%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ALG006-1 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n032.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 : Thu Jul 14 17:40:16 EDT 2022 % Result : Unsatisfiable 97.62s 97.80s % Output : Proof 97.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.10 % Problem : ALG006-1 : TPTP v8.1.0. Released v2.2.0. % 0.02/0.10 % Command : moca.sh %s % 0.08/0.29 % Computer : n032.cluster.edu % 0.08/0.29 % Model : x86_64 x86_64 % 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.29 % Memory : 8042.1875MB % 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.29 % CPULimit : 300 % 0.08/0.29 % WCLimit : 600 % 0.08/0.29 % DateTime : Thu Jun 9 06:26:07 EDT 2022 % 0.08/0.30 % CPUTime : % 97.62/97.80 % SZS status Unsatisfiable % 97.62/97.80 % SZS output start Proof % 97.62/97.80 The input problem is unsatisfiable because % 97.62/97.80 % 97.62/97.80 [1] the following set of Horn clauses is unsatisfiable: % 97.62/97.80 % 97.62/97.80 difference(X, difference(Y, X)) = X % 97.62/97.80 difference(X, difference(X, Y)) = difference(Y, difference(Y, X)) % 97.62/97.80 difference(difference(X, Y), Z) = difference(difference(X, Z), difference(Y, Z)) % 97.62/97.80 difference(difference(a, c), b) = difference(difference(a, b), c) ==> \bottom % 97.62/97.80 % 97.62/97.80 This holds because % 97.62/97.80 % 97.62/97.80 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 97.62/97.80 % 97.62/97.80 E: % 97.62/97.80 difference(X, difference(X, Y)) = difference(Y, difference(Y, X)) % 97.62/97.80 difference(X, difference(Y, X)) = X % 97.62/97.80 difference(difference(X, Y), Z) = difference(difference(X, Z), difference(Y, Z)) % 97.62/97.80 f1(difference(difference(a, b), c)) = false__ % 97.62/97.80 f1(difference(difference(a, c), b)) = true__ % 97.62/97.80 G: % 97.62/97.80 true__ = false__ % 97.62/97.80 % 97.62/97.80 This holds because % 97.62/97.80 % 97.62/97.80 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 97.62/97.80 % 97.62/97.80 difference(X, difference(X, Y)) = difference(Y, difference(Y, X)) % 97.62/97.80 difference(X1, X1) = difference(difference(Y2, Y2), Y1) % 97.62/97.80 difference(X2, X2) = difference(difference(Y1, Y2), Y1) % 97.62/97.80 difference(Y0, Y0) = difference(X1, X1) % 97.62/97.80 difference(Y0, difference(Y0, difference(X1, difference(X1, difference(Y1, Y0))))) = difference(Y3, Y3) % 97.62/97.80 difference(Y0, difference(Y0, difference(difference(Y2, Y0), X1))) = difference(Y3, Y3) % 97.62/97.80 difference(Y0, difference(Y0, difference(difference(difference(X1, Y0), difference(X2, Y0)), Y2))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(X, Y), Z) = difference(difference(X, Z), difference(Y, Z)) % 97.62/97.80 difference(difference(X0, X1), difference(X0, Y1)) = difference(Y1, difference(Y1, difference(X0, X1))) % 97.62/97.80 difference(difference(X0, X1), difference(difference(X0, X2), X1)) = difference(difference(X2, X1), difference(difference(X2, X1), difference(X0, X1))) % 97.62/97.80 difference(difference(X0, Y1), Y2) = difference(difference(X0, Y2), Y1) % 97.62/97.80 difference(difference(X1, X1), Y1) = difference(Y1, Y1) % 97.62/97.80 difference(difference(X1, Y1), difference(difference(X1, Y1), difference(Y1, Y2))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(X1, Y2), difference(difference(X1, Y2), difference(Y1, difference(Y1, Y2)))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(X1, difference(X1, Y0)), Y2) = difference(difference(Y0, Y2), difference(Y0, X1)) % 