%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN065-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 09:13:33 EDT 2022 % Result : Unsatisfiable 1.12s 1.28s % Output : Proof 1.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN065-1 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n007.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jul 11 22:16:03 EDT 2022 % 0.12/0.34 % CPUTime : % 1.12/1.28 % SZS status Unsatisfiable % 1.12/1.28 % SZS output start Proof % 1.12/1.28 The input problem is unsatisfiable because % 1.12/1.28 % 1.12/1.28 [1] the following set of Horn clauses is unsatisfiable: % 1.12/1.28 % 1.12/1.28 big_f(X, f(X)) % 1.12/1.28 big_g(X, g(X)) % 1.12/1.28 big_f(X, Y) & big_f(Y, Z) ==> big_h(X, Z) % 1.12/1.28 big_f(X, Y) & big_g(Y, Z) ==> big_h(X, Z) % 1.12/1.28 big_g(X, Y) & big_f(Y, Z) ==> big_h(X, Z) % 1.12/1.28 big_g(X, Y) & big_g(Y, Z) ==> big_h(X, Z) % 1.12/1.28 big_h(a, X) ==> \bottom % 1.12/1.28 % 1.12/1.28 This holds because % 1.12/1.28 % 1.12/1.28 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.12/1.28 % 1.12/1.28 E: % 1.12/1.28 big_f(X, f(X)) = true__ % 1.12/1.28 big_g(X, g(X)) = true__ % 1.12/1.28 f1(true__, X, Z) = big_h(X, Z) % 1.12/1.28 f2(big_f(Y, Z), X, Y, Z) = true__ % 1.12/1.28 f2(true__, X, Y, Z) = f1(big_f(X, Y), X, Z) % 1.12/1.28 f3(true__, X, Z) = big_h(X, Z) % 1.12/1.28 f4(big_g(Y, Z), X, Y, Z) = true__ % 1.12/1.28 f4(true__, X, Y, Z) = f3(big_f(X, Y), X, Z) % 1.12/1.28 f5(true__, X, Z) = big_h(X, Z) % 1.12/1.28 f6(big_f(Y, Z), X, Y, Z) = true__ % 1.12/1.28 f6(true__, X, Y, Z) = f5(big_g(X, Y), X, Z) % 1.12/1.28 f7(true__, X, Z) = big_h(X, Z) % 1.12/1.28 f8(big_g(Y, Z), X, Y, Z) = true__ % 1.12/1.28 f8(true__, X, Y, Z) = f7(big_g(X, Y), X, Z) % 1.12/1.28 f9(big_h(a, X)) = true__ % 1.12/1.28 f9(true__) = false__ % 1.12/1.28 G: % 1.12/1.28 true__ = false__ % 1.12/1.28 % 1.12/1.28 This holds because % 1.12/1.28 % 1.12/1.28 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.12/1.28 % 1.12/1.28 % 1.12/1.28 big_f(X, f(X)) -> true__ % 1.12/1.28 big_g(X, g(X)) -> true__ % 1.12/1.28 big_h(X, Z) -> f5(true__, X, Z) % 1.12/1.28 f1(big_f(Y2, Y0), Y2, f(Y0)) -> true__ % 1.12/1.28 f1(true__, X, Z) -> big_h(X, Z) % 1.12/1.28 f2(big_f(Y, Z), X, Y, Z) -> true__ % 1.12/1.28 f2(true__, X, Y, Z) -> f1(big_f(X, Y), X, Z) % 1.12/1.28 f3(big_f(Y2, Y0), Y2, g(Y0)) -> true__ % 1.12/1.28 f3(true__, X, Z) -> big_h(X, Z) % 1.12/1.28 f4(big_g(Y, Z), X, Y, Z) -> true__ % 1.12/1.28 f4(true__, X, Y, Z) -> f3(big_f(X, Y), X, Z) % 1.12/1.28 f5(big_g(Y2, Y0), Y2, f(Y0)) -> true__ % 1.12/1.28 f5(true__, Y0, f(f(Y0))) -> true__ % 1.12/1.28 f5(true__, Y0, f(g(Y0))) -> true__ % 1.12/1.28 f5(true__, Y0, g(f(Y0))) -> true__ % 1.12/1.28 f5(true__, Y0, g(g(Y0))) -> true__ % 1.12/1.28 f6(big_f(Y, Z), X, Y, Z) -> true__ % 1.12/1.28 f6(true__, X, Y, Z) -> f5(big_g(X, Y), X, Z) % 1.12/1.28 f7(big_g(Y2, Y0), Y2, g(Y0)) -> true__ % 1.12/1.28 f7(true__, X, Z) -> big_h(X, Z) % 1.12/1.28 f8(big_g(Y, Z), X, Y, Z) -> true__ % 1.12/1.28 f8(true__, X, Y, Z) -> f7(big_g(X, Y), X, Z) % 1.12/1.28 f9(big_h(a, X)) -> true__ % 1.12/1.28 f9(f5(true__, a, Y0)) -> true__ % 1.12/1.28 f9(true__) -> false__ % 1.12/1.28 false__ -> true__ % 1.12/1.28 with the LPO induced by % 1.12/1.28 a > f9 > f8 > f6 > big_g > f4 > f2 > big_f > f7 > f3 > f1 > big_h > f5 > g > f > false__ > true__ % 1.12/1.28 % 1.12/1.28 % SZS output end Proof % 1.12/1.28 %------------------------------------------------------------------------------