%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : HEN005-6 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n023.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 12:59:00 EDT 2022 % Result : Unsatisfiable 6.34s 6.33s % Output : Proof 6.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : HEN005-6 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n023.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 : Fri Jul 1 14:42:44 EDT 2022 % 0.13/0.34 % CPUTime : % 6.34/6.33 % SZS status Unsatisfiable % 6.34/6.33 % SZS output start Proof % 6.34/6.33 The input problem is unsatisfiable because % 6.34/6.33 % 6.34/6.33 [1] the following set of Horn clauses is unsatisfiable: % 6.34/6.33 % 6.34/6.33 less_equal(X, Y) ==> divide(X, Y) = zero % 6.34/6.33 divide(X, Y) = zero ==> less_equal(X, Y) % 6.34/6.33 less_equal(divide(X, Y), X) % 6.34/6.33 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) % 6.34/6.33 less_equal(zero, X) % 6.34/6.33 less_equal(X, Y) & less_equal(Y, X) ==> X = Y % 6.34/6.33 less_equal(X, identity) % 6.34/6.33 divide(X, identity) = zero % 6.34/6.33 divide(zero, X) = zero % 6.34/6.33 less_equal(a, b) % 6.34/6.33 less_equal(b, c) % 6.34/6.33 less_equal(a, c) ==> \bottom % 6.34/6.33 % 6.34/6.33 This holds because % 6.34/6.33 % 6.34/6.33 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.34/6.33 % 6.34/6.33 E: % 6.34/6.33 divide(X, identity) = zero % 6.34/6.33 divide(zero, X) = zero % 6.34/6.33 f1(less_equal(X, Y), X, Y) = zero % 6.34/6.33 f1(true__, X, Y) = divide(X, Y) % 6.34/6.33 f2(divide(X, Y), X, Y) = true__ % 6.34/6.33 f2(zero, X, Y) = less_equal(X, Y) % 6.34/6.33 f3(true__, X, Y) = X % 6.34/6.33 f4(less_equal(Y, X), X, Y) = Y % 6.34/6.33 f4(true__, X, Y) = f3(less_equal(X, Y), X, Y) % 6.34/6.33 f5(less_equal(a, c)) = true__ % 6.34/6.33 f5(true__) = false__ % 6.34/6.33 less_equal(X, identity) = true__ % 6.34/6.33 less_equal(a, b) = true__ % 6.34/6.33 less_equal(b, c) = true__ % 6.34/6.33 less_equal(divide(X, Y), X) = true__ % 6.34/6.33 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) = true__ % 6.34/6.33 less_equal(zero, X) = true__ % 6.34/6.33 G: % 6.34/6.33 true__ = false__ % 6.34/6.33 % 6.34/6.33 This holds because % 6.34/6.33 % 6.34/6.33 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.34/6.33 % 6.34/6.33 % 6.34/6.33 divide(X, Y) -> f1(true__, X, Y) % 6.34/6.33 divide(X, identity) -> zero % 6.34/6.33 divide(zero, X) -> zero % 6.34/6.33 f1(f2(zero, Y0, Y1), Y0, Y1) -> zero % 6.34/6.33 f1(less_equal(X, Y), X, Y) -> zero % 6.34/6.33 f1(true__, X0, X0) -> zero % 6.34/6.33 f1(true__, Y0, identity) -> zero % 6.34/6.33 f1(true__, a, b) -> zero % 6.34/6.33 f1(true__, a, c) -> zero % 6.34/6.33 f1(true__, b, c) -> zero % 6.34/6.33 f1(true__, f1(true__, X0, X0), zero) -> zero % 6.34/6.33 f1(true__, f1(true__, X0, X1), f1(true__, identity, X1)) -> zero % 6.34/6.33 f1(true__, f1(true__, X0, f1(true__, X0, zero)), zero) -> zero % 6.34/6.33 f1(true__, f1(true__, Y1, X1), Y1) -> zero % 6.34/6.33 f1(true__, f1(true__, a, Y2), f1(true__, b, Y2)) -> zero % 6.34/6.33 f1(true__, f1(true__, a, c), zero) -> zero % 6.34/6.33 f1(true__, f1(true__, b, X0), f1(true__, c, X0)) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, X0, X1), f1(true__, X2, X1)), f1(true__, f1(true__, X0, X2), X1)) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, X0, X1), f1(true__, identity, X1)), zero) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, Y0, Y1), zero), f1(true__, f1(true__, Y0, zero), Y1)) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, Y0, b), zero), f1(true__, f1(true__, Y0, a), b)) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, Y0, c), zero), f1(true__, f1(true__, Y0, a), c)) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, Y0, c), zero), f1(true__, f1(true__, Y0, b), c)) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, Y0, f1(true__, Y0, zero)), zero), zero) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, a, X0), b), zero) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, a, Y1), f1(true__, b, Y1)), zero) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, a, Y1), f1(true__, c, Y1)), zero) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, a, c), zero), zero) -> zero % 6.34/6.33 f1(true__, f1(true__, f1(true__, b, Y1), f1(true__, c, Y1)), zero) -> zero % 6.34/6.33 f1(true__, zero, Y1) -> zero % 6.34/6.33 f2(divide(X, Y), X, Y) -> true__ % 6.34/6.33 f2(f1(true__, Y0, Y1), Y0, Y1) -> true__ % 6.34/6.33 f2(zero, Y0, identity) -> true__ % 6.34/6.33 f2(zero, Y1, Y1) -> true__ % 6.34/6.33 f2(zero, a, b) -> true__ % 6.34/6.33 f2(zero, a, c) -> true__ % 6.34/6.33 f2(zero, b, c) -> true__ % 6.34/6.33 f2(zero, f1(true__, X0, X0), zero) -> true__ % 6.34/6.33 f2(zero, f1(true__, X0, X1), f1(true__, identity, X1)) -> true__ % 6.34/6.33 f2(zero, f1(true__, Y0, Y1), Y0) -> true__ % 6.34/6.33 f2(zero, f1(true__, a, X0), f1(true__, b, X0)) -> true__ % 6.34/6.33 f2(zero, f1(true__, a, c), zero) -> true__ % 6.34/6.33 f2(zero, f1(true__, b, X0), f1(true__, c, X0)) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, Y0, Y1), f1(true__, Y2, Y1)), f1(true__, f1(true__, Y0, Y2), Y1)) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, Y0, Y1), f1(true__, identity, Y1)), zero) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, Y0, Y1), zero), f1(true__, f1(true__, Y0, Y1), Y1)) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, Y0, Y1), zero), f1(true__, f1(true__, Y0, zero), Y1)) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, Y0, b), zero), f1(true__, f1(true__, Y0, a), b)) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, Y0, c), zero), f1(true__, f1(true__, Y0, a), c)) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, Y0, c), zero), f1(true__, f1(true__, Y0, b), c)) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, Y0, f1(true__, Y0, zero)), zero), zero) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, Y1, Y1), zero), zero) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, a, Y1), f1(true__, b, Y1)), zero) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, a, Y1), f1(true__, c, Y1)), zero) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, a, c), zero), zero) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, b, Y1), f1(true__, c, Y1)), zero) -> true__ % 6.34/6.33 f2(zero, f1(true__, f1(true__, f1(true__, a, X1), b), zero), zero) -> true__ % 6.34/6.33 f2(zero, zero, Y0) -> true__ % 6.34/6.33 f2(zero, zero, zero) -> true__ % 6.34/6.33 f3(f2(zero, Y1, f1(true__, Y1, X1)), Y1, f1(true__, Y1, X1)) -> f1(true__, Y1, X1) % 6.34/6.33 f3(f2(zero, Y1, zero), Y1, zero) -> zero % 6.34/6.33 f3(f2(zero, b, a), b, a) -> a % 6.34/6.33 f3(f2(zero, c, a), c, a) -> a % 6.34/6.33 f3(f2(zero, c, b), c, b) -> b % 6.34/6.33 f3(f2(zero, f1(true__, b, X0), f1(true__, a, X0)), f1(true__, b, X0), f1(true__, a, X0)) -> f1(true__, a, X0) % 6.34/6.33 f3(f2(zero, f1(true__, c, X0), f1(true__, b, X0)), f1(true__, c, X0), f1(true__, b, X0)) -> f1(true__, b, X0) % 6.34/6.33 f3(f2(zero, f1(true__, f1(true__, X0, X2), X1), f1(true__, f1(true__, X0, X1), f1(true__, X2, X1))), f1(true__, f1(true__, X0, X2), X1), f1(true__, f1(true__, X0, X1), f1(true__, X2, X1))) -> f1(true__, f1(true__, X0, X1), f1(true__, X2, X1)) % 6.34/6.33 f3(f2(zero, f1(true__, f1(true__, Y0, a), b), f1(true__, f1(true__, Y0, b), zero)), f1(true__, f1(true__, Y0, a), b), f1(true__, f1(true__, Y0, b), zero)) -> f1(true__, f1(true__, Y0, b), zero) % 6.34/6.33 f3(f2(zero, f1(true__, f1(true__, Y0, b), c), f1(true__, f1(true__, Y0, c), zero)), f1(true__, f1(true__, Y0, b), c), f1(true__, f1(true__, Y0, c), zero)) -> f1(true__, f1(true__, Y0, c), zero) % 6.34/6.33 f3(f2(zero, f1(true__, f1(true__, Y0, zero), Y2), f1(true__, f1(true__, Y0, Y2), zero)), f1(true__, f1(true__, Y0, zero), Y2), f1(true__, f1(true__, Y0, Y2), zero)) -> f1(true__, f1(true__, Y0, Y2), zero) % 6.34/6.33 f3(f2(zero, f1(true__, identity, X1), f1(true__, X0, X1)), f1(true__, identity, X1), f1(true__, X0, X1)) -> f1(true__, X0, X1) % 6.34/6.33 f3(f2(zero, identity, Y0), identity, Y0) -> Y0 % 6.34/6.33 f3(true__, X, Y) -> X % 6.34/6.33 f4(f2(zero, Y0, Y1), Y1, Y0) -> Y0 % 6.34/6.33 f4(less_equal(Y, X), X, Y) -> Y % 6.34/6.33 f4(true__, X, Y) -> f3(less_equal(X, Y), X, Y) % 6.34/6.33 f5(f2(zero, a, c)) -> true__ % 6.34/6.33 f5(less_equal(a, c)) -> true__ % 6.34/6.33 f5(true__) -> false__ % 6.34/6.33 false__ -> true__ % 6.34/6.33 less_equal(X, Y) -> f2(zero, X, Y) % 6.34/6.33 less_equal(X, identity) -> true__ % 6.34/6.33 less_equal(a, b) -> true__ % 6.34/6.33 less_equal(b, c) -> true__ % 6.34/6.33 less_equal(divide(X, Y), X) -> true__ % 6.34/6.33 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) -> true__ % 6.34/6.33 less_equal(zero, X) -> true__ % 6.34/6.33 with the LPO induced by % 6.34/6.33 f5 > c > b > a > f4 > f3 > less_equal > divide > f1 > zero > identity > f2 > false__ > true__ % 6.34/6.33 % 6.34/6.33 % SZS output end Proof % 6.34/6.33 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