97.62/97.80 difference(difference(X1, difference(X1, Y0)), Y2) = difference(difference(Y0, Y2), difference(difference(Y0, X1), Y2)) % 97.62/97.80 difference(difference(X1, difference(X1, Y0)), difference(Y0, difference(difference(Y0, X1), Y2))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(X1, difference(X1, Y0)), difference(Y2, difference(Y0, X1))) = difference(difference(Y0, Y2), difference(Y0, X1)) % 97.62/97.80 difference(difference(X1, difference(X1, difference(Y0, Y1))), difference(Y0, difference(difference(Y0, Y1), X1))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(Y0, X1), Y2) = difference(difference(Y0, Y2), difference(difference(X1, difference(X1, Y0)), Y2)) % 97.62/97.80 difference(difference(Y0, X1), difference(Y0, difference(difference(X1, difference(X1, Y0)), Y2))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(Y0, X1), difference(Y0, difference(difference(Y0, difference(Y0, X1)), Y2))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(Y0, Y1), difference(Y0, difference(X1, difference(X1, Y1)))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(Y0, Y1), difference(Y0, difference(X1, difference(Y0, Y1)))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(Y0, Y1), difference(Y0, difference(Y1, X1))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(Y0, Y1), difference(Y0, difference(difference(X1, difference(Y0, Y1)), difference(X2, difference(Y0, Y1))))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(Y0, difference(Y0, Y1)), difference(Y1, difference(X1, difference(Y0, difference(Y0, Y1))))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(Y0, difference(Y2, difference(X1, Y0))), difference(Y0, Y2)) = difference(Y3, Y3) % 97.62/97.80 difference(difference(Y1, X1), difference(difference(Y1, X1), difference(difference(X1, difference(X1, Y1)), Y2))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(difference(X0, X2), X1), difference(X0, X1)) = difference(Y2, Y2) % 97.62/97.80 difference(difference(difference(X0, Y1), X1), Y2) = difference(difference(difference(X0, X1), Y2), Y1) % 97.62/97.80 difference(difference(difference(X0, Y1), difference(X1, Y1)), Y2) = difference(difference(difference(X0, X1), Y2), difference(Y1, Y2)) % 97.62/97.80 difference(difference(difference(X0, Y1), difference(X1, Y1)), difference(X0, X1)) = difference(Y2, Y2) % 97.62/97.80 difference(difference(difference(X1, Y1), difference(X2, Y1)), difference(difference(difference(X1, Y1), difference(X2, Y1)), difference(Y1, Y2))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(difference(X1, Y2), difference(Y1, Y2)), difference(difference(X1, Y2), Y1)) = difference(Y3, Y3) % 97.62/97.80 difference(difference(difference(X1, difference(X1, Y0)), Y2), difference(Y0, Y2)) = difference(Y3, Y3) % 97.62/97.80 difference(difference(difference(X1, difference(X1, difference(Y0, Y1))), Y3), Y0) = difference(Y4, Y4) % 97.62/97.80 difference(difference(difference(Y0, Y1), X1), difference(Y0, difference(X1, difference(X1, difference(Y0, Y1))))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(difference(Y0, Y1), X1), difference(Y0, difference(difference(Y0, Y1), difference(difference(Y0, Y1), X1)))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(difference(Y0, Y1), difference(X1, difference(X1, Y0))), difference(Y0, X1)) = difference(Y3, Y3) % 97.62/97.80 