%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN310-1 : TPTP v8.1.0. Released v1.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n014.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 09:15:10 EDT 2022 % Result : Unsatisfiable 3.95s 3.98s % Output : Proof 3.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN310-1 : TPTP v8.1.0. Released v1.2.0. % 0.11/0.13 % Command : moca.sh %s % 0.12/0.33 % Computer : n014.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 : Tue Jul 12 02:58:49 EDT 2022 % 0.12/0.34 % CPUTime : % 3.95/3.98 % SZS status Unsatisfiable % 3.95/3.98 % SZS output start Proof % 3.95/3.98 The input problem is unsatisfiable because % 3.95/3.98 % 3.95/3.98 [1] the following set of Horn clauses is unsatisfiable: % 3.95/3.98 % 3.95/3.98 p(X2, X1, X) ==> p(X, X1, X2) % 3.95/3.98 p(X1, X, X2) ==> p(X, X1, X2) % 3.95/3.98 p(X, X1, g(X2)) ==> p(X, X1, X2) % 3.95/3.98 p(f(X), X1, X2) ==> p(X, X1, X2) % 3.95/3.98 p(a, b, c) ==> \bottom % 3.95/3.98 p(f(g(a)), f(g(b)), f(g(c))) % 3.95/3.98 % 3.95/3.98 This holds because % 3.95/3.98 % 3.95/3.98 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.95/3.98 % 3.95/3.98 E: % 3.95/3.98 f1(p(X2, X1, X), X, X1, X2) = true__ % 3.95/3.98 f1(true__, X, X1, X2) = p(X, X1, X2) % 3.95/3.98 f2(p(X1, X, X2), X, X1, X2) = true__ % 3.95/3.98 f2(true__, X, X1, X2) = p(X, X1, X2) % 3.95/3.98 f3(p(X, X1, g(X2)), X, X1, X2) = true__ % 3.95/3.98 f3(true__, X, X1, X2) = p(X, X1, X2) % 3.95/3.98 f4(p(f(X), X1, X2), X, X1, X2) = true__ % 3.95/3.98 f4(true__, X, X1, X2) = p(X, X1, X2) % 3.95/3.98 f5(p(a, b, c)) = true__ % 3.95/3.98 f5(true__) = false__ % 3.95/3.98 p(f(g(a)), f(g(b)), f(g(c))) = true__ % 3.95/3.98 G: % 3.95/3.98 true__ = false__ % 3.95/3.98 % 3.95/3.98 This holds because % 3.95/3.98 % 3.95/3.98 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.95/3.98 % 3.95/3.98 % 3.95/3.98 f1(f3(true__, Y0, Y1, Y2), Y2, Y1, Y0) -> true__ % 3.95/3.98 f1(p(X2, X1, X), X, X1, X2) -> true__ % 3.95/3.98 f1(true__, X, X1, X2) -> p(X, X1, X2) % 3.95/3.98 f2(f3(true__, Y0, Y1, Y2), Y1, Y0, Y2) -> true__ % 3.95/3.98 f2(p(X1, X, X2), X, X1, X2) -> true__ % 3.95/3.98 f2(true__, X, X1, X2) -> p(X, X1, X2) % 3.95/3.98 f3(f3(true__, Y0, Y1, g(Y2)), Y0, Y1, Y2) -> true__ % 3.95/3.98 f3(p(X, X1, g(X2)), X, X1, X2) -> true__ % 3.95/3.98 f3(true__, a, b, c) -> true__ % 3.95/3.98 f3(true__, a, b, f(g(c))) -> true__ % 3.95/3.98 f3(true__, a, b, g(c)) -> true__ % 3.95/3.98 f3(true__, a, c, b) -> true__ % 3.95/3.98 f3(true__, a, c, f(g(b))) -> true__ % 3.95/3.98 