%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP147-1 : TPTP v8.1.0. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n024.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 10:53:25 EDT 2022 % Result : Unsatisfiable 142.99s 142.40s % Output : Proof 142.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP147-1 : TPTP v8.1.0. Bugfixed v1.2.1. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n024.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jun 13 16:41:03 EDT 2022 % 0.12/0.33 % CPUTime : % 142.99/142.40 % SZS status Unsatisfiable % 142.99/142.40 % SZS output start Proof % 142.99/142.40 The input problem is unsatisfiable because % 142.99/142.40 % 142.99/142.40 [1] the following set of Horn clauses is unsatisfiable: % 142.99/142.40 % 142.99/142.40 multiply(identity, X) = X % 142.99/142.40 multiply(inverse(X), X) = identity % 142.99/142.40 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 142.99/142.40 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 142.99/142.40 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 142.99/142.40 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 142.99/142.40 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 142.99/142.40 least_upper_bound(X, X) = X % 142.99/142.40 greatest_lower_bound(X, X) = X % 142.99/142.40 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 142.99/142.40 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 142.99/142.40 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 142.99/142.40 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 142.99/142.40 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 142.99/142.40 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 142.99/142.40 greatest_lower_bound(a, c) = a % 142.99/142.40 greatest_lower_bound(b, c) = b % 142.99/142.40 greatest_lower_bound(least_upper_bound(a, b), c) = least_upper_bound(a, b) ==> \bottom % 142.99/142.40 % 142.99/142.40 This holds because % 142.99/142.40 % 142.99/142.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 142.99/142.40 % 142.99/142.40 E: % 142.99/142.40 f1(greatest_lower_bound(least_upper_bound(a, b), c)) = true__ % 142.99/142.40 f1(least_upper_bound(a, b)) = false__ % 142.99/142.40 greatest_lower_bound(X, X) = X % 142.99/142.40 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 142.99/142.40 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 142.99/142.40 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 142.99/142.40 greatest_lower_bound(a, c) = a % 142.99/142.40 greatest_lower_bound(b, c) = b % 142.99/142.40 least_upper_bound(X, X) = X % 142.99/142.40 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 142.99/142.40 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 142.99/142.40 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 142.99/142.40 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 142.99/142.40 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 142.99/142.40 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 142.99/142.40 multiply(identity, X) = X % 142.99/142.40 multiply(inverse(X), X) = identity % 142.99/142.40 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 142.99/142.40 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 142.99/142.40 G: % 142.99/142.40 true__ = false__ % 142.99/142.40 % 142.99/142.40 This holds because % 142.99/142.40 % 142.99/142.