%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : HEN002-4 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n003.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 12:58:54 EDT 2022 % Result : Unsatisfiable 0.88s 1.02s % Output : Proof 0.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : HEN002-4 : TPTP v8.1.0. Released v1.0.0. % 0.12/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n003.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % 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 13:43:37 EDT 2022 % 0.12/0.34 % CPUTime : % 0.88/1.02 % SZS status Unsatisfiable % 0.88/1.02 % SZS output start Proof % 0.88/1.02 The input problem is unsatisfiable because % 0.88/1.02 % 0.88/1.02 [1] the following set of Horn clauses is unsatisfiable: % 0.88/1.02 % 0.88/1.02 less_equal(X, Y) ==> divide(X, Y) = zero % 0.88/1.02 divide(X, Y) = zero ==> less_equal(X, Y) % 0.88/1.02 less_equal(divide(X, Y), X) % 0.88/1.02 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) % 0.88/1.02 less_equal(zero, X) % 0.88/1.02 less_equal(X, Y) & less_equal(Y, X) ==> X = Y % 0.88/1.02 less_equal(X, identity) % 0.88/1.02 divide(X, identity) = zero % 0.88/1.02 divide(zero, a) = zero ==> \bottom % 0.88/1.02 % 0.88/1.02 This holds because % 0.88/1.02 % 0.88/1.02 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.88/1.02 % 0.88/1.02 E: % 0.88/1.02 divide(X, identity) = zero % 0.88/1.02 f1(less_equal(X, Y), X, Y) = zero % 0.88/1.02 f1(true__, X, Y) = divide(X, Y) % 0.88/1.02 f2(divide(X, Y), X, Y) = true__ % 0.88/1.02 f2(zero, X, Y) = less_equal(X, Y) % 0.88/1.02 f3(true__, X, Y) = X % 0.88/1.02 f4(less_equal(Y, X), X, Y) = Y % 0.88/1.02 f4(true__, X, Y) = f3(less_equal(X, Y), X, Y) % 0.88/1.02 f5(divide(zero, a)) = true__ % 0.88/1.02 f5(zero) = false__ % 0.88/1.02 less_equal(X, identity) = true__ % 0.88/1.02 less_equal(divide(X, Y), X) = true__ % 0.88/1.02 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) = true__ % 0.88/1.02 less_equal(zero, X) = true__ % 0.88/1.02 G: % 0.88/1.02 true__ = false__ % 0.88/1.02 % 0.88/1.02 This holds because % 0.88/1.02 % 0.88/1.02 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.88/1.02 % 0.88/1.02 % 0.88/1.02 divide(X, identity) -> zero % 0.88/1.02 divide(zero, Y1) -> zero % 0.88/1.02 f1(less_equal(X, Y), X, Y) -> zero % 0.88/1.02 f1(true__, X, Y) -> divide(X, Y) % 0.88/1.02 f2(divide(X, Y), X, Y) -> true__ % 0.88/1.02 f2(zero, zero, Y0) -> true__ % 0.88/1.02 f3(true__, X, Y) -> X % 0.88/1.02 f4(less_equal(Y, X), X, Y) -> Y % 0.88/1.02 f4(true__, X, Y) -> f3(f2(zero, X, Y), X, Y) % 0.88/1.02 f5(divide(zero, a)) -> true__ % 0.88/1.02 f5(zero) -> false__ % 0.88/1.02 less_equal(X, Y) -> f2(zero, X, Y) % 0.88/1.02 less_equal(X, identity) -> true__ % 0.88/1.02 less_equal(divide(X, Y), X) -> true__ % 0.88/1.02 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) -> true__ % 0.88/1.02 true__ -> false__ % 0.88/1.02 with the LPO induced by % 0.88/1.02 f4 > less_equal > f2 > f3 > identity > zero > f1 > divide > a > f5 > true__ > false__ % 0.88/1.02 % 0.88/1.02 % SZS output end Proof % 0.88/1.02 %------------------------------------------------------------------------------