%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ROB030-1 : TPTP v8.1.0. Released v3.1.0. % 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 : Mon Jul 18 20:54:53 EDT 2022 % Result : Unsatisfiable 0.20s 0.39s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : ROB030-1 : TPTP v8.1.0. Released v3.1.0. % 0.04/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n022.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 : Thu Jun 9 13:20:34 EDT 2022 % 0.12/0.34 % CPUTime : % 0.20/0.39 % SZS status Unsatisfiable % 0.20/0.39 % SZS output start Proof % 0.20/0.39 The input problem is unsatisfiable because % 0.20/0.39 % 0.20/0.39 [1] the following set of Horn clauses is unsatisfiable: % 0.20/0.39 % 0.20/0.39 add(X, Y) = add(Y, X) % 0.20/0.39 add(add(X, Y), Z) = add(X, add(Y, Z)) % 0.20/0.39 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X % 0.20/0.39 add(c, d) = d % 0.20/0.39 negate(add(A, B)) = negate(B) ==> \bottom % 0.20/0.39 % 0.20/0.39 This holds because % 0.20/0.39 % 0.20/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.20/0.39 % 0.20/0.39 E: % 0.20/0.39 add(X, Y) = add(Y, X) % 0.20/0.39 add(add(X, Y), Z) = add(X, add(Y, Z)) % 0.20/0.39 add(c, d) = d % 0.20/0.39 f1(negate(B), B) = false__ % 0.20/0.39 f1(negate(add(A, B)), B) = true__ % 0.20/0.39 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X % 0.20/0.39 G: % 0.20/0.39 true__ = false__ % 0.20/0.39 % 0.20/0.39 This holds because % 0.20/0.39 % 0.20/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.20/0.39 % 0.20/0.39 add(X, Y) = add(Y, X) % 0.20/0.39 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2)) % 0.20/0.39 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2)) % 0.20/0.39 add(add(X, Y), Z) -> add(X, add(Y, Z)) % 0.20/0.39 add(c, add(d, Y2)) -> add(d, Y2) % 0.20/0.39 add(c, d) -> d % 0.20/0.39 f1(X0, add(negate(add(X0, X1)), negate(add(X0, negate(X1))))) -> false__ % 0.20/0.39 f1(negate(B), B) -> false__ % 0.20/0.39 f1(negate(add(A, B)), B) -> true__ % 0.20/0.39 f1(negate(add(Y1, Y0)), Y1) -> true__ % 0.20/0.39 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) -> X % 0.20/0.39 negate(add(negate(d), negate(add(c, negate(d))))) -> c % 0.20/0.39 true__ -> false__ % 0.20/0.39 with the LPO induced by % 0.20/0.39 negate > d > add > c > f1 > true__ > false__ % 0.20/0.39 % 0.20/0.39 % SZS output end Proof % 0.20/0.39 %------------------------------------------------------------------------------