%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN005-1.010 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 09:12:58 EDT 2022 % Result : Unsatisfiable 1.41s 1.57s % Output : Proof 1.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SYN005-1.010 : TPTP v8.1.0. Released v1.0.0. % 0.04/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n020.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 : Tue Jul 12 04:44:57 EDT 2022 % 0.13/0.34 % CPUTime : % 1.41/1.57 % SZS status Unsatisfiable % 1.41/1.57 % SZS output start Proof % 1.41/1.57 The input problem is unsatisfiable because % 1.41/1.57 % 1.41/1.57 [1] the following set of Horn clauses is unsatisfiable: % 1.41/1.57 % 1.41/1.57 p_1(X1, X2) & p_2(X2, X3) & p_3(X3, X4) & p_4(X4, X5) & p_5(X5, X6) & p_6(X6, X7) & p_7(X7, X8) & p_8(X8, X9) & p_9(X9, X10) & p_10(X10, X1) ==> \bottom % 1.41/1.57 p_1(a, a) % 1.41/1.57 p_2(a, a) % 1.41/1.57 p_3(a, a) % 1.41/1.57 p_4(a, a) % 1.41/1.57 p_5(a, a) % 1.41/1.57 p_6(a, a) % 1.41/1.57 p_7(a, a) % 1.41/1.57 p_8(a, a) % 1.41/1.57 p_9(a, a) % 1.41/1.57 p_10(a, a) % 1.41/1.57 % 1.41/1.57 This holds because % 1.41/1.57 % 1.41/1.57 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.41/1.57 % 1.41/1.57 E: % 1.41/1.57 f1(true__) = false__ % 1.41/1.57 f10(p_10(X10, X1), X9, X10, X8, X7, X6, X5, X4, X3, X2, X1) = true__ % 1.41/1.57 f10(true__, X9, X10, X8, X7, X6, X5, X4, X3, X2, X1) = f9(p_9(X9, X10), X8, X9, X7, X6, X5, X4, X3, X2, X1) % 1.41/1.57 f2(true__, X1, X2) = f1(p_1(X1, X2)) % 1.41/1.57 f3(true__, X2, X3, X1) = f2(p_2(X2, X3), X1, X2) % 1.41/1.57 f4(true__, X3, X4, X2, X1) = f3(p_3(X3, X4), X2, X3, X1) % 1.41/1.57 f5(true__, X4, X5, X3, X2, X1) = f4(p_4(X4, X5), X3, X4, X2, X1) % 1.41/1.57 f6(true__, X5, X6, X4, X3, X2, X1) = f5(p_5(X5, X6), X4, X5, X3, X2, X1) % 1.41/1.57 f7(true__, X6, X7, X5, X4, X3, X2, X1) = f6(p_6(X6, X7), X5, X6, X4, X3, X2, X1) % 1.41/1.57 f8(true__, X7, X8, X6, X5, X4, X3, X2, X1) = f7(p_7(X7, X8), X6, X7, X5, X4, X3, X2, X1) % 1.41/1.57 f9(true__, X8, X9, X7, X6, X5, X4, X3, X2, X1) = f8(p_8(X8, X9), X7, X8, X6, X5, X4, X3, X2, X1) % 1.41/1.57 p_1(a, a) = true__ % 1.41/1.57 p_10(a, a) = true__ % 1.41/1.57 p_2(a, a) = true__ % 1.41/1.57 p_3(a, a) = true__ % 1.41/1.57 p_4(a, a) = true__ % 1.41/1.57 p_5(a, a) = true__ % 1.41/1.57 p_6(a, a) = true__ % 1.41/1.57 p_7(a, a) = true__ % 1.41/1.57 p_8(a, a) = true__ % 1.41/1.57 p_9(a, a) = true__ % 1.41/1.57 G: % 1.41/1.57 true__ = false__ % 1.41/1.57 % 1.41/1.57 This holds because % 