%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP562-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.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 10:56:17 EDT 2022 % Result : Unsatisfiable 2.09s 2.28s % Output : Proof 2.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP562-1 : TPTP v8.1.0. Released v2.6.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n011.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 09:51:33 EDT 2022 % 0.13/0.34 % CPUTime : % 2.09/2.28 % SZS status Unsatisfiable % 2.09/2.28 % SZS output start Proof % 2.09/2.28 The input problem is unsatisfiable because % 2.09/2.28 % 2.09/2.28 [1] the following set of Horn clauses is unsatisfiable: % 2.09/2.28 % 2.09/2.28 divide(divide(divide(A, inverse(B)), C), divide(A, C)) = B % 2.09/2.28 multiply(A, B) = divide(A, inverse(B)) % 2.09/2.28 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 2.09/2.28 % 2.09/2.28 This holds because % 2.09/2.28 % 2.09/2.28 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.09/2.28 % 2.09/2.28 E: % 2.09/2.28 divide(divide(divide(A, inverse(B)), C), divide(A, C)) = B % 2.09/2.28 f1(a2) = false__ % 2.09/2.28 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 2.09/2.28 multiply(A, B) = divide(A, inverse(B)) % 2.09/2.28 G: % 2.09/2.28 true__ = false__ % 2.09/2.28 % 2.09/2.28 This holds because % 2.09/2.28 % 2.09/2.28 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.09/2.28 % 2.09/2.28 divide(Y0, X1) = divide(inverse(X1), inverse(Y0)) % 2.09/2.28 divide(inverse(inverse(Y1)), inverse(Y0)) = divide(Y0, inverse(Y1)) % 2.09/2.28 divide(X1, divide(Y0, divide(inverse(X1), inverse(divide(Y0, inverse(Y1)))))) -> Y1 % 2.09/2.28 divide(X1, divide(divide(X0, inverse(X1)), divide(X0, inverse(Y1)))) -> Y1 % 2.09/2.28 divide(X1, divide(divide(inverse(Y2), inverse(divide(Y1, inverse(X1)))), Y1)) -> Y2 % 2.09/2.28 divide(X1, divide(inverse(Y1), inverse(X1))) -> Y1 % 2.09/2.28 divide(X2, divide(Y0, divide(divide(X1, inverse(divide(Y0, inverse(Y1)))), divide(X1, inverse(X2))))) -> Y1 % 2.09/2.28 divide(Y0, divide(X1, divide(divide(inverse(Y0), inverse(X1)), inverse(Y2)))) -> Y2 % 2.09/2.28 divide(Y0, divide(divide(divide(inverse(Y2), inverse(X1)), inverse(Y0)), X1)) -> Y2 % 2.09/2.28 divide(Y0, multiply(inverse(inverse(Y0)), inverse(Y1))) -> Y1 % 2.09/2.28 divide(Y1, divide(Y2, Y2)) -> Y1 % 2.09/2.28 divide(divide(X1, X1), inverse(Y1)) -> Y1 % 2.09/2.28 divide(divide(X1, Y2), divide(divide(inverse(Y1), inverse(X1)), Y2)) -> Y1 % 2.09/2.28 divide(divide(Y1, inverse(Y3)), Y1) -> Y3 % 2.09/2.28 divide(divide(divide(A, inverse(B)), C), divide(A, C)) -> B % 2.09/2.28 divide(divide(divide(Y0, inverse(Y1)), divide(divide(X1, inverse(Y0)), divide(X1, inverse(X2)))), X2) -> Y1 % 2.09/2.28 divide(divide(divide(Y0, inverse(Y1)), divide(inverse(X1), inverse(Y0))), X1) -> Y1 % 2.09/2.28 divide(divide(divide(Y0, inverse(divide(X1, X1))), inverse(Y2)), Y0) -> Y2 % 2.09/2.28 divide(divide(divide(divide(Y2, inverse(X1)), inverse(Y1)), Y2), X1) -> Y1 % 2.09/2.28 divide(divide(divide(divide(divide(X0, inverse(X1)), X2), inverse(Y1)), divide(X0, X2)), X1) -> Y1 % 2.09/2.28 divide(inverse(Y0), inverse(divide(Y0, inverse(Y1)))) -> Y1 % 2.09/2.28 divide(inverse(Y0), inverse(divide(inverse(inverse(Y1)), inverse(Y0)))) -> Y1 % 2.09/2.28 divide(inverse(divide(X1, X1)), inverse(Y0)) -> Y0 % 2.09/2.28 divide(inverse(inverse(X0)), inverse(X1)) -> divide(X0, inverse(X1)) % 2.09/2.28 divide(inverse(inverse(X1)), inverse(divide(X0, X0))) -> X1 % 2.09/2.28 divide(inverse(inverse(divide(X0, X0))), inverse(Y1)) -> Y1 % 2.09/2.28 divide(multiply(inverse(inverse(Y1)), Y0), Y0) -> Y1 % 2.09/2.28 f1(a2) -> false__ % 2.09/2.28 f1(divide(divide(inverse(b2), inverse(b2)), inverse(a2))) -> true__ % 2.09/2.28 f1(multiply(divide(b2, b2), a2)) -> true__ % 2.09/2.28 multiply(A, B) -> divide(A, inverse(B)) % 2.09/2.28 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1 % 2.09/2.28 multiply(inverse(divide(X1, X1)), Y0) -> Y0 % 2.09/2.28 multiply(inverse(inverse(Y1)), divide(Y0, Y0)) -> Y1 % 2.09/2.28 true__ -> false__ % 2.09/2.28 with the LPO induced by % 2.09/2.28 b2 > multiply > divide > inverse > a2 > f1 > true__ > false__ % 2.09/2.28 % 2.09/2.28 % SZS output end Proof % 2.09/2.28 %------------------------------------------------------------------------------