%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO021-1 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n017.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 : Thu Jul 14 23:46:31 EDT 2022 % Result : Unsatisfiable 2.22s 2.36s % Output : Proof 2.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : BOO021-1 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n017.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 % 0.12/0.33 % DateTime : Wed Jun 1 22:16:12 EDT 2022 % 0.12/0.33 % CPUTime : % 2.22/2.36 % SZS status Unsatisfiable % 2.22/2.36 % SZS output start Proof % 2.22/2.36 The input problem is unsatisfiable because % 2.22/2.36 % 2.22/2.36 [1] the following set of Horn clauses is unsatisfiable: % 2.22/2.36 % 2.22/2.36 multiply(add(X, Y), Y) = Y % 2.22/2.36 multiply(X, add(Y, Z)) = add(multiply(Y, X), multiply(Z, X)) % 2.22/2.36 add(X, inverse(X)) = n1 % 2.22/2.36 add(multiply(X, Y), Y) = Y % 2.22/2.36 add(X, multiply(Y, Z)) = multiply(add(Y, X), add(Z, X)) % 2.22/2.36 multiply(X, inverse(X)) = n0 % 2.22/2.36 multiply(b, a) = multiply(a, b) ==> \bottom % 2.22/2.36 % 2.22/2.36 This holds because % 2.22/2.36 % 2.22/2.36 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.22/2.36 % 2.22/2.36 E: % 2.22/2.36 add(X, inverse(X)) = n1 % 2.22/2.36 add(X, multiply(Y, Z)) = multiply(add(Y, X), add(Z, X)) % 2.22/2.36 add(multiply(X, Y), Y) = Y % 2.22/2.36 f1(multiply(a, b)) = false__ % 2.22/2.36 f1(multiply(b, a)) = true__ % 2.22/2.36 multiply(X, add(Y, Z)) = add(multiply(Y, X), multiply(Z, X)) % 2.22/2.36 multiply(X, inverse(X)) = n0 % 2.22/2.36 multiply(add(X, Y), Y) = Y % 2.22/2.36 G: % 2.22/2.36 true__ = false__ % 2.22/2.36 % 2.22/2.36 This holds because % 2.22/2.36 % 2.22/2.36 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.22/2.36 % 2.22/2.36 add(inverse(n1), Y1) = add(Y1, inverse(n1)) % 2.22/2.36 add(inverse(n1), multiply(Y2, inverse(Y0))) = multiply(inverse(Y0), add(Y0, Y2)) % 2.22/2.36 add(multiply(Y0, inverse(Y2)), inverse(n1)) = multiply(inverse(Y2), add(Y0, Y2)) % 2.22/2.36 multiply(X, add(Y, Z)) = add(multiply(Y, X), multiply(Z, X)) % 2.22/2.36 multiply(Y0, Y2) = multiply(Y2, Y0) % 2.22/2.36 multiply(Y0, n1) = add(multiply(Y1, Y0), multiply(inverse(Y1), Y0)) % 2.22/2.36 add(X, inverse(X)) -> n1 % 2.22/2.36 add(Y0, n1) -> n1 % 2.22/2.36 add(Y1, Y1) -> Y1 % 2.22/2.36 add(Y1, inverse(n1)) -> Y1 % 2.22/2.36 add(inverse(Y0), Y0) -> n1 % 2.22/2.36 add(inverse(Y0), multiply(Y0, Y2)) -> add(Y2, inverse(Y0)) % 2.22/2.36 add(inverse(n1), inverse(Y0)) -> inverse(Y0) % 2.22/2.36 add(multiply(X, Y), Y) -> Y % 2.22/2.36 add(multiply(Y1, Y0), multiply(inverse(Y1), Y0)) -> Y0 % 2.22/2.36 add(multiply(Y1, n1), multiply(inverse(Y1), n1)) -> n1 % 2.22/2.36 add(multiply(false__, inverse(n1)), multiply(inverse(false__), inverse(n1))) -> inverse(n1) % 2.22/2.36 add(n1, inverse(Y0)) -> n1 % 2.22/2.36 add(n1, multiply(inverse(n1), Y1)) -> add(Y1, n1) % 2.22/2.36 f1(multiply(a, b)) -> false__ % 2.22/2.36 f1(multiply(b, a)) -> true__ % 2.22/2.36 inverse(inverse(n1)) -> n1 % 2.22/2.36 multiply(X, inverse(X)) -> inverse(n1) % 2.22/2.36 multiply(Y1, Y1) -> Y1 % 2.22/2.36 multiply(Y1, n1) -> Y1 % 2.22/2.36 multiply(add(X, Y), Y) -> Y % 2.22/2.36 multiply(add(Y, X), add(Z, X)) -> add(X, multiply(Y, Z)) % 2.22/2.36 multiply(add(Y0, inverse(Y2)), n1) -> add(inverse(Y2), multiply(Y0, Y2)) % 2.22/2.36 multiply(n1, Y1) -> Y1 % 2.22/2.36 n0 -> inverse(n1) % 2.22/2.36 true__ -> false__ % 2.22/2.36 with the LPO induced by % 2.22/2.36 b > a > f1 > multiply > add > n0 > inverse > n1 > true__ > false__ % 2.22/2.36 % 2.22/2.36 % SZS output end Proof % 2.22/2.36 %------------------------------------------------------------------------------