%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN057-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n016.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 09:13:27 EDT 2022 % Result : Unsatisfiable 3.07s 3.12s % Output : Proof 3.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYN057-1 : TPTP v8.1.0. Released v1.0.0. % 0.12/0.14 % Command : moca.sh %s % 0.14/0.36 % Computer : n016.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Mon Jul 11 21:13:28 EDT 2022 % 0.14/0.36 % CPUTime : % 3.07/3.12 % SZS status Unsatisfiable % 3.07/3.12 % SZS output start Proof % 3.07/3.12 The input problem is unsatisfiable because % 3.07/3.12 % 3.07/3.12 [1] the following set of Horn clauses is unsatisfiable: % 3.07/3.12 % 3.07/3.12 big_f(a) % 3.07/3.12 big_g(a) ==> \bottom % 3.07/3.12 big_f(X) ==> big_h(X) % 3.07/3.12 big_j(X) & big_i(X) ==> big_f(X) % 3.07/3.12 big_h(X) & big_i(Y) & big_h(Y) ==> big_g(X) % 3.07/3.12 big_j(b) % 3.07/3.12 big_i(b) % 3.07/3.12 % 3.07/3.12 This holds because % 3.07/3.12 % 3.07/3.12 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.07/3.12 % 3.07/3.12 E: % 3.07/3.12 big_f(a) = true__ % 3.07/3.12 big_i(b) = true__ % 3.07/3.12 big_j(b) = true__ % 3.07/3.12 f1(big_g(a)) = true__ % 3.07/3.12 f1(true__) = false__ % 3.07/3.12 f2(big_f(X), X) = true__ % 3.07/3.12 f2(true__, X) = big_h(X) % 3.07/3.12 f3(true__, X) = big_f(X) % 3.07/3.12 f4(big_i(X), X) = true__ % 3.07/3.12 f4(true__, X) = f3(big_j(X), X) % 3.07/3.12 f5(true__, X) = big_g(X) % 3.07/3.12 f6(true__, X) = f5(big_h(X), X) % 3.07/3.12 f7(big_h(Y), Y, X) = true__ % 3.07/3.12 f7(true__, Y, X) = f6(big_i(Y), X) % 3.07/3.12 G: % 3.07/3.12 true__ = false__ % 3.07/3.12 % 3.07/3.12 This holds because % 3.07/3.12 % 3.07/3.12 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.07/3.12 % 3.07/3.12 % 3.07/3.12 big_f(X) -> f3(true__, X) % 3.07/3.12 big_g(X) -> f5(true__, X) % 3.07/3.12 big_h(X) -> f2(true__, X) % 3.07/3.12 big_i(b) -> true__ % 3.07/3.12 big_j(b) -> true__ % 3.07/3.12 f1(big_g(a)) -> true__ % 3.07/3.12 f1(f5(true__, a)) -> true__ % 3.07/3.12 f1(true__) -> false__ % 3.07/3.12 f2(f3(true__, Y0), Y0) -> true__ % 3.07/3.12 f2(true__, a) -> true__ % 3.07/3.12 f2(true__, b) -> true__ % 3.07/3.12 f3(big_j(X), X) -> f4(true__, X) % 3.07/3.12 f3(true__, a) -> true__ % 3.07/3.12 f3(true__, b) -> true__ % 3.07/3.12 f4(big_i(X), X) -> true__ % 3.07/3.12 f4(true__, b) -> true__ % 3.07/3.12 f5(f2(true__, Y1), Y1) -> true__ % 3.07/3.12 f5(true__, a) -> true__ % 3.07/3.12 f5(true__, b) -> true__ % 3.07/3.12 f6(big_i(a), Y1) -> true__ % 3.07/3.12 f6(true__, Y1) -> true__ % 3.07/3.12 f7(f2(true__, Y0), Y0, Y1) -> true__ % 3.07/3.12 f7(true__, Y, X) -> f6(big_i(Y), X) % 3.07/3.12 false__ -> true__ % 3.07/3.12 with the LPO induced by % 3.07/3.12 big_j > f4 > big_f > f3 > a > big_g > f5 > f7 > f6 > big_h > f2 > b > big_i > f1 > false__ > true__ % 3.07/3.12 % 3.07/3.12 % SZS output end Proof % 3.07/3.12 %------------------------------------------------------------------------------