f3(true__, a, c, g(b)) -> true__ % 3.95/3.98 f3(true__, a, f(g(b)), c) -> true__ % 3.95/3.98 f3(true__, a, f(g(b)), f(g(c))) -> true__ % 3.95/3.98 f3(true__, a, f(g(b)), g(c)) -> true__ % 3.95/3.98 f3(true__, a, f(g(c)), b) -> true__ % 3.95/3.98 f3(true__, a, f(g(c)), f(g(b))) -> true__ % 3.95/3.98 f3(true__, a, f(g(c)), g(b)) -> true__ % 3.95/3.98 f3(true__, a, g(b), c) -> true__ % 3.95/3.98 f3(true__, a, g(b), f(g(c))) -> true__ % 3.95/3.98 f3(true__, a, g(b), g(c)) -> true__ % 3.95/3.98 f3(true__, a, g(c), b) -> true__ % 3.95/3.98 f3(true__, a, g(c), f(g(b))) -> true__ % 3.95/3.98 f3(true__, a, g(c), g(b)) -> true__ % 3.95/3.98 f3(true__, b, a, c) -> true__ % 3.95/3.98 f3(true__, b, a, f(g(c))) -> true__ % 3.95/3.98 f3(true__, b, a, g(c)) -> true__ % 3.95/3.98 f3(true__, b, c, a) -> true__ % 3.95/3.98 f3(true__, b, f(g(c)), a) -> true__ % 3.95/3.98 f3(true__, b, g(c), a) -> true__ % 3.95/3.98 f3(true__, c, a, b) -> true__ % 3.95/3.98 f3(true__, c, a, f(g(b))) -> true__ % 3.95/3.98 f3(true__, c, a, g(b)) -> true__ % 3.95/3.98 f3(true__, c, b, a) -> true__ % 3.95/3.98 f3(true__, c, f(g(b)), a) -> true__ % 3.95/3.98 f3(true__, c, f(g(b)), g(a)) -> true__ % 3.95/3.98 f3(true__, c, g(b), a) -> true__ % 3.95/3.98 f3(true__, f(g(a)), f(g(b)), f(g(c))) -> true__ % 3.95/3.98 f3(true__, f(g(a)), f(g(b)), g(c)) -> true__ % 3.95/3.98 f3(true__, f(g(a)), f(g(c)), f(g(b))) -> true__ % 3.95/3.98 f3(true__, f(g(a)), g(b), f(g(c))) -> true__ % 3.95/3.98 f3(true__, f(g(a)), g(c), f(g(b))) -> true__ % 3.95/3.98 f3(true__, f(g(b)), a, c) -> true__ % 3.95/3.98 f3(true__, f(g(b)), a, f(g(c))) -> true__ % 3.95/3.98 f3(true__, f(g(b)), a, g(c)) -> true__ % 3.95/3.98 f3(true__, f(g(b)), c, a) -> true__ % 3.95/3.98 f3(true__, f(g(b)), f(g(a)), f(g(c))) -> true__ % 3.95/3.98 f3(true__, f(g(b)), f(g(a)), g(c)) -> true__ % 3.95/3.98 f3(true__, f(g(b)), f(g(c)), a) -> true__ % 3.95/3.98 f3(true__, f(g(b)), f(g(c)), f(g(a))) -> true__ % 3.95/3.98 f3(true__, f(g(b)), f(g(c)), g(a)) -> true__ % 3.95/3.98 f3(true__, f(g(b)), g(a), c) -> true__ % 3.95/3.98 f3(true__, f(g(b)), g(a), f(g(c))) -> true__ % 3.95/3.98 f3(true__, f(g(b)), g(a), g(c)) -> true__ % 3.95/3.98 f3(true__, f(g(b)), g(c), a) -> true__ % 3.95/3.98 f3(true__, f(g(b)), g(c), f(g(a))) -> true__ % 3.95/3.98 f3(true__, f(g(b)), g(c), g(a)) -> true__ % 3.95/3.98 f3(true__, f(g(c)), a, b) -> true__ % 3.95/3.98 f3(true__, f(g(c)), a, f(g(b))) -> true__ % 3.95/3.98 f3(true__, f(g(c)), a, g(b)) -> true__ % 3.95/3.98 f3(true__, f(g(c)), b, a) -> true__ % 3.95/3.98 