difference(difference(difference(difference(X0, X1), Y1), Y2), difference(difference(X0, Y2), difference(X1, Y2))) = difference(Y3, Y3) % 97.62/97.80 difference(difference(difference(difference(X0, Y1), difference(X1, Y1)), Y2), difference(difference(X0, X1), Y2)) = difference(Y3, Y3) % 97.62/97.80 difference(difference(difference(difference(X1, difference(X1, Y0)), Y2), Y3), Y0) = difference(Y4, Y4) % 97.62/97.80 difference(difference(difference(difference(Y2, X1), X2), Y1), Y2) = difference(Y3, Y3) % 97.62/97.80 difference(X, difference(Y, X)) -> X % 97.62/97.80 difference(X1, difference(X1, difference(X0, difference(X0, X1)))) -> difference(X1, difference(X1, X0)) % 97.62/97.80 difference(X1, difference(X1, difference(Y0, difference(Y0, X1)))) -> difference(Y0, difference(Y0, X1)) % 97.62/97.80 difference(X1, difference(X2, difference(X0, X1))) -> difference(X1, X2) % 97.62/97.80 difference(Y0, difference(X1, X1)) -> Y0 % 97.62/97.80 difference(Y0, difference(X1, difference(X1, difference(Y1, Y0)))) -> Y0 % 97.62/97.80 difference(Y0, difference(Y1, difference(Y1, Y0))) -> difference(Y0, Y1) % 97.62/97.80 difference(Y0, difference(Y2, difference(difference(X1, Y0), X2))) -> difference(Y0, Y2) % 97.62/97.80 difference(Y0, difference(difference(X0, Y0), difference(X1, Y0))) -> Y0 % 97.62/97.80 difference(Y0, difference(difference(X1, X1), difference(Y2, Y0))) -> Y0 % 97.62/97.80 difference(Y0, difference(difference(X1, Y0), X2)) -> Y0 % 97.62/97.80 difference(Y0, difference(difference(Y1, Y0), difference(X1, X1))) -> Y0 % 97.62/97.80 difference(Y0, difference(difference(Y1, Y0), difference(difference(X0, Y0), difference(X1, Y0)))) -> Y0 % 97.62/97.80 difference(Y0, difference(difference(difference(X0, Y0), difference(X1, Y0)), difference(Y2, Y0))) -> Y0 % 97.62/97.80 difference(Y0, difference(difference(difference(X1, Y0), X2), Y2)) -> Y0 % 97.62/97.80 difference(Y1, difference(Y1, difference(Y1, X1))) -> difference(Y1, X1) % 97.62/97.80 difference(Y1, difference(Y1, difference(difference(Y1, X1), X2))) -> difference(difference(Y1, X1), X2) % 97.62/97.80 difference(Y1, difference(Y1, difference(difference(difference(Y1, X1), X2), X3))) -> difference(difference(difference(Y1, X1), X2), X3) % 97.62/97.80 difference(difference(X0, X1), difference(difference(X0, Y1), difference(X1, Y1))) -> difference(Y1, difference(Y1, difference(X0, X1))) % 97.62/97.80 difference(difference(X0, X1), difference(difference(X1, X1), difference(Y2, difference(X0, X1)))) -> difference(X0, X1) % 97.62/97.80 difference(difference(X0, X1), difference(difference(Y1, difference(X0, X1)), difference(X1, X1))) -> difference(X0, X1) % 97.62/97.80 difference(difference(X0, X2), difference(difference(X0, X2), difference(difference(X0, X1), X2))) -> difference(difference(X0, X1), X2) % 97.62/97.80 difference(difference(X0, Y1), difference(X0, Y1)) -> difference(Y1, Y1) % 97.62/97.80 difference(difference(X1, X1), difference(Y1, Y1)) -> difference(Y1, Y1) % 97.62/97.80 difference(difference(X1, X2), difference(difference(X0, X1), Y2)) -> difference(X1, X2) % 97.62/97.80 difference(difference(X1, Y1), Y1) -> difference(X1, Y1) % 97.62/97.80 difference(difference(X1, Y1), difference(X1, difference(X2, Y1))) -> difference(X1, difference(X1, difference(X2, Y1))) % 97.62/97.80 difference(difference(X1, Y1), difference(X2, Y1)) -> difference(difference(X1, Y1), X2) % 97.62/97.80 difference(difference(X1, Y1), difference(Y1, Y2)) -> difference(X1, Y1) % 