%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : HEN003-3 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n008.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 12:58:55 EDT 2022 % Result : Unsatisfiable 4.76s 4.77s % Output : Proof 4.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : HEN003-3 : TPTP v8.1.0. Released v1.0.0. % 0.12/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n008.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Fri Jul 1 14:22:23 EDT 2022 % 0.14/0.35 % CPUTime : % 4.76/4.77 % SZS status Unsatisfiable % 4.76/4.77 % SZS output start Proof % 4.76/4.77 The input problem is unsatisfiable because % 4.76/4.77 % 4.76/4.77 [1] the following set of Horn clauses is unsatisfiable: % 4.76/4.77 % 4.76/4.77 less_equal(X, Y) ==> divide(X, Y) = zero % 4.76/4.77 divide(X, Y) = zero ==> less_equal(X, Y) % 4.76/4.77 less_equal(divide(X, Y), X) % 4.76/4.77 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) % 4.76/4.77 less_equal(zero, X) % 4.76/4.77 less_equal(X, Y) & less_equal(Y, X) ==> X = Y % 4.76/4.77 less_equal(X, identity) % 4.76/4.77 divide(a, a) = zero ==> \bottom % 4.76/4.77 % 4.76/4.77 This holds because % 4.76/4.77 % 4.76/4.77 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.76/4.77 % 4.76/4.77 E: % 4.76/4.77 f1(less_equal(X, Y), X, Y) = zero % 4.76/4.77 f1(true__, X, Y) = divide(X, Y) % 4.76/4.77 f2(divide(X, Y), X, Y) = true__ % 4.76/4.77 f2(zero, X, Y) = less_equal(X, Y) % 4.76/4.77 f3(true__, X, Y) = X % 4.76/4.77 f4(less_equal(Y, X), X, Y) = Y % 4.76/4.77 f4(true__, X, Y) = f3(less_equal(X, Y), X, Y) % 4.76/4.77 f5(divide(a, a)) = true__ % 4.76/4.77 f5(zero) = false__ % 4.76/4.77 less_equal(X, identity) = true__ % 4.76/4.77 less_equal(divide(X, Y), X) = true__ % 4.76/4.77 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) = true__ % 4.76/4.77 less_equal(zero, X) = true__ % 4.76/4.77 G: % 4.76/4.77 true__ = false__ % 4.76/4.77 % 4.76/4.77 This holds because % 4.76/4.77 % 4.76/4.77 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.76/4.77 % 4.76/4.77 % 4.76/4.77 divide(X, Y) -> f1(true__, X, Y) % 4.76/4.77 f1(f2(zero, Y0, Y1), Y0, Y1) -> zero % 4.76/4.77 f1(true__, X0, X0) -> zero % 4.76/4.77 f1(true__, Y0, identity) -> zero % 4.76/4.77 f1(true__, f1(true__, X0, X1), f1(true__, identity, X1)) -> zero % 4.76/4.77 f1(true__, f1(true__, X0, f1(true__, identity, zero)), zero) -> zero % 4.76/4.77 f1(true__, f1(true__, Y1, X1), Y1) -> zero % 4.76/4.77 f1(true__, f1(true__, f1(true__, X0, X1), X2), X0) -> zero % 4.76/4.77 f1(true__, f1(true__, f1(true__, X0, X1), X2), f1(true__, X0, X2)) -> zero % 4.76/4.77 f1(true__, f1(true__, f1(true__, X0, X1), X2), f1(true__, identity, X1)) -> zero % 4.76/4.77 f1(true__, f1(true__, f1(true__, X0, X1), zero), f1(true__, f1(true__, X0, zero), X1)) -> zero % 4.76/4.77 f1(true__, f1(true__, f1(true__, Y0, f1(true__, Y0, zero)), zero), zero) -> zero % 4.76/4.77 f1(true__, zero, Y1) -> zero % 4.76/4.77 f2(f1(true__, Y0, Y1), Y0, Y1) -> true__ % 4.76/4.77 f2(zero, Y0, identity) -> true__ % 4.76/4.77 f2(zero, Y1, Y1) -> true__ % 4.76/4.77 f2(zero, divide(divide(Y0, Y1), divide(Y2, Y1)), divide(divide(Y0, Y2), Y1)) -> true__ % 4.76/4.77 f2(zero, divide(divide(Y0, Y1), zero), divide(divide(Y0, divide(Y1, X1)), Y1)) -> true__ % 4.76/4.77 f2(zero, f1(true__, X0, X1), f1(true__, identity, X1)) -> true__ % 4.76/4.77 f2(zero, f1(true__, Y0, Y1), Y0) -> true__ % 4.76/4.77 f2(zero, f1(true__, f1(true__, X0, X1), X2), f1(true__, X0, X2)) -> true__ % 4.76/4.77 f2(zero, f1(true__, f1(true__, X0, X1), X2), f1(true__, identity, X1)) -> true__ % 4.76/4.77 f2(zero, f1(true__, f1(true__, Y0, Y1), zero), f1(true__, f1(true__, Y0, zero), Y1)) -> true__ % 4.76/4.77 f2(zero, f1(true__, f1(true__, Y0, f1(true__, Y0, zero)), zero), zero) -> true__ % 4.76/4.77 f2(zero, f1(true__, f1(true__, Y0, f1(true__, identity, zero)), zero), zero) -> true__ % 4.76/4.77 f2(zero, f1(true__, f1(true__, Y1, X1), X2), Y1) -> true__ % 4.76/4.77 f2(zero, zero, Y1) -> true__ % 4.76/4.77 f3(f2(zero, Y1, f1(true__, Y1, X1)), Y1, f1(true__, Y1, X1)) -> f1(true__, Y1, X1) % 4.76/4.77 f3(f2(zero, Y1, zero), Y1, zero) -> zero % 4.76/4.77 f3(f2(zero, identity, Y0), identity, Y0) -> Y0 % 4.76/4.77 f3(true__, X, Y) -> X % 4.76/4.77 f4(f2(zero, Y0, Y1), Y1, Y0) -> Y0 % 4.76/4.77 f4(true__, X, Y) -> f3(f2(zero, X, Y), X, Y) % 4.76/4.77 f5(f1(true__, a, a)) -> true__ % 4.76/4.77 f5(zero) -> false__ % 4.76/4.77 less_equal(X, Y) -> f2(zero, X, Y) % 4.76/4.77 true__ -> false__ % 4.76/4.77 with the LPO induced by % 4.76/4.77 f4 > less_equal > f2 > divide > f1 > zero > a > f3 > identity > f5 > true__ > false__ % 4.76/4.77 % 4.76/4.77 % SZS output end Proof % 4.76/4.77 %------------------------------------------------------------------------------