f3(true__, f(g(c)), f(g(a)), f(g(b))) -> true__ % 3.95/3.98 f3(true__, f(g(c)), f(g(a)), g(b)) -> true__ % 3.95/3.98 f3(true__, f(g(c)), f(g(b)), a) -> true__ % 3.95/3.98 f3(true__, f(g(c)), f(g(b)), f(g(a))) -> true__ % 3.95/3.98 f3(true__, f(g(c)), f(g(b)), g(a)) -> true__ % 3.95/3.98 f3(true__, f(g(c)), g(a), b) -> true__ % 3.95/3.98 f3(true__, f(g(c)), g(a), f(g(b))) -> true__ % 3.95/3.98 f3(true__, f(g(c)), g(a), g(b)) -> true__ % 3.95/3.98 f3(true__, f(g(c)), g(b), a) -> true__ % 3.95/3.98 f3(true__, f(g(c)), g(b), g(a)) -> true__ % 3.95/3.98 f3(true__, g(a), f(g(b)), c) -> true__ % 3.95/3.98 f3(true__, g(a), f(g(b)), f(g(c))) -> true__ % 3.95/3.98 f3(true__, g(a), f(g(b)), g(c)) -> true__ % 3.95/3.98 f3(true__, g(a), f(g(c)), g(b)) -> true__ % 3.95/3.98 f3(true__, g(a), g(b), f(g(c))) -> true__ % 3.95/3.98 f3(true__, g(a), g(c), f(g(b))) -> true__ % 3.95/3.98 f3(true__, g(a), g(c), g(b)) -> true__ % 3.95/3.98 f3(true__, g(b), a, c) -> true__ % 3.95/3.98 f3(true__, g(b), a, f(g(c))) -> true__ % 3.95/3.98 f3(true__, g(b), a, g(c)) -> true__ % 3.95/3.98 f3(true__, g(b), c, a) -> true__ % 3.95/3.98 f3(true__, g(b), f(g(a)), f(g(c))) -> true__ % 3.95/3.98 f3(true__, g(b), f(g(c)), a) -> true__ % 3.95/3.98 f3(true__, g(b), f(g(c)), g(a)) -> true__ % 3.95/3.98 f3(true__, g(b), g(a), f(g(c))) -> true__ % 3.95/3.98 f3(true__, g(b), g(c), a) -> true__ % 3.95/3.98 f3(true__, g(b), g(c), g(a)) -> true__ % 3.95/3.98 f3(true__, g(c), a, b) -> true__ % 3.95/3.98 f3(true__, g(c), a, f(g(b))) -> true__ % 3.95/3.98 f3(true__, g(c), a, g(b)) -> true__ % 3.95/3.98 f3(true__, g(c), b, a) -> true__ % 3.95/3.98 f3(true__, g(c), f(g(b)), a) -> true__ % 3.95/3.98 f3(true__, g(c), f(g(b)), f(g(a))) -> true__ % 3.95/3.98 f3(true__, g(c), f(g(b)), g(a)) -> true__ % 3.95/3.98 f3(true__, g(c), g(a), f(g(b))) -> true__ % 3.95/3.98 f3(true__, g(c), g(b), a) -> true__ % 3.95/3.98 f4(f3(true__, f(Y0), Y1, Y2), Y0, Y1, Y2) -> true__ % 3.95/3.98 f4(p(f(X), X1, X2), X, X1, X2) -> true__ % 3.95/3.98 f4(true__, X, X1, X2) -> p(X, X1, X2) % 3.95/3.98 f5(f3(true__, a, b, c)) -> true__ % 3.95/3.98 f5(p(a, b, c)) -> true__ % 3.95/3.98 f5(true__) -> false__ % 3.95/3.98 false__ -> true__ % 3.95/3.98 p(X, X1, X2) -> f3(true__, X, X1, X2) % 3.95/3.98 p(f(g(a)), f(g(b)), f(g(c))) -> true__ % 3.95/3.98 with the LPO induced by % 3.95/3.98 c > b > a > f5 > f > f4 > f2 > f1 > p > f3 > g > false__ > true__ % 3.95/3.98 % 3.95/3.98 % SZS output end Proof % 3.95/3.98 %------------------------------------------------------------------------------