%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LDA007-3 : TPTP v8.1.0. Released v1.0.0. % 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 : Sun Jul 17 16:45:05 EDT 2022 % Result : Unsatisfiable 0.17s 0.39s % Output : Proof 0.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : LDA007-3 : TPTP v8.1.0. Released v1.0.0. % 0.11/0.12 % Command : moca.sh %s % 0.11/0.32 % Computer : n017.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Mon May 30 02:57:10 EDT 2022 % 0.11/0.33 % CPUTime : % 0.17/0.39 % SZS status Unsatisfiable % 0.17/0.39 % SZS output start Proof % 0.17/0.39 The input problem is unsatisfiable because % 0.17/0.39 % 0.17/0.39 [1] the following set of Horn clauses is unsatisfiable: % 0.17/0.39 % 0.17/0.39 f(X, f(Y, Z)) = f(f(X, Y), f(X, Z)) % 0.17/0.39 tt = f(t, t) % 0.17/0.39 ts = f(t, s) % 0.17/0.39 tt_ts = f(tt, ts) % 0.17/0.39 tk = f(t, k) % 0.17/0.39 tsk = f(ts, k) % 0.17/0.39 f(t, tsk) = f(tt_ts, tk) ==> \bottom % 0.17/0.39 % 0.17/0.39 This holds because % 0.17/0.39 % 0.17/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.17/0.39 % 0.17/0.39 E: % 0.17/0.39 f(X, f(Y, Z)) = f(f(X, Y), f(X, Z)) % 0.17/0.39 f1(f(t, tsk)) = true__ % 0.17/0.39 f1(f(tt_ts, tk)) = false__ % 0.17/0.39 tk = f(t, k) % 0.17/0.39 ts = f(t, s) % 0.17/0.39 tsk = f(ts, k) % 0.17/0.39 tt = f(t, t) % 0.17/0.39 tt_ts = f(tt, ts) % 0.17/0.39 G: % 0.17/0.39 true__ = false__ % 0.17/0.39 % 0.17/0.39 This holds because % 0.17/0.39 % 0.17/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.17/0.39 % 0.17/0.39 f(f(f(t, X0), tk), tk) = f(t, f(f(X0, k), k)) % 0.17/0.39 f(f(t, Y1), tk) = f(t, f(Y1, k)) % 0.17/0.39 f(f(tt, f(t, X0)), tk) = f(t, f(f(t, X0), k)) % 0.17/0.39 f(f(X, Y), f(X, Z)) -> f(X, f(Y, Z)) % 0.17/0.39 f(f(X0, f(X1, X2)), f(f(X0, X1), Y2)) -> f(f(X0, X1), f(f(X0, X2), Y2)) % 0.17/0.39 f(f(Y0, t), f(f(Y0, k), Y3)) -> f(f(Y0, tk), f(f(Y0, t), Y3)) % 0.17/0.39 f(f(Y0, t), f(f(Y0, t), Y3)) -> f(f(Y0, tt), f(f(Y0, t), Y3)) % 0.17/0.39 f(f(t, Y1), tt) -> f(t, f(Y1, t)) % 0.17/0.39 f(t, f(k, Y2)) -> f(tk, f(t, Y2)) % 0.17/0.39 f(t, f(t, Y2)) -> f(tt, f(t, Y2)) % 0.17/0.39 f(t, k) -> tk % 0.17/0.39 f(t, t) -> tt % 0.17/0.39 f(t, tk) -> f(tt, tk) % 0.17/0.39 f(t, tt) -> f(tt, tt) % 0.17/0.39 f1(f(f(tt, f(t, s)), tk)) -> false__ % 0.17/0.39 f1(f(t, f(f(t, s), k))) -> true__ % 0.17/0.39 f1(f(t, tsk)) -> true__ % 0.17/0.39 f1(f(tt_ts, tk)) -> false__ % 0.17/0.39 true__ -> false__ % 0.17/0.39 ts -> f(t, s) % 0.17/0.39 tsk -> f(ts, k) % 0.17/0.39 tt_ts -> f(tt, ts) % 0.17/0.39 with the LPO induced by % 0.17/0.39 f1 > tsk > tt_ts > k > tk > ts > t > tt > f > s > true__ > false__ % 0.17/0.39 % 0.17/0.39 % SZS output end Proof % 0.17/0.39 %------------------------------------------------------------------------------