%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN080-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n015.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 09:13:44 EDT 2022 % Result : Unsatisfiable 0.18s 0.37s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYN080-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n015.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jul 12 03:01:10 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.37 % SZS status Unsatisfiable % 0.18/0.37 % SZS output start Proof % 0.18/0.37 The input problem is unsatisfiable because % 0.18/0.37 % 0.18/0.37 [1] the following set of Horn clauses is unsatisfiable: % 0.18/0.37 % 0.18/0.37 f(X) = g(Y) % 0.18/0.37 f(f(a)) = f(g(b)) ==> \bottom % 0.18/0.37 % 0.18/0.37 This holds because % 0.18/0.37 % 0.18/0.37 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.18/0.37 % 0.18/0.37 E: % 0.18/0.37 f(X) = g(Y) % 0.18/0.37 f1(f(f(a))) = true__ % 0.18/0.37 f1(f(g(b))) = false__ % 0.18/0.37 G: % 0.18/0.37 true__ = false__ % 0.18/0.37 % 0.18/0.37 This holds because % 0.18/0.37 % 0.18/0.37 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.18/0.37 % 0.18/0.37 f(X) = g(Y) % 0.18/0.37 f(X1) = f(Y1) % 0.18/0.37 f1(f(X1)) -> false__ % 0.18/0.37 f1(f(X1)) -> true__ % 0.18/0.37 f1(f(f(X1))) -> false__ % 0.18/0.37 f1(f(f(a))) -> true__ % 0.18/0.37 f1(f(f(false__))) -> true__ % 0.18/0.37 f1(f(false__)) -> false__ % 0.18/0.37 f1(f(false__)) -> true__ % 0.18/0.37 f1(f(g(b))) -> false__ % 0.18/0.37 true__ -> false__ % 0.18/0.37 with the LPO induced by % 0.18/0.37 a > b > f1 > g > f > true__ > false__ % 0.18/0.37 % 0.18/0.37 % SZS output end Proof % 0.18/0.37 %------------------------------------------------------------------------------