, multiply(Y2, inverse(X2))), multiply(X2, inverse(Y2))) -> Y1 % 48.83/48.97 multiply(multiply(Y2, multiply(X2, inverse(X0))), multiply(multiply(X0, X1), inverse(Y2))) -> multiply(X2, X1) % 48.83/48.97 multiply(multiply(Y3, Y2), multiply(Y1, inverse(multiply(Y1, Y2)))) -> Y3 % 48.83/48.97 multiply(multiply(false__, Y2), multiply(multiply(Y0, inverse(false__)), multiply(X0, inverse(multiply(X0, Y2))))) -> Y0 % 48.83/48.97 multiply(multiply(multiply(X0, X1), Y2), inverse(X1)) -> multiply(X0, Y2) % 48.83/48.97 multiply(multiply(multiply(X0, Y1), X1), multiply(Y2, inverse(multiply(Y2, Y1)))) -> multiply(X0, X1) % 48.83/48.97 multiply(multiply(multiply(X0, multiply(Y1, inverse(multiply(Y1, Y2)))), X1), Y2) -> multiply(X0, X1) % 48.83/48.97 multiply(multiply(multiply(Y2, inverse(X1)), Y1), X1) -> multiply(Y2, Y1) % 48.83/48.97 true__ -> false__ % 48.83/48.97 with the LPO induced by % 48.83/48.97 c3 > b3 > a3 > f1 > inverse > multiply > true__ > false__ % 48.83/48.97 % 48.83/48.97 % SZS output end Proof % 48.83/48.97 %------------------------------------------------------------------------------