97.62/97.80 difference(difference(X1, Y1), difference(Y1, difference(Y2, difference(X1, Y1)))) -> difference(X1, Y1) % 97.62/97.80 difference(difference(X1, Y1), difference(Y1, difference(difference(Y2, difference(X1, Y1)), difference(Y3, difference(X1, Y1))))) -> difference(X1, Y1) % 97.62/97.80 difference(difference(X1, Y1), difference(difference(Y1, Y2), Y3)) -> difference(X1, Y1) % 97.62/97.80 difference(difference(X1, Y1), difference(difference(Y1, difference(Y2, difference(X1, Y1))), difference(Y3, difference(X1, Y1)))) -> difference(X1, Y1) % 97.62/97.80 difference(difference(X1, Y2), difference(Y1, difference(Y1, Y2))) -> difference(X1, Y2) % 97.62/97.80 difference(difference(X1, Y2), difference(difference(Y1, difference(X1, Y2)), difference(Y2, difference(Y3, difference(X1, Y2))))) -> difference(X1, Y2) % 97.62/97.80 difference(difference(X1, difference(X1, Y0)), difference(Y0, difference(Y0, X1))) -> difference(X1, X1) % 97.62/97.80 difference(difference(X1, difference(X1, Y0)), difference(difference(Y2, Y0), difference(Y0, X1))) -> difference(Y0, difference(Y0, X1)) % 97.62/97.80 difference(difference(X1, difference(X1, Y1)), difference(difference(Y1, X1), Y2)) -> difference(X1, difference(X1, Y1)) % 97.62/97.80 difference(difference(X1, difference(X1, Y1)), difference(difference(Y1, X1), difference(Y2, difference(X1, difference(X1, Y1))))) -> difference(X1, difference(X1, Y1)) % 97.62/97.80 difference(difference(X1, difference(X1, Y2)), difference(difference(Y1, difference(X1, difference(X1, Y2))), difference(Y2, X1))) -> difference(X1, difference(X1, Y2)) % 97.62/97.80 difference(difference(X2, X1), difference(difference(Y1, difference(X2, X1)), difference(difference(X0, X2), X1))) -> difference(X2, X1) % 97.62/97.80 difference(difference(X2, X1), difference(difference(difference(X0, X2), X1), difference(Y2, difference(X2, X1)))) -> difference(X2, X1) % 97.62/97.80 difference(difference(Y0, Y1), difference(Y0, difference(X1, difference(Y0, Y1)))) -> difference(false__, false__) % 97.62/97.80 difference(difference(Y0, Y2), difference(X1, Y0)) -> difference(Y0, difference(Y2, difference(X1, Y0))) % 97.62/97.80 difference(difference(Y0, Y2), difference(difference(X1, Y0), Y2)) -> difference(Y0, Y2) % 97.62/97.80 difference(difference(Y0, Y2), difference(difference(X1, Y0), difference(X2, Y0))) -> difference(Y0, difference(Y2, difference(difference(X1, Y0), difference(X2, Y0)))) % 97.62/97.80 difference(difference(Y0, Y2), difference(difference(X1, Y2), Y2)) -> difference(difference(Y0, Y2), difference(X1, Y2)) % 97.62/97.80 difference(difference(Y0, Y2), difference(difference(Y0, difference(Y0, X1)), Y2)) -> difference(difference(Y0, X1), Y2) % 97.62/97.80 difference(difference(Y0, Y2), difference(difference(difference(X1, Y0), difference(X2, Y0)), Y2)) -> difference(Y0, Y2) % 97.62/97.80 difference(difference(Y0, difference(Y0, X1)), difference(X1, difference(X1, Y0))) -> difference(X1, X1) % 97.62/97.80 difference(difference(Y0, difference(Y2, X1)), difference(X1, difference(X1, Y2))) -> difference(difference(Y0, Y2), difference(Y2, X1)) % 97.62/97.80 difference(difference(Y1, X1), difference(X1, difference(X1, Y1))) -> difference(Y1, X1) % 97.62/97.80 difference(difference(Y1, X1), difference(difference(X1, difference(X1, Y1)), Y2)) -> difference(Y1, X1) % 97.62/97.80 