%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ROB013-1 : TPTP v8.1.0. Released v1.0.0. % 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 20:54:46 EDT 2022 % Result : Unsatisfiable 1.52s 1.69s % Output : Proof 1.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : ROB013-1 : TPTP v8.1.0. Released v1.0.0. % 0.04/0.12 % Command : moca.sh %s % 0.14/0.33 % Computer : n022.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 600 % 0.14/0.33 % DateTime : Thu Jun 9 13:41:49 EDT 2022 % 0.14/0.33 % CPUTime : % 1.52/1.69 % SZS status Unsatisfiable % 1.52/1.69 % SZS output start Proof % 1.52/1.69 The input problem is unsatisfiable because % 1.52/1.69 % 1.52/1.69 [1] the following set of Horn clauses is unsatisfiable: % 1.52/1.69 % 1.52/1.69 add(X, Y) = add(Y, X) % 1.52/1.69 add(add(X, Y), Z) = add(X, add(Y, Z)) % 1.52/1.69 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X % 1.52/1.69 negate(add(a, b)) = c % 1.52/1.69 negate(add(c, negate(add(negate(b), a)))) = a ==> \bottom % 1.52/1.69 % 1.52/1.69 This holds because % 1.52/1.69 % 1.52/1.69 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.52/1.69 % 1.52/1.69 E: % 1.52/1.69 add(X, Y) = add(Y, X) % 1.52/1.69 add(add(X, Y), Z) = add(X, add(Y, Z)) % 1.52/1.69 f1(a) = false__ % 1.52/1.69 f1(negate(add(c, negate(add(negate(b), a))))) = true__ % 1.52/1.69 negate(add(a, b)) = c % 1.52/1.69 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X % 1.52/1.69 G: % 1.52/1.69 true__ = false__ % 1.52/1.69 % 1.52/1.69 This holds because % 1.52/1.69 % 1.52/1.69 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.52/1.69 % 1.52/1.69 add(X, Y) = add(Y, X) % 1.52/1.69 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2)) % 1.52/1.69 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2)) % 1.52/1.69 add(add(X, Y), Z) -> add(X, add(Y, Z)) % 1.52/1.69 f1(a) -> false__ % 1.52/1.69 f1(negate(add(c, negate(add(a, negate(b)))))) -> true__ % 1.52/1.69 f1(negate(add(c, negate(add(negate(b), a))))) -> true__ % 1.52/1.69 negate(add(a, b)) -> c % 1.52/1.69 negate(add(a, negate(add(a, add(c, negate(b)))))) -> c % 1.52/1.69 negate(add(a, negate(add(c, negate(negate(add(a, negate(b)))))))) -> c % 1.52/1.69 negate(add(c, negate(add(a, negate(b))))) -> a % 1.52/1.69 negate(add(c, negate(add(negate(a), b)))) -> b % 1.52/1.69 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) -> X % 1.52/1.69 negate(add(negate(add(Y0, Y1)), negate(add(negate(Y0), Y1)))) -> Y1 % 1.52/1.69 negate(add(negate(add(Y0, Y1)), negate(add(negate(Y1), Y0)))) -> Y0 % 1.52/1.69 negate(add(negate(add(Y0, add(a, b))), negate(add(c, Y0)))) -> Y0 % 1.52/1.69 negate(add(negate(add(Y0, c)), negate(add(Y0, add(a, b))))) -> Y0 % 1.52/1.69 negate(add(negate(add(Y1, Y0)), negate(add(Y0, negate(Y1))))) -> Y0 % 1.52/1.69 negate(add(negate(add(a, add(b, Y1))), negate(add(Y1, c)))) -> Y1 % 1.52/1.69 true__ -> false__ % 1.52/1.69 with the LPO induced by % 1.52/1.69 f1 > b > c > add > a > negate > true__ > false__ % 1.52/1.69 % 1.52/1.69 % SZS output end Proof % 1.52/1.69 %------------------------------------------------------------------------------