%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n024.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 18:42:13 EDT 2022 % Result : Unsatisfiable 1.99s 2.08s % Output : Proof 1.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0. % 0.06/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n024.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jul 9 14:19:43 EDT 2022 % 0.12/0.33 % CPUTime : % 1.99/2.08 % SZS status Unsatisfiable % 1.99/2.08 % SZS output start Proof % 1.99/2.08 The input problem is unsatisfiable because % 1.99/2.08 % 1.99/2.08 [1] the following set of Horn clauses is unsatisfiable: % 1.99/2.08 % 1.99/2.08 f(N, one) = s(one) % 1.99/2.08 f(one, s(X)) = s(s(f(one, X))) % 1.99/2.08 f(s(N), s(X)) = f(N, f(s(N), X)) % 1.99/2.08 d(one) % 1.99/2.08 d(X) ==> d(s(X)) % 1.99/2.08 d(f(s(s(one)), s(s(one)))) ==> \bottom % 1.99/2.08 % 1.99/2.08 This holds because % 1.99/2.08 % 1.99/2.08 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.99/2.08 % 1.99/2.08 E: % 1.99/2.08 d(one) = true__ % 1.99/2.08 f(N, one) = s(one) % 1.99/2.08 f(one, s(X)) = s(s(f(one, X))) % 1.99/2.08 f(s(N), s(X)) = f(N, f(s(N), X)) % 1.99/2.08 f1(d(X), X) = true__ % 1.99/2.08 f1(true__, X) = d(s(X)) % 1.99/2.08 f2(d(f(s(s(one)), s(s(one))))) = true__ % 1.99/2.08 f2(true__) = false__ % 1.99/2.08 G: % 1.99/2.08 true__ = false__ % 1.99/2.08 % 1.99/2.08 This holds because % 1.99/2.08 % 1.99/2.08 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.99/2.08 % 1.99/2.08 % 1.99/2.08 d(one) -> true__ % 1.99/2.08 d(s(one)) -> true__ % 1.99/2.08 d(s(s(one))) -> true__ % 1.99/2.08 d(s(s(s(one)))) -> true__ % 1.99/2.08 d(s(s(s(s(one))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(one)))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(one))))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(s(one)))))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(s(s(one))))))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(s(s(s(one)))))))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(one))))))))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))) -> true__ % 1.99/2.08 d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))))) -> true__ % 1.99/2.08 f(N, one) -> s(one) % 1.99/2.08 f(one, s(X)) -> s(s(f(one, X))) % 1.99/2.08 f(s(N), s(X)) -> f(N, f(s(N), X)) % 1.99/2.08 f1(d(X), X) -> true__ % 1.99/2.08 f1(true__, X) -> d(s(X)) % 1.99/2.08 f2(d(f(s(s(one)), s(s(one))))) -> true__ % 1.99/2.08 f2(d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))))) -> true__ % 1.99/2.08 f2(true__) -> false__ % 1.99/2.08 false__ -> true__ % 1.99/2.08 with the LPO induced by % 1.99/2.08 f2 > f1 > d > f > s > one > false__ > true__ % 1.99/2.08 % 1.99/2.08 % SZS output end Proof % 1.99/2.08 %------------------------------------------------------------------------------