%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : HEN002-2 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n021.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 0.21s 0.47s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : HEN002-2 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.14 % Command : moca.sh %s % 0.14/0.35 % Computer : n021.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % 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 13:14:29 EDT 2022 % 0.14/0.35 % CPUTime : % 0.21/0.47 % SZS status Unsatisfiable % 0.21/0.47 % SZS output start Proof % 0.21/0.47 The input problem is unsatisfiable because % 0.21/0.47 % 0.21/0.47 [1] the following set of Horn clauses is unsatisfiable: % 0.21/0.47 % 0.21/0.47 less_equal(X, Y) ==> quotient(X, Y, zero) % 0.21/0.47 quotient(X, Y, zero) ==> less_equal(X, Y) % 0.21/0.47 quotient(X, Y, Z) ==> less_equal(Z, X) % 0.21/0.47 quotient(X, Y, V1) & quotient(Y, Z, V2) & quotient(X, Z, V3) & quotient(V3, V2, V4) & quotient(V1, Z, V5) ==> less_equal(V4, V5) % 0.21/0.47 less_equal(zero, X) % 0.21/0.47 less_equal(X, Y) & less_equal(Y, X) ==> X = Y % 0.21/0.47 less_equal(X, identity) % 0.21/0.47 quotient(X, Y, divide(X, Y)) % 0.21/0.47 quotient(X, Y, Z) & quotient(X, Y, W) ==> Z = W % 0.21/0.47 quotient(X, identity, zero) % 0.21/0.47 quotient(zero, x, zero) ==> \bottom % 0.21/0.47 % 0.21/0.47 This holds because % 0.21/0.47 % 0.21/0.47 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.21/0.47 % 0.21/0.47 E: % 0.21/0.47 f1(less_equal(X, Y), X, Y) = true__ % 0.21/0.47 f1(true__, X, Y) = quotient(X, Y, zero) % 0.21/0.47 f10(less_equal(Y, X), X, Y) = Y % 0.21/0.47 f10(true__, X, Y) = f9(less_equal(X, Y), X, Y) % 0.21/0.47 f11(true__, Z, W) = Z % 0.21/0.47 f12(quotient(X, Y, W), X, Y, Z, W) = W % 0.21/0.47 f12(true__, X, Y, Z, W) = f11(quotient(X, Y, Z), Z, W) % 0.21/0.47 f13(quotient(zero, x, zero)) = true__ % 0.21/0.47 f13(true__) = false__ % 0.21/0.47 f2(quotient(X, Y, zero), X, Y) = true__ % 0.21/0.47 f2(true__, X, Y) = less_equal(X, Y) % 0.21/0.47 f3(quotient(X, Y, Z), Z, X) = true__ % 0.21/0.47 f3(true__, Z, X) = less_equal(Z, X) % 0.21/0.47 f4(true__, V4, V5) = less_equal(V4, V5) % 0.21/0.47 f5(true__, X, Y, V1, V4, V5) = f4(quotient(X, Y, V1), V4, V5) % 0.21/0.47 f6(true__, Y, Z, V2, X, V1, V4, V5) = f5(quotient(Y, Z, V2), X, Y, V1, V4, V5) % 0.21/0.47 f7(true__, X, Z, V3, Y, V2, V1, V4, V5) = f6(quotient(X, Z, V3), Y, Z, V2, X, V1, V4, V5) % 0.21/0.47 f8(quotient(V1, Z, V5), V3, V2, V4, X, Z, Y, V1, V5) = true__ % 0.21/0.47 f8(true__, V3, V2, V4, X, Z, Y, V1, V5) = f7(quotient(V3, V2, V4), X, Z, V3, Y, V2, V1, V4, V5) % 0.21/0.47 f9(true__, X, Y) = X % 0.21/0.47 less_equal(X, identity) = true__ % 0.21/0.47 less_equal(zero, X) = true__ % 