%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : HEN002-3 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 : Sat Jul 16 12:58:53 EDT 2022 % Result : Unsatisfiable 0.18s 0.40s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : HEN002-3 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.33 % Computer : n007.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 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Fri Jul 1 14:02:09 EDT 2022 % 0.12/0.34 % CPUTime : % 0.18/0.40 % SZS status Unsatisfiable % 0.18/0.40 % SZS output start Proof % 0.18/0.40 The input problem is unsatisfiable because % 0.18/0.40 % 0.18/0.40 [1] the following set of Horn clauses is unsatisfiable: % 0.18/0.40 % 0.18/0.40 less_equal(X, Y) ==> divide(X, Y) = zero % 0.18/0.40 divide(X, Y) = zero ==> less_equal(X, Y) % 0.18/0.40 less_equal(divide(X, Y), X) % 0.18/0.40 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) % 0.18/0.40 less_equal(zero, X) % 0.18/0.40 less_equal(X, Y) & less_equal(Y, X) ==> X = Y % 0.18/0.40 less_equal(X, identity) % 0.18/0.40 divide(zero, a) = zero ==> \bottom % 0.18/0.40 % 0.18/0.40 This holds because % 0.18/0.40 % 0.18/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.18/0.40 % 0.18/0.40 E: % 0.18/0.40 f1(less_equal(X, Y), X, Y) = zero % 0.18/0.40 f1(true__, X, Y) = divide(X, Y) % 0.18/0.40 f2(divide(X, Y), X, Y) = true__ % 0.18/0.40 f2(zero, X, Y) = less_equal(X, Y) % 0.18/0.40 f3(true__, X, Y) = X % 0.18/0.40 f4(less_equal(Y, X), X, Y) = Y % 0.18/0.40 f4(true__, X, Y) = f3(less_equal(X, Y), X, Y) % 0.18/0.40 f5(divide(zero, a)) = true__ % 0.18/0.40 f5(zero) = false__ % 0.18/0.40 less_equal(X, identity) = true__ % 0.18/0.40 less_equal(divide(X, Y), X) = true__ % 0.18/0.40 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) = true__ % 0.18/0.40 less_equal(zero, X) = true__ % 0.18/0.40 G: % 0.18/0.40 true__ = false__ % 0.18/0.40 % 0.18/0.40 This holds because % 0.18/0.40 % 0.18/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.18/0.40 % 0.18/0.40 % 0.18/0.40 divide(X, Y) -> f1(true__, X, Y) % 0.18/0.40 f1(f2(zero, Y0, Y1), Y0, Y1) -> zero % 0.18/0.40 f1(less_equal(X, Y), X, Y) -> zero % 0.18/0.40 f1(true__, Y0, identity) -> zero % 0.18/0.40 f1(true__, f1(true__, Y1, X1), Y1) -> zero % 0.18/0.40 f1(true__, zero, Y1) -> zero % 0.18/0.40 f2(divide(X, Y), X, Y) -> true__ % 0.18/0.40 f2(f1(true__, Y0, Y1), Y0, Y1) -> true__ % 0.18/0.40 f2(zero, Y0, identity) -> true__ % 0.18/0.40 f2(zero, f1(true__, Y0, Y1), Y0) -> true__ % 0.18/0.40 f2(zero, f1(true__, f1(true__, Y0, Y1), f1(true__, Y2, Y1)), f1(true__, f1(true__, Y0, Y2), Y1)) -> true__ % 0.18/0.40 f2(zero, zero, Y1) -> true__ % 0.18/0.40 f3(f2(zero, Y1, f1(true__, Y1, X1)), Y1, f1(true__, Y1, X1)) -> f1(true__, Y1, X1) % 0.18/0.40 f3(f2(zero, Y1, zero), Y1, zero) -> zero % 0.18/0.40 f3(f2(zero, identity, Y0), identity, Y0) -> Y0 % 0.18/0.40 f3(true__, X, Y) -> X % 0.18/0.40 f4(f2(zero, Y0, Y1), Y1, Y0) -> Y0 % 0.18/0.40 f4(less_equal(Y, X), X, Y) -> Y % 0.18/0.40 f4(true__, X, Y) -> f3(less_equal(X, Y), X, Y) % 0.18/0.40 f5(divide(zero, a)) -> true__ % 0.18/0.40 f5(zero) -> false__ % 0.18/0.40 false__ -> true__ % 0.18/0.40 less_equal(X, Y) -> f2(zero, X, Y) % 0.18/0.40 less_equal(X, identity) -> true__ % 0.18/0.40 less_equal(divide(X, Y), X) -> true__ % 0.18/0.40 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) -> true__ % 0.18/0.40 less_equal(zero, X) -> true__ % 0.18/0.40 with the LPO induced by % 0.18/0.40 a > divide > f1 > f4 > f3 > less_equal > f5 > identity > f2 > zero > false__ > true__ % 0.18/0.40 % 0.18/0.40 % SZS output end Proof % 0.18/0.40 %------------------------------------------------------------------------------