%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN721-1 : TPTP v8.1.0. Released v2.5.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 09:18:30 EDT 2022 % Result : Unsatisfiable 0.61s 0.83s % Output : Proof 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN721-1 : TPTP v8.1.0. Released v2.5.0. % 0.12/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jul 11 15:50:10 EDT 2022 % 0.13/0.34 % CPUTime : % 0.61/0.83 % SZS status Unsatisfiable % 0.61/0.83 % SZS output start Proof % 0.61/0.83 The input problem is unsatisfiable because % 0.61/0.83 % 0.61/0.83 [1] the following set of Horn clauses is unsatisfiable: % 0.61/0.83 % 0.61/0.83 r(a, b) % 0.61/0.83 r(A, B) ==> q(A, A) % 0.61/0.83 q(A, B) ==> r(C, B) % 0.61/0.83 q(A, a) & r(b, A) ==> \bottom % 0.61/0.83 % 0.61/0.83 This holds because % 0.61/0.83 % 0.61/0.83 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.61/0.83 % 0.61/0.83 E: % 0.61/0.83 f1(r(A, B), A) = true__ % 0.61/0.83 f1(true__, A) = q(A, A) % 0.61/0.83 f2(q(A, B), C, B) = true__ % 0.61/0.83 f2(true__, C, B) = r(C, B) % 0.61/0.83 f3(true__) = false__ % 0.61/0.83 f4(r(b, A), A) = true__ % 0.61/0.83 f4(true__, A) = f3(q(A, a)) % 0.61/0.83 r(a, b) = true__ % 0.61/0.83 G: % 0.61/0.83 true__ = false__ % 0.61/0.83 % 0.61/0.83 This holds because % 0.61/0.83 % 0.61/0.83 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.61/0.83 % 0.61/0.83 % 0.61/0.83 f1(f2(true__, Y0, Y1), Y0) -> true__ % 0.61/0.83 f1(r(A, B), A) -> true__ % 0.61/0.83 f1(true__, Y0) -> true__ % 0.61/0.83 f1(true__, a) -> true__ % 0.61/0.83 f2(f1(true__, Y1), Y2, Y1) -> true__ % 0.61/0.83 f2(q(A, B), C, B) -> true__ % 0.61/0.83 f2(true__, Y1, a) -> true__ % 0.61/0.83 f2(true__, a, b) -> true__ % 0.61/0.83 f3(f1(true__, a)) -> f4(true__, a) % 0.61/0.83 f3(q(A, a)) -> f4(true__, A) % 0.61/0.83 f3(true__) -> false__ % 0.61/0.83 f4(f2(true__, b, Y0), Y0) -> true__ % 0.61/0.83 f4(r(b, A), A) -> true__ % 0.61/0.83 f4(true__, a) -> false__ % 0.61/0.83 false__ -> true__ % 0.61/0.83 q(A, A) -> f1(true__, A) % 0.61/0.83 r(C, B) -> f2(true__, C, B) % 0.61/0.83 r(a, b) -> true__ % 0.61/0.83 with the LPO induced by % 0.61/0.83 f3 > f4 > q > f1 > a > b > r > f2 > false__ > true__ % 0.61/0.83 % 0.61/0.83 % SZS output end Proof % 0.61/0.83 %------------------------------------------------------------------------------