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 142.99/142.40 % 142.99/142.40 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 142.99/142.40 greatest_lower_bound(Y0, a) = greatest_lower_bound(a, Y0) % 142.99/142.40 greatest_lower_bound(c, Y0) = greatest_lower_bound(Y0, c) % 142.99/142.40 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 142.99/142.40 least_upper_bound(Y0, c) = least_upper_bound(c, Y0) % 142.99/142.40 f1(greatest_lower_bound(c, least_upper_bound(a, b))) -> true__ % 142.99/142.40 f1(greatest_lower_bound(c, least_upper_bound(b, a))) -> true__ % 142.99/142.40 f1(greatest_lower_bound(least_upper_bound(a, b), c)) -> true__ % 142.99/142.40 f1(least_upper_bound(a, b)) -> false__ % 142.99/142.40 f1(least_upper_bound(b, a)) -> false__ % 142.99/142.40 greatest_lower_bound(X, X) -> X % 142.99/142.40 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X % 142.99/142.40 greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y0)) -> greatest_lower_bound(Y0, Y1) % 142.99/142.40 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0 % 142.99/142.40 greatest_lower_bound(Y1, greatest_lower_bound(X1, Y1)) -> greatest_lower_bound(X1, Y1) % 142.99/142.40 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2) % 142.99/142.40 greatest_lower_bound(a, c) -> a % 142.99/142.40 greatest_lower_bound(a, greatest_lower_bound(Y0, c)) -> greatest_lower_bound(a, Y0) % 142.99/142.40 greatest_lower_bound(a, greatest_lower_bound(c, Y2)) -> greatest_lower_bound(a, Y2) % 142.99/142.40 greatest_lower_bound(a, least_upper_bound(Y0, c)) -> a % 142.99/142.40 greatest_lower_bound(a, least_upper_bound(c, X1)) -> a % 142.99/142.40 greatest_lower_bound(b, c) -> b % 142.99/142.40 greatest_lower_bound(b, greatest_lower_bound(Y0, c)) -> greatest_lower_bound(b, Y0) % 142.99/142.40 greatest_lower_bound(b, greatest_lower_bound(c, Y2)) -> greatest_lower_bound(b, Y2) % 142.99/142.40 greatest_lower_bound(b, least_upper_bound(Y0, c)) -> b % 142.99/142.40 greatest_lower_bound(b, least_upper_bound(c, X1)) -> b % 142.99/142.40 greatest_lower_bound(c, a) -> a % 142.99/142.40 greatest_lower_bound(c, b) -> b % 142.99/142.40 greatest_lower_bound(c, greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, a) % 142.99/142.40 greatest_lower_bound(c, greatest_lower_bound(Y0, b)) -> greatest_lower_bound(b, Y0) % 142.99/142.40 greatest_lower_bound(c, greatest_lower_bound(a, Y0)) -> greatest_lower_bound(a, Y0) % 142.99/142.40 greatest_lower_bound(c, greatest_lower_bound(b, Y2)) -> greatest_lower_bound(b, Y2) % 142.99/142.40 greatest_lower_bound(c, least_upper_bound(a, greatest_lower_bound(X1, c))) -> least_upper_bound(a, greatest_lower_bound(X1, c)) % 142.99/142.40 greatest_lower_bound(c, least_upper_bound(a, greatest_lower_bound(c, X1))) -> least_upper_bound(a, greatest_lower_bound(c, X1)) % 142.99/142.40 greatest_lower_bound(c, least_upper_bound(b, a)) -> least_upper_bound(b, a) % 142.99/142.40 greatest_lower_bound(c, least_upper_bound(b, greatest_lower_bound(c, X1))) -> least_upper_bound(b, greatest_lower_bound(c, X1)) % 142.99/142.40 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z)) % 142.99/142.40 greatest_lower_bound(least_upper_bound(X0, a), least_upper_bound(c, X0)) -> least_upper_bound(X0, a) % 142.99/142.40 greatest_lower_bound(least_upper_bound(X0, b), least_upper_bound(c, X0)) -> least_upper_bound(X0, b) % 142.99/142.40 greatest_lower_bound(least_upper_bound(X0, c), least_upper_bound(c, X0)) -> least_upper_bound(X0, c) % 142.99/142.40 greatest_lower_bound(least_upper_bound(Y0, b), least_upper_bound(Y0, c)) -> least_upper_bound(Y0, b) % 142.99/142.40 greatest_lower_bound(least_upper_bound(Y0, c), a) -> a % 142.99/142.40 greatest_lower_bound(least_upper_bound(Y0, c), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a) % 142.99/142.40 greatest_lower_bound(least_upper_bound(a, X0), least_upper_bound(c, X0)) -> least_upper_bound(a, X0) % 142.99/142.40 greatest_lower_bound(least_upper_bound(a, Y0), least_upper_bound(Y0, c)) -> least_upper_bound(a, Y0) % 142.99/142.40 greatest_lower_bound(least_upper_bound(b, X0), least_upper_bound(c, X0)) -> least_upper_bound(b, X0) % 142.99/142.40 greatest_lower_bound(least_upper_bound(c, Y0), a) -> a % 142.99/142.40 greatest_lower_bound(least_upper_bound(c, Y0), least_upper_bound(Y0, a)) -> least_upper_bound(Y0, a) % 142.99/142.40 greatest_lower_bound(least_upper_bound(c, Y0), least_upper_bound(Y0, b)) -> least_upper_bound(Y0, b) % 142.99/142.40 greatest_lower_bound(least_upper_bound(c, Y0), least_upper_bound(Y0, c)) -> least_upper_bound(Y0, c) % 142.99/142.40 greatest_lower_bound(least_upper_bound(c, Y0), least_upper_bound(a, Y0)) -> least_upper_bound(a, Y0) % 142.99/142.40 greatest_lower_bound(multiply(Y0, a), multiply(Y0, c)) -> multiply(Y0, a) % 142.99/142.40 greatest_lower_bound(multiply(Y0, b), multiply(Y0, c)) -> multiply(Y0, b) % 142.99/142.40 inverse(identity) -> identity % 142.99/142.40 inverse(inverse(Y1)) -> Y1 % 142.99/142.40 least_upper_bound(X, X) -> X % 142.99/142.40 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X % 142.99/142.40 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0 % 142.99/142.40 least_upper_bound(Y0, least_upper_bound(Y1, Y0)) -> least_upper_bound(Y0, Y1) % 142.99/142.40 least_upper_bound(Y1, least_upper_bound(X1, Y1)) -> least_upper_bound(X1, Y1) % 142.99/142.40 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2) % 142.99/142.40 least_upper_bound(a, c) -> c % 142.99/142.40 least_upper_bound(a, greatest_lower_bound(c, least_upper_bound(X1, a))) -> greatest_lower_bound(c, least_upper_bound(X1, a)) % 142.99/142.40 least_upper_bound(a, greatest_lower_bound(c, least_upper_bound(a, X1))) -> greatest_lower_bound(c, least_upper_bound(a, X1)) % 142.99/142.40 least_upper_bound(a, least_upper_bound(Y0, c)) -> least_upper_bound(c, Y0) % 142.99/142.40 least_upper_bound(a, least_upper_bound(c, Y2)) -> least_upper_bound(c, Y2) % 142.99/142.40 least_upper_bound(b, c) -> c % 142.99/142.40 least_upper_bound(b, greatest_lower_bound(c, least_upper_bound(X1, b))) -> greatest_lower_bound(c, least_upper_bound(X1, b)) % 142.99/142.40 least_upper_bound(b, greatest_lower_bound(c, least_upper_bound(b, X1))) -> greatest_lower_bound(c, least_upper_bound(b, X1)) % 142.99/142.40 least_upper_bound(b, least_upper_bound(Y0, c)) -> least_upper_bound(Y0, c) % 142.99/142.40 least_upper_bound(b, least_upper_bound(c, Y2)) -> least_upper_bound(c, Y2) % 142.99/142.40 least_upper_bound(c, a) -> c % 142.99/142.40 least_upper_bound(c, b) -> c % 142.99/142.40 least_upper_bound(c, greatest_lower_bound(X1, a)) -> c % 142.99/142.40 least_upper_bound(c, greatest_lower_bound(Y0, b)) -> c % 142.99/142.40 least_upper_bound(c, greatest_lower_bound(a, X1)) -> c % 142.99/142.40 least_upper_bound(c, greatest_lower_bound(b, X0)) -> c % 142.99/142.40 least_upper_bound(c, least_upper_bound(X0, a)) -> least_upper_bound(c, X0) % 142.99/142.40 least_upper_bound(c, least_upper_bound(X0, b)) -> least_upper_bound(c, X0) % 142.99/142.40 least_upper_bound(c, least_upper_bound(a, Y0)) -> least_upper_bound(c, Y0) % 142.99/142.40 least_upper_bound(c, least_upper_bound(b, Y2)) -> least_upper_bound(c, Y2) % 142.99/142.40 