difference(difference(Y1, X1), difference(difference(X1, difference(X1, Y1)), difference(Y2, difference(Y1, X1)))) -> difference(Y1, X1) % 97.62/97.80 difference(difference(Y1, Y1), difference(X1, X1)) -> difference(Y1, Y1) % 97.62/97.80 difference(difference(Y1, Y2), Y1) -> difference(Y1, Y1) % 97.62/97.80 difference(difference(Y1, Y2), Y1) -> difference(false__, false__) % 97.62/97.80 difference(difference(Y2, X1), difference(difference(Y1, difference(Y2, X1)), difference(X1, difference(X1, Y2)))) -> difference(Y2, X1) % 97.62/97.80 difference(difference(difference(X0, X1), Y1), difference(difference(X0, Y1), difference(X1, Y1))) -> difference(Y1, Y1) % 97.62/97.80 difference(difference(difference(X0, X2), X1), difference(X2, X1)) -> difference(difference(X0, X1), difference(X2, X1)) % 97.62/97.80 difference(difference(difference(X0, Y1), difference(X1, Y1)), difference(X0, X1)) -> difference(X1, X1) % 97.62/97.80 difference(difference(difference(X0, Y1), difference(X1, Y1)), difference(X0, X1)) -> difference(false__, false__) % 97.62/97.80 difference(difference(difference(X0, Y1), difference(X1, Y1)), difference(difference(X0, X1), Y1)) -> difference(Y1, Y1) % 97.62/97.80 difference(difference(difference(X1, Y1), X2), difference(Y1, Y2)) -> difference(difference(X1, Y1), X2) % 97.62/97.80 difference(difference(difference(X1, Y1), X2), difference(Y1, difference(Y2, difference(difference(X1, Y1), X2)))) -> difference(difference(X1, Y1), X2) % 97.62/97.80 difference(difference(difference(X1, Y1), difference(X2, Y1)), difference(Y1, Y2)) -> difference(difference(X1, Y1), difference(X2, Y1)) % 97.62/97.80 difference(difference(difference(X1, Y1), difference(X2, Y1)), difference(Y1, difference(Y2, difference(difference(X1, Y1), difference(X2, Y1))))) -> difference(difference(X1, Y1), difference(X2, Y1)) % 97.62/97.80 difference(difference(difference(X1, Y2), Y1), Y2) -> difference(difference(X1, Y2), difference(Y1, Y2)) % 97.62/97.80 difference(difference(difference(X1, difference(X1, Y0)), Y2), Y0) -> difference(false__, false__) % 97.62/97.80 difference(difference(difference(Y1, X1), Y2), Y1) -> difference(false__, false__) % 97.62/97.80 difference(difference(difference(Y1, X1), Y2), difference(Y1, Y2)) -> difference(false__, false__) % 97.62/97.80 difference(difference(difference(Y2, X1), Y1), difference(difference(X1, difference(X1, Y2)), Y1)) -> difference(difference(Y2, X1), Y1) % 97.62/97.80 difference(difference(difference(difference(X0, Y1), difference(X1, Y1)), Y2), difference(X0, X1)) -> difference(false__, false__) % 97.62/97.80 difference(difference(difference(difference(X1, Y1), X2), X3), Y1) -> difference(difference(difference(X1, Y1), X2), X3) % 97.62/97.80 difference(difference(difference(difference(X1, Y2), difference(X2, Y2)), Y1), difference(Y2, Y1)) -> difference(difference(difference(X1, Y2), difference(X2, Y2)), Y1) % 97.62/97.80 difference(difference(difference(difference(Y1, X1), X2), Y2), difference(Y1, Y2)) -> difference(false__, false__) % 97.62/97.80 f1(difference(difference(a, b), c)) -> false__ % 97.62/97.80 f1(difference(difference(a, b), difference(c, b))) -> true__ % 97.62/97.80 f1(difference(difference(a, c), b)) -> true__ % 97.62/97.80 true__ -> false__ % 97.62/97.80 with the LPO induced by % 97.62/97.80 c > b > a > f1 > difference > true__ > false__ % 97.62/97.80 % 97.62/97.80 % SZS output end Proof % 97.62/97.80 %------------------------------------------------------------------------------