%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYO611-1 : TPTP v8.1.0. Released v7.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n018.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 18:46:05 EDT 2022 % Result : Unsatisfiable 0.12s 0.38s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SYO611-1 : TPTP v8.1.0. Released v7.1.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n018.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 06:29:41 EDT 2022 % 0.12/0.33 % CPUTime : % 0.12/0.38 % SZS status Unsatisfiable % 0.12/0.38 % SZS output start Proof % 0.12/0.38 The input problem is unsatisfiable because % 0.12/0.38 % 0.12/0.38 [1] the following set of Horn clauses is unsatisfiable: % 0.12/0.38 % 0.12/0.38 le(A, A) % 0.12/0.38 le(max(A, B), C) ==> le(A, C) % 0.12/0.38 le(max(A, B), C) ==> le(B, C) % 0.12/0.38 eq(f(A), a0) % 0.12/0.38 eq(f(A0), a0) & eq(f(A1), a0) & le(s(A0), A1) ==> \bottom % 0.12/0.38 % 0.12/0.38 This holds because % 0.12/0.38 % 0.12/0.38 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.12/0.38 % 0.12/0.38 E: % 0.12/0.38 eq(f(A), a0) = true__ % 0.12/0.38 f1(le(max(A, B), C), A, C) = true__ % 0.12/0.38 f1(true__, A, C) = le(A, C) % 0.12/0.38 f2(le(max(A, B), C), B, C) = true__ % 0.12/0.38 f2(true__, B, C) = le(B, C) % 0.12/0.38 f3(true__) = false__ % 0.12/0.38 f4(true__, A0) = f3(eq(f(A0), a0)) % 0.12/0.38 f5(le(s(A0), A1), A1, A0) = true__ % 0.12/0.38 f5(true__, A1, A0) = f4(eq(f(A1), a0), A0) % 0.12/0.38 le(A, A) = true__ % 0.12/0.38 G: % 0.12/0.38 true__ = false__ % 0.12/0.38 % 0.12/0.38 This holds because % 0.12/0.38 % 0.12/0.38 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.12/0.38 % 0.12/0.38 % 0.12/0.38 eq(f(A), a0) -> true__ % 0.12/0.38 f1(f1(true__, max(Y0, Y1), Y2), Y0, Y2) -> true__ % 0.12/0.38 f1(le(max(A, B), C), A, C) -> true__ % 0.12/0.38 f1(true__, Y0, max(Y0, Y1)) -> true__ % 0.12/0.38 f1(true__, Y1, Y1) -> true__ % 0.12/0.38 f1(true__, Y1, max(Y0, Y1)) -> true__ % 0.12/0.38 f2(f1(true__, max(Y0, Y1), Y2), Y1, Y2) -> true__ % 0.12/0.38 f2(le(max(A, B), C), B, C) -> true__ % 0.12/0.38 f2(true__, B, C) -> f1(true__, B, C) % 0.12/0.38 f3(true__) -> false__ % 0.12/0.38 f4(true__, A0) -> false__ % 0.12/0.38 f5(f1(true__, s(Y0), Y1), Y1, Y0) -> true__ % 0.12/0.38 f5(le(s(A0), A1), A1, A0) -> true__ % 0.12/0.38 f5(true__, A1, A0) -> false__ % 0.12/0.38 le(A, A) -> true__ % 0.12/0.38 le(A, C) -> f1(true__, A, C) % 0.12/0.38 true__ -> false__ % 0.12/0.38 with the LPO induced by % 0.12/0.38 s > f5 > f4 > a0 > f3 > f > eq > f2 > le > f1 > max > true__ > false__ % 0.12/0.38 % 0.12/0.38 % SZS output end Proof % 0.12/0.38 %------------------------------------------------------------------------------