least_upper_bound(greatest_lower_bound(X0, a), greatest_lower_bound(a, X0)) -> greatest_lower_bound(X0, a) % 142.99/142.40 least_upper_bound(greatest_lower_bound(X0, b), greatest_lower_bound(b, X0)) -> greatest_lower_bound(X0, b) % 142.99/142.40 least_upper_bound(greatest_lower_bound(X0, c), greatest_lower_bound(a, X0)) -> greatest_lower_bound(X0, c) % 142.99/142.40 least_upper_bound(greatest_lower_bound(X0, c), greatest_lower_bound(b, X0)) -> greatest_lower_bound(X0, c) % 142.99/142.40 least_upper_bound(greatest_lower_bound(Y0, b), c) -> c % 142.99/142.40 least_upper_bound(greatest_lower_bound(Y0, b), greatest_lower_bound(Y0, c)) -> greatest_lower_bound(Y0, c) % 142.99/142.40 least_upper_bound(greatest_lower_bound(Y0, b), greatest_lower_bound(c, Y0)) -> greatest_lower_bound(c, Y0) % 142.99/142.40 least_upper_bound(greatest_lower_bound(Y0, c), greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, c) % 142.99/142.40 least_upper_bound(greatest_lower_bound(a, Y0), greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, a) % 142.99/142.40 least_upper_bound(greatest_lower_bound(a, Y0), greatest_lower_bound(Y0, c)) -> greatest_lower_bound(Y0, c) % 142.99/142.40 least_upper_bound(greatest_lower_bound(b, X0), greatest_lower_bound(c, X0)) -> greatest_lower_bound(c, X0) % 142.99/142.40 least_upper_bound(greatest_lower_bound(b, Y0), c) -> c % 142.99/142.40 least_upper_bound(greatest_lower_bound(b, Y0), greatest_lower_bound(Y0, b)) -> greatest_lower_bound(Y0, b) % 142.99/142.40 least_upper_bound(greatest_lower_bound(b, Y0), greatest_lower_bound(Y0, c)) -> greatest_lower_bound(Y0, c) % 142.99/142.40 least_upper_bound(greatest_lower_bound(c, X0), greatest_lower_bound(a, X0)) -> greatest_lower_bound(c, X0) % 142.99/142.40 least_upper_bound(greatest_lower_bound(c, Y0), greatest_lower_bound(Y0, a)) -> greatest_lower_bound(Y0, c) % 142.99/142.40 least_upper_bound(greatest_lower_bound(c, Y0), greatest_lower_bound(Y0, a)) -> greatest_lower_bound(c, Y0) % 142.99/142.40 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z)) % 142.99/142.40 least_upper_bound(multiply(Y0, a), multiply(Y0, c)) -> multiply(Y0, c) % 142.99/142.40 multiply(X, greatest_lower_bound(Y, Z)) -> greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 142.99/142.40 multiply(X, least_upper_bound(Y, Z)) -> least_upper_bound(multiply(X, Y), multiply(X, Z)) % 142.99/142.40 multiply(X0, inverse(X0)) -> identity % 142.99/142.40 multiply(X0, multiply(inverse(X0), Y1)) -> Y1 % 142.99/142.40 multiply(Y0, identity) -> Y0 % 142.99/142.40 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity % 142.99/142.40 multiply(greatest_lower_bound(Y, Z), X) -> greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 142.99/142.40 multiply(greatest_lower_bound(Y0, identity), Y1) -> greatest_lower_bound(Y1, multiply(Y0, Y1)) % 142.99/142.40 multiply(identity, X) -> X % 142.99/142.40 multiply(inverse(X), X) -> identity % 142.99/142.40 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2 % 142.99/142.40 multiply(least_upper_bound(Y, Z), X) -> least_upper_bound(multiply(Y, X), multiply(Z, X)) % 142.99/142.40 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 142.99/142.40 true__ -> false__ % 142.99/142.40 with the LPO induced by % 142.99/142.40 f1 > multiply > greatest_lower_bound > least_upper_bound > a > c > b > identity > inverse > true__ > false__ % 142.99/142.40 % 142.99/142.40 % SZS output end Proof % 142.99/142.40 %------------------------------------------------------------------------------