%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN049-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n029.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 09:13:20 EDT 2022 % Result : Unsatisfiable 0.13s 0.37s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN049-1 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.33 % Computer : n029.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 : Tue Jul 12 00:04:02 EDT 2022 % 0.13/0.33 % CPUTime : % 0.13/0.37 % SZS status Unsatisfiable % 0.13/0.37 % SZS output start Proof % 0.13/0.37 The input problem is unsatisfiable because % 0.13/0.37 % 0.13/0.37 [1] the following set of Horn clauses is unsatisfiable: % 0.13/0.37 % 0.13/0.37 big_p(f(X)) ==> big_q(g(X)) % 0.13/0.37 big_p(X) % 0.13/0.37 big_q(X) ==> \bottom % 0.13/0.37 % 0.13/0.37 This holds because % 0.13/0.37 % 0.13/0.37 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.13/0.37 % 0.13/0.37 E: % 0.13/0.37 big_p(X) = true__ % 0.13/0.37 f1(big_p(f(X)), X) = true__ % 0.13/0.37 f1(true__, X) = big_q(g(X)) % 0.13/0.37 f2(big_q(X)) = true__ % 0.13/0.37 f2(true__) = false__ % 0.13/0.37 G: % 0.13/0.37 true__ = false__ % 0.13/0.37 % 0.13/0.37 This holds because % 0.13/0.37 % 0.13/0.37 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.13/0.37 % 0.13/0.37 % 0.13/0.37 big_p(X) -> true__ % 0.13/0.37 big_q(g(Y0)) -> true__ % 0.13/0.37 f1(big_p(f(X)), X) -> true__ % 0.13/0.37 f1(true__, X) -> big_q(g(X)) % 0.13/0.37 f2(big_q(X)) -> true__ % 0.13/0.37 f2(true__) -> false__ % 0.13/0.37 false__ -> true__ % 0.13/0.37 with the LPO induced by % 0.13/0.37 f2 > f > big_p > f1 > g > big_q > false__ > true__ % 0.13/0.37 % 0.13/0.37 % SZS output end Proof % 0.13/0.37 %------------------------------------------------------------------------------