%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : KRS004-1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n032.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 03:19:23 EDT 2022 % Result : Unsatisfiable 0.13s 0.32s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.09 % Problem : KRS004-1 : TPTP v8.1.0. Released v2.0.0. % 0.02/0.09 % Command : moca.sh %s % 0.09/0.28 % Computer : n032.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 600 % 0.09/0.28 % DateTime : Tue Jun 7 08:19:05 EDT 2022 % 0.09/0.28 % CPUTime : % 0.13/0.32 % SZS status Unsatisfiable % 0.13/0.32 % SZS output start Proof % 0.13/0.32 The input problem is unsatisfiable because % 0.13/0.32 % 0.13/0.32 [1] the following set of Horn clauses is unsatisfiable: % 0.13/0.32 % 0.13/0.32 c(exist) % 0.13/0.32 c(X1) ==> d(X1) % 0.13/0.32 c(X1) & d(X1) ==> \bottom % 0.13/0.32 d(X1) & c(X1) ==> \bottom % 0.13/0.32 % 0.13/0.32 This holds because % 0.13/0.32 % 0.13/0.32 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.13/0.32 % 0.13/0.32 E: % 0.13/0.32 c(exist) = true__ % 0.13/0.32 f1(c(X1), X1) = true__ % 0.13/0.32 f1(true__, X1) = d(X1) % 0.13/0.32 f2(true__) = false__ % 0.13/0.32 f3(d(X1), X1) = true__ % 0.13/0.32 f3(true__, X1) = f2(c(X1)) % 0.13/0.32 f4(true__) = false__ % 0.13/0.32 f5(c(X1), X1) = true__ % 0.13/0.32 f5(true__, X1) = f4(d(X1)) % 0.13/0.32 G: % 0.13/0.32 true__ = false__ % 0.13/0.32 % 0.13/0.32 This holds because % 0.13/0.32 % 0.13/0.32 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.13/0.32 % 0.13/0.32 % 0.13/0.32 c(exist) -> true__ % 0.13/0.32 d(X1) -> f1(true__, X1) % 0.13/0.32 f1(c(X1), X1) -> true__ % 0.13/0.32 f1(true__, exist) -> true__ % 0.13/0.32 f2(c(X1)) -> f3(true__, X1) % 0.13/0.32 f2(true__) -> false__ % 0.13/0.32 f3(d(X1), X1) -> true__ % 0.13/0.32 f3(f1(true__, Y0), Y0) -> true__ % 0.13/0.32 f3(true__, exist) -> false__ % 0.13/0.32 f4(f1(true__, exist)) -> true__ % 0.13/0.32 f4(true__) -> false__ % 0.13/0.32 f5(c(X1), X1) -> true__ % 0.13/0.32 f5(true__, X1) -> f4(d(X1)) % 0.13/0.32 false__ -> true__ % 0.13/0.32 with the LPO induced by % 0.13/0.32 exist > f5 > d > f4 > f2 > f3 > c > f1 > false__ > true__ % 0.13/0.32 % 0.13/0.32 % SZS output end Proof % 0.13/0.32 %------------------------------------------------------------------------------