%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP001-5 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n005.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 10:51:40 EDT 2022 % Result : Unsatisfiable 5.65s 5.68s % Output : Proof 5.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GRP001-5 : TPTP v8.1.0. Released v1.0.0. % 0.12/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n005.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 : Mon Jun 13 12:21:24 EDT 2022 % 0.13/0.34 % CPUTime : % 5.65/5.68 % SZS status Unsatisfiable % 5.65/5.68 % SZS output start Proof % 5.65/5.68 The input problem is unsatisfiable because % 5.65/5.68 % 5.65/5.68 [1] the following set of Horn clauses is unsatisfiable: % 5.65/5.68 % 5.65/5.68 product(identity, X, X) % 5.65/5.68 product(X, identity, X) % 5.65/5.68 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 5.65/5.68 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 5.65/5.68 product(X, X, identity) % 5.65/5.68 product(a, b, c) % 5.65/5.68 product(b, a, c) ==> \bottom % 5.65/5.68 % 5.65/5.68 This holds because % 5.65/5.68 % 5.65/5.68 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.65/5.68 % 5.65/5.68 E: % 5.65/5.68 f1(true__, X, V, W) = product(X, V, W) % 5.65/5.68 f2(true__, X, Y, U, V, W) = f1(product(X, Y, U), X, V, W) % 5.65/5.68 f3(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 5.65/5.68 f3(true__, Y, Z, V, X, U, W) = f2(product(Y, Z, V), X, Y, U, V, W) % 5.65/5.68 f4(true__, U, Z, W) = product(U, Z, W) % 5.65/5.68 f5(true__, X, Y, U, Z, W) = f4(product(X, Y, U), U, Z, W) % 5.65/5.68 f6(product(X, V, W), Y, Z, V, X, U, W) = true__ % 5.65/5.68 f6(true__, Y, Z, V, X, U, W) = f5(product(Y, Z, V), X, Y, U, Z, W) % 5.65/5.68 f7(product(b, a, c)) = true__ % 5.65/5.68 f7(true__) = false__ % 5.65/5.68 product(X, X, identity) = true__ % 5.65/5.68 product(X, identity, X) = true__ % 5.65/5.68 product(a, b, c) = true__ % 5.65/5.68 product(identity, X, X) = true__ % 5.65/5.68 G: % 5.65/5.68 true__ = false__ % 5.65/5.68 % 5.65/5.68 This holds because % 5.65/5.68 % 5.65/5.68 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.65/5.68 % 5.65/5.68 % 5.65/5.68 f1(f1(true__, Y2, Y1, Y3), Y2, Y1, Y3) -> true__ % 5.65/5.68 f1(f1(true__, Y2, a, a), Y2, c, c) -> true__ % 5.65/5.68 f1(f1(true__, Y2, b, a), Y2, identity, c) -> true__ % 5.65/5.68 f1(f1(true__, Y2, c, a), Y2, a, c) -> true__ % 5.65/5.68 f1(f1(true__, Y2, identity, Y3), Y2, identity, Y3) -> true__ % 5.65/5.68 f1(f1(true__, Y2, identity, a), Y2, b, c) -> true__ % 5.65/5.68 f1(f1(true__, Y3, Y1, Y1), Y3, identity, identity) -> true__ % 5.65/5.68 f1(f1(true__, Y3, Y1, identity), Y3, identity, Y1) -> true__ % 5.65/5.68 f1(f1(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__ % 5.65/5.68 f1(f1(true__, Y3, a, b), Y3, c, identity) -> true__ % 5.65/5.68 f1(f1(true__, Y3, a, c), Y3, b, identity) -> true__ % 5.65/5.68 f1(f1(true__, Y3, a, identity), Y3, b, c) -> true__ % 5.65/5.68 f1(f1(true__, Y3, a, identity), Y3, c, b) -> true__ % 5.65/5.68 f1(f1(true__, Y3, b, c), Y3, a, identity) -> true__ % 5.65/5.68 f1(f1(true__, Y3, b, identity), Y3, a, c) -> true__ % 5.65/5.68 f1(f1(true__, Y3, b, identity), Y3, c, a) -> true__ % 5.65/5.68 f1(f1(true__, Y3, c, a), Y3, b, identity) -> true__ % 5.65/5.68 f1(f1(true__, Y3, c, b), Y3, a, identity) -> true__ % 5.65/5.68 f1(f1(true__, Y3, c, identity), Y3, a, b) -> true__ % 5.65/5.68 f1(f1(true__, Y3, c, identity), Y3, b, a) -> true__ % 5.65/5.68 f1(f1(true__, Y3, identity, Y2), Y3, Y2, identity) -> true__ % 5.65/5.68 f1(f1(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 5.65/5.68 f1(true__, Y1, Y1, identity) -> true