%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : NUM019-1 : TPTP v8.1.0. Bugfixed v4.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 12:32:14 EDT 2022 % Result : Unsatisfiable 0.97s 1.12s % Output : Proof 0.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : NUM019-1 : TPTP v8.1.0. Bugfixed v4.0.0. % 0.04/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n007.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 Jul 7 05:40:29 EDT 2022 % 0.12/0.34 % CPUTime : % 0.97/1.12 % SZS status Unsatisfiable % 0.97/1.12 % SZS output start Proof % 0.97/1.12 The input problem is unsatisfiable because % 0.97/1.12 % 0.97/1.12 [1] the following set of Horn clauses is unsatisfiable: % 0.97/1.12 % 0.97/1.12 equalish(add(A, n0), A) % 0.97/1.12 equalish(add(A, successor(B)), successor(add(A, B))) % 0.97/1.12 equalish(multiply(A, n0), n0) % 0.97/1.12 equalish(multiply(A, successor(B)), add(multiply(A, B), A)) % 0.97/1.12 equalish(successor(A), successor(B)) ==> equalish(A, B) % 0.97/1.12 equalish(A, B) ==> equalish(successor(A), successor(B)) % 0.97/1.12 equalish(X, X) % 0.97/1.12 equalish(X, Y) & equalish(X, Z) ==> equalish(Y, Z) % 0.97/1.12 equalish(successor(A), n0) ==> \bottom % 0.97/1.12 equalish(a, aa) % 0.97/1.12 equalish(aa, a) ==> \bottom % 0.97/1.12 % 0.97/1.12 This holds because % 0.97/1.12 % 0.97/1.12 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.97/1.12 % 0.97/1.12 E: % 0.97/1.12 equalish(X, X) = true__ % 0.97/1.12 equalish(a, aa) = true__ % 0.97/1.12 equalish(add(A, n0), A) = true__ % 0.97/1.12 equalish(add(A, successor(B)), successor(add(A, B))) = true__ % 0.97/1.12 equalish(multiply(A, n0), n0) = true__ % 0.97/1.12 equalish(multiply(A, successor(B)), add(multiply(A, B), A)) = true__ % 0.97/1.12 f1(equalish(successor(A), successor(B)), A, B) = true__ % 0.97/1.12 f1(true__, A, B) = equalish(A, B) % 0.97/1.12 f2(equalish(A, B), A, B) = true__ % 0.97/1.12 f2(true__, A, B) = equalish(successor(A), successor(B)) % 0.97/1.12 f3(true__, Y, Z) = equalish(Y, Z) % 0.97/1.12 f4(equalish(X, Z), X, Y, Z) = true__ % 0.97/1.12 f4(true__, X, Y, Z) = f3(equalish(X, Y), Y, Z) % 0.97/1.12 f5(equalish(successor(A), n0)) = true__ % 0.97/1.12 f5(true__) = false__ % 0.97/1.12 f6(equalish(aa, a)) = true__ % 0.97/1.12 f6(true__) = false__ % 0.97/1.12 G: % 0.97/1.12 true__ = false__ % 0.97/1.12 % 0.97/1.12 This holds because % 0.97/1.12 % 0.97/1.12 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.97/1.12 % 0.97/1.12 % 0.97/1.12 equalish(X, X) -> true__ % 0.97/1.12 equalish(Y, Z) -> f3(true__, Y, Z) % 0.97/1.12 equalish(a, aa) -> true__ % 0.97/1.12 equalish(add(A, n0), A) -> true__ % 0.97/1.12 equalish(add(A, successor(B)), successor(add(A, B))) -> true__ % 0.97/1.12 equalish(multiply(A, n0), n0) -> true__ % 0.97/1.12 equalish(multiply(A, successor(B)), add(multiply(A, B), A)) -> true__ % 0.97/1.12 f1(equalish(successor(A), successor(B)), A, B) -> true__ % 0.97/1.12 f1(f3(true__, successor(Y0), successor(Y1)), Y0, Y1) -> true__ % 0.97/1.12 f1(true__, A, B) -> equalish(A, B) % 0.97/1.12 f2(equalish(A, B), A, B) -> true__ % 0.97/1.12 f2(f3(true__, Y0, Y1), Y0, Y1) -> true__ % 0.97/1.12 f2(true__, A, B) -> equalish(successor(A), successor(B)) % 0.97/1.12 f3(f3(true__, Y1, Y2), Y2, Y1) -> true__ % 0.97/1.12 f3(f3(true__, a, Y2), Y2, aa) -> true__ % 0.97/1.12 f3(f3(true__, add(Y1, n0), Y2), Y2, Y1) -> true__ % 0.97/1.12 f3(f3(true__, multiply(X0, n0), Y2), Y2, n0) -> true__ % 0.97/1.12 f3(true__, Y1, Y1) -> true__ % 0.97/1.12 f3(true__, Y1, add(Y1, n0)) -> true__ % 0.97/1.12 f3(true__, a, aa) -> true__ % 0.97/1.12 f3(true__, aa, a) -> true__ % 0.97/1.12 f3(true__, add(Y1, n0), Y1) -> true__ % 0.97/1.12 f3(true__, multiply(X0, n0), n0) -> true__ % 0.97/1.12 f3(true__, successor(Y1), successor(Y1)) -> true__ % 0.97/1.12 f3(true__, successor(a), successor(aa)) -> true__ % 0.97/1.12 f3(true__, successor(aa), successor(a)) -> true__ % 0.97/1.12 f3(true__, successor(add(Y1, n0)), successor(Y1)) -> true__ % 0.97/1.12 f3(true__, successor(multiply(X0, n0)), successor(n0)) -> true__ % 0.97/1.12 f4(equalish(X, Z), X, Y, Z) -> true__ % 0.97/1.12 f4(f3(true__, Y0, Y1), Y0, Y2, Y1) -> true__ % 0.97/1.12 f4(true__, X, Y, Z) -> f3(equalish(X, Y), Y, Z) % 0.97/1.12 f5(equalish(successor(A), n0)) -> true__ % 0.97/1.12 f5(f3(true__, successor(Y0), n0)) -> true__ % 0.97/1.12 f5(true__) -> false__ % 0.97/1.12 f6(equalish(aa, a)) -> true__ % 0.97/1.12 f6(f3(true__, aa, a)) -> true__ % 0.97/1.12 f6(true__) -> false__ % 0.97/1.12 false__ -> true__ % 0.97/1.12 with the LPO induced by % 0.97/1.12 f6 > aa > a > f5 > f2 > f1 > f4 > equalish > f3 > successor > multiply > n0 > add > false__ > true__ % 0.97/1.12 % 0.97/1.12 % SZS output end Proof % 0.97/1.12 %------------------------------------------------------------------------------