0.21/0.47 quotient(X, Y, divide(X, Y)) = true__ % 0.21/0.47 quotient(X, identity, zero) = true__ % 0.21/0.47 G: % 0.21/0.47 true__ = false__ % 0.21/0.47 % 0.21/0.47 This holds because % 0.21/0.47 % 0.21/0.47 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.21/0.47 % 0.21/0.47 % 0.21/0.47 f1(f2(true__, Y0, Y1), Y0, Y1) -> true__ % 0.21/0.47 f1(less_equal(X, Y), X, Y) -> true__ % 0.21/0.47 f1(true__, X, Y) -> quotient(X, Y, zero) % 0.21/0.47 f10(f2(true__, Y0, Y1), Y1, Y0) -> Y0 % 0.21/0.47 f10(less_equal(Y, X), X, Y) -> Y % 0.21/0.47 f10(true__, X, Y) -> f9(less_equal(X, Y), X, Y) % 0.21/0.47 f11(quotient(X, Y, Z), Z, W) -> f12(true__, X, Y, Z, W) % 0.21/0.47 f11(true__, Z, W) -> Z % 0.21/0.47 f12(quotient(X, Y, W), X, Y, Z, W) -> W % 0.21/0.47 f12(true__, Y0, identity, Y3, zero) -> zero % 0.21/0.47 f12(true__, Y0, identity, zero, Y3) -> zero % 0.21/0.47 f12(true__, zero, Y1, Y3, zero) -> zero % 0.21/0.47 f12(true__, zero, Y1, zero, Y3) -> zero % 0.21/0.47 f13(quotient(zero, x, zero)) -> true__ % 0.21/0.47 f13(true__) -> false__ % 0.21/0.47 f2(quotient(X, Y, zero), X, Y) -> true__ % 0.21/0.47 f2(true__, Y0, identity) -> true__ % 0.21/0.47 f2(true__, zero, Y1) -> true__ % 0.21/0.47 f3(quotient(X, Y, Z), Z, X) -> true__ % 0.21/0.47 f3(true__, Z, X) -> less_equal(Z, X) % 0.21/0.47 f4(true__, V4, V5) -> less_equal(V4, V5) % 0.21/0.47 f5(quotient(Y, Z, V2), X, Y, V1, V4, V5) -> f6(true__, Y, Z, V2, X, V1, V4, V5) % 0.21/0.47 f5(true__, X, Y, V1, V4, V5) -> f4(quotient(X, Y, V1), V4, V5) % 0.21/0.47 f6(quotient(X, Z, V3), Y, Z, V2, X, V1, V4, V5) -> f7(true__, X, Z, V3, Y, V2, V1, V4, V5) % 0.21/0.47 f6(true__, Y0, identity, zero, Y3, Y4, Y5, Y6) -> f4(quotient(Y3, Y0, Y4), Y5, Y6) % 0.21/0.47 f7(quotient(V3, V2, V4), X, Z, V3, Y, V2, V1, V4, V5) -> f8(true__, V3, V2, V4, X, Z, Y, V1, V5) % 0.21/0.47 f8(quotient(V1, Z, V5), V3, V2, V4, X, Z, Y, V1, V5) -> true__ % 0.21/0.47 f8(true__, Y3, Y4, Y5, Y6, identity, Y7, Y0, zero) -> true__ % 0.21/0.47 f9(f2(true__, Y1, zero), Y1, zero) -> zero % 0.21/0.47 f9(f2(true__, identity, Y0), identity, Y0) -> Y0 % 0.21/0.47 f9(true__, X, Y) -> X % 0.21/0.47 false__ -> true__ % 0.21/0.47 less_equal(X, Y) -> f2(true__, X, Y) % 0.21/0.47 less_equal(X, identity) -> true__ % 0.21/0.47 less_equal(zero, X) -> true__ % 0.21/0.47 quotient(X, Y, divide(X, Y)) -> true__ % 0.21/0.47 quotient(X, identity, zero) -> true__ % 0.21/0.47 quotient(zero, Y1, zero) -> true__ % 0.21/0.47 with the LPO induced by % 0.21/0.47 x > f13 > f11 > f12 > f1 > f10 > f9 > divide > f5 > f6 > f7 > f8 > quotient > zero > f4 > f3 > less_equal > f2 > identity > false__ > true__ % 0.21/0.47 % 0.21/0.47 % SZS output end Proof % 0.21/0.47 %------------------------------------------------------------------------------