%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN068-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 09:13:36 EDT 2022 % Result : Unsatisfiable 0.91s 1.06s % Output : Proof 0.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : SYN068-1 : TPTP v8.1.0. Released v1.0.0. % 0.10/0.12 % Command : moca.sh %s % 0.11/0.33 % Computer : n025.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Mon Jul 11 22:36:47 EDT 2022 % 0.11/0.33 % CPUTime : % 0.91/1.06 % SZS status Unsatisfiable % 0.91/1.06 % SZS output start Proof % 0.91/1.06 The input problem is unsatisfiable because % 0.91/1.06 % 0.91/1.06 [1] the following set of Horn clauses is unsatisfiable: % 0.91/1.06 % 0.91/1.06 big_f(X) ==> big_g(f(X)) % 0.91/1.06 big_f(X) ==> big_h(X, f(X)) % 0.91/1.06 big_f(X) ==> big_g(g(X)) % 0.91/1.06 big_f(X) & big_h(X, g(X)) ==> \bottom % 0.91/1.06 big_j(a) % 0.91/1.06 big_g(X) ==> big_h(a, X) % 0.91/1.06 big_j(X) ==> big_f(X) % 0.91/1.06 % 0.91/1.06 This holds because % 0.91/1.06 % 0.91/1.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.91/1.06 % 0.91/1.06 E: % 0.91/1.06 big_j(a) = true__ % 0.91/1.06 f1(big_f(X), X) = true__ % 0.91/1.06 f1(true__, X) = big_g(f(X)) % 0.91/1.06 f2(big_f(X), X) = true__ % 0.91/1.06 f2(true__, X) = big_h(X, f(X)) % 0.91/1.06 f3(big_f(X), X) = true__ % 0.91/1.06 f3(true__, X) = big_g(g(X)) % 0.91/1.06 f4(true__) = false__ % 0.91/1.06 f5(big_h(X, g(X)), X) = true__ % 0.91/1.06 f5(true__, X) = f4(big_f(X)) % 0.91/1.06 f6(big_g(X), X) = true__ % 0.91/1.06 f6(true__, X) = big_h(a, X) % 0.91/1.06 f7(big_j(X), X) = true__ % 0.91/1.06 f7(true__, X) = big_f(X) % 0.91/1.06 G: % 0.91/1.06 true__ = false__ % 0.91/1.06 % 0.91/1.06 This holds because % 0.91/1.06 % 0.91/1.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.91/1.06 % 0.91/1.06 % 0.91/1.06 big_f(X) -> f7(true__, X) % 0.91/1.06 big_g(f(X)) -> f1(true__, X) % 0.91/1.06 big_g(g(X)) -> f3(true__, X) % 0.91/1.06 big_h(X, f(X)) -> f2(true__, X) % 0.91/1.06 big_h(a, g(a)) -> true__ % 0.91/1.06 big_j(a) -> true__ % 0.91/1.06 f1(big_f(X), X) -> true__ % 0.91/1.06 f1(f7(true__, Y0), Y0) -> true__ % 0.91/1.06 f1(true__, a) -> true__ % 0.91/1.06 f2(big_f(X), X) -> true__ % 0.91/1.06 f2(f7(true__, Y0), Y0) -> true__ % 0.91/1.06 f2(true__, a) -> true__ % 0.91/1.06 f3(big_f(X), X) -> true__ % 0.91/1.06 f3(f7(true__, Y0), Y0) -> true__ % 0.91/1.06 f3(true__, a) -> true__ % 0.91/1.06 f4(true__) -> false__ % 0.91/1.06 f5(big_h(X, g(X)), X) -> true__ % 0.91/1.06 f5(true__, X) -> f4(big_f(X)) % 0.91/1.06 f6(big_g(X), X) -> true__ % 0.91/1.06 f6(f1(true__, X0), f(X0)) -> true__ % 0.91/1.06 f6(f3(true__, X0), g(X0)) -> true__ % 0.91/1.06 f6(true__, X) -> big_h(a, X) % 0.91/1.06 f7(big_j(X), X) -> true__ % 0.91/1.06 f7(true__, a) -> true__ % 0.91/1.06 false__ -> true__ % 0.91/1.06 with the LPO induced by % 0.91/1.06 f5 > f4 > big_f > f7 > f6 > a > big_h > big_g > f3 > f1 > g > f2 > big_j > f > false__ > true__ % 0.91/1.06 % 0.91/1.06 % SZS output end Proof % 0.91/1.06 %------------------------------------------------------------------------------