%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN079-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n003.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 09:13:43 EDT 2022 % Result : Unsatisfiable 0.71s 0.88s % Output : Proof 0.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN079-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n003.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 04:43:00 EDT 2022 % 0.13/0.33 % CPUTime : % 0.71/0.88 % SZS status Unsatisfiable % 0.71/0.88 % SZS output start Proof % 0.71/0.88 The input problem is unsatisfiable because % 0.71/0.88 % 0.71/0.88 [1] the following set of Horn clauses is unsatisfiable: % 0.71/0.88 % 0.71/0.88 big_f(f(a, b), f(b, c)) % 0.71/0.88 big_f(f(b, c), f(a, c)) % 0.71/0.88 big_f(X, Y) & big_f(Y, Z) ==> big_f(X, Z) % 0.71/0.88 big_f(f(a, b), f(a, c)) ==> \bottom % 0.71/0.88 % 0.71/0.88 This holds because % 0.71/0.88 % 0.71/0.88 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.71/0.88 % 0.71/0.88 E: % 0.71/0.88 big_f(f(a, b), f(b, c)) = true__ % 0.71/0.88 big_f(f(b, c), f(a, c)) = true__ % 0.71/0.88 f1(true__, X, Z) = big_f(X, Z) % 0.71/0.88 f2(big_f(Y, Z), X, Y, Z) = true__ % 0.71/0.88 f2(true__, X, Y, Z) = f1(big_f(X, Y), X, Z) % 0.71/0.88 f3(big_f(f(a, b), f(a, c))) = true__ % 0.71/0.88 f3(true__) = false__ % 0.71/0.88 G: % 0.71/0.88 true__ = false__ % 0.71/0.88 % 0.71/0.88 This holds because % 0.71/0.88 % 0.71/0.88 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.71/0.88 % 0.71/0.88 % 0.71/0.88 big_f(X, Z) -> f1(true__, X, Z) % 0.71/0.88 big_f(f(a, b), f(b, c)) -> true__ % 0.71/0.88 big_f(f(b, c), f(a, c)) -> true__ % 0.71/0.88 f1(f1(true__, Y2, f(a, b)), Y2, f(a, c)) -> true__ % 0.71/0.88 f1(f1(true__, Y2, f(a, b)), Y2, f(b, c)) -> true__ % 0.71/0.88 f1(f1(true__, Y2, f(b, c)), Y2, f(a, c)) -> true__ % 0.71/0.88 f1(true__, f(a, b), f(a, c)) -> true__ % 0.71/0.88 f1(true__, f(a, b), f(b, c)) -> true__ % 0.71/0.88 f1(true__, f(b, c), f(a, c)) -> true__ % 0.71/0.88 f2(big_f(Y, Z), X, Y, Z) -> true__ % 0.71/0.88 f2(f1(true__, Y0, Y1), Y2, Y0, Y1) -> true__ % 0.71/0.88 f2(true__, X, Y, Z) -> f1(big_f(X, Y), X, Z) % 0.71/0.88 f3(big_f(f(a, b), f(a, c))) -> true__ % 0.71/0.88 f3(f1(true__, f(a, b), f(a, c))) -> true__ % 0.71/0.88 f3(true__) -> false__ % 0.71/0.88 false__ -> true__ % 0.71/0.88 with the LPO induced by % 0.71/0.88 f3 > f2 > big_f > f1 > c > b > a > f > false__ > true__ % 0.71/0.88 % 0.71/0.88 % SZS output end Proof % 0.71/0.88 %------------------------------------------------------------------------------