%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN083-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n004.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 21 09:13:46 EDT 2022 % Result : Unsatisfiable 0.13s 0.38s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN083-1 : TPTP v8.1.0. Released v1.0.0. % 0.11/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n004.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jul 11 14:09:52 EDT 2022 % 0.13/0.34 % CPUTime : % 0.13/0.38 % SZS status Unsatisfiable % 0.13/0.38 % SZS output start Proof % 0.13/0.38 The input problem is unsatisfiable because % 0.13/0.38 % 0.13/0.38 [1] the following set of Horn clauses is unsatisfiable: % 0.13/0.38 % 0.13/0.38 f(X, f(Y, Z)) = f(f(X, Y), Z) % 0.13/0.38 f(a, f(b, f(c, d))) = f(f(f(a, b), c), d) ==> \bottom % 0.13/0.38 % 0.13/0.38 This holds because % 0.13/0.38 % 0.13/0.38 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.13/0.38 % 0.13/0.38 E: % 0.13/0.38 f(X, f(Y, Z)) = f(f(X, Y), Z) % 0.13/0.38 f1(f(a, f(b, f(c, d)))) = true__ % 0.13/0.38 f1(f(f(f(a, b), c), d)) = false__ % 0.13/0.38 G: % 0.13/0.38 true__ = false__ % 0.13/0.38 % 0.13/0.38 This holds because % 0.13/0.38 % 0.13/0.38 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.13/0.38 % 0.13/0.38 % 0.13/0.38 f(f(X, Y), Z) -> f(X, f(Y, Z)) % 0.13/0.38 f1(f(a, f(b, f(c, d)))) -> true__ % 0.13/0.38 f1(f(f(f(a, b), c), d)) -> false__ % 0.13/0.38 true__ -> false__ % 0.13/0.38 with the LPO induced by % 0.13/0.38 d > c > b > a > f1 > f > true__ > false__ % 0.13/0.38 % 0.13/0.38 % SZS output end Proof % 0.13/0.38 %------------------------------------------------------------------------------