1.41/1.57 % 1.41/1.57 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.41/1.57 % 1.41/1.57 % 1.41/1.57 f1(p_1(X1, X2)) -> f2(true__, X1, X2) % 1.41/1.57 f1(true__) -> false__ % 1.41/1.57 f10(p_10(X10, X1), X9, X10, X8, X7, X6, X5, X4, X3, X2, X1) -> true__ % 1.41/1.57 f10(true__, Y2, a, Y3, Y4, Y5, Y6, Y7, Y8, Y9, a) -> true__ % 1.41/1.57 f2(p_2(X2, X3), X1, X2) -> f3(true__, X2, X3, X1) % 1.41/1.57 f2(true__, Y2, a) -> f3(true__, a, a, Y2) % 1.41/1.57 f2(true__, a, a) -> false__ % 1.41/1.57 f3(p_3(X3, X4), X2, X3, X1) -> f4(true__, X3, X4, X2, X1) % 1.41/1.57 f3(true__, Y2, a, Y3) -> f4(true__, a, a, Y2, Y3) % 1.41/1.57 f4(p_4(X4, X5), X3, X4, X2, X1) -> f5(true__, X4, X5, X3, X2, X1) % 1.41/1.57 f4(true__, Y2, a, Y3, Y4) -> f5(true__, a, a, Y2, Y3, Y4) % 1.41/1.57 f5(p_5(X5, X6), X4, X5, X3, X2, X1) -> f6(true__, X5, X6, X4, X3, X2, X1) % 1.41/1.57 f5(true__, Y2, a, Y3, Y4, Y5) -> f6(true__, a, a, Y2, Y3, Y4, Y5) % 1.41/1.57 f6(p_6(X6, X7), X5, X6, X4, X3, X2, X1) -> f7(true__, X6, X7, X5, X4, X3, X2, X1) % 1.41/1.57 f6(true__, Y2, a, Y3, Y4, Y5, Y6) -> f7(true__, a, a, Y2, Y3, Y4, Y5, Y6) % 1.41/1.57 f7(p_7(X7, X8), X6, X7, X5, X4, X3, X2, X1) -> f8(true__, X7, X8, X6, X5, X4, X3, X2, X1) % 1.41/1.57 f7(true__, Y2, a, Y3, Y4, Y5, Y6, Y7) -> f8(true__, a, a, Y2, Y3, Y4, Y5, Y6, Y7) % 1.41/1.57 f7(true__, a, a, a, a, a, a, a) -> false__ % 1.41/1.57 f8(p_8(X8, X9), X7, X8, X6, X5, X4, X3, X2, X1) -> f9(true__, X8, X9, X7, X6, X5, X4, X3, X2, X1) % 1.41/1.57 f8(true__, Y2, a, Y3, Y4, Y5, Y6, Y7, Y8) -> f9(true__, a, a, Y2, Y3, Y4, Y5, Y6, Y7, Y8) % 1.41/1.57 f9(p_9(X9, X10), X8, X9, X7, X6, X5, X4, X3, X2, X1) -> f10(true__, X9, X10, X8, X7, X6, X5, X4, X3, X2, X1) % 1.41/1.57 f9(true__, Y2, a, Y3, Y4, Y5, Y6, Y7, Y8, Y9) -> f10(true__, a, a, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9) % 1.41/1.57 false__ -> true__ % 1.41/1.57 p_1(a, a) -> true__ % 1.41/1.57 p_10(a, a) -> true__ % 1.41/1.57 p_2(a, a) -> true__ % 1.41/1.57 p_3(a, a) -> true__ % 1.41/1.57 p_4(a, a) -> true__ % 1.41/1.57 p_5(a, a) -> true__ % 1.41/1.57 p_6(a, a) -> true__ % 1.41/1.57 p_7(a, a) -> true__ % 1.41/1.57 p_8(a, a) -> true__ % 1.41/1.57 p_9(a, a) -> true__ % 1.41/1.57 with the LPO induced by % 1.41/1.57 a > p_10 > f1 > f2 > p_1 > f3 > f4 > f5 > f6 > f7 > f8 > f9 > f10 > p_9 > p_8 > p_7 > p_6 > p_5 > p_4 > p_3 > p_2 > false__ > true__ % 1.41/1.57 % 1.41/1.57 % SZS output end Proof % 1.41/1.57 %------------------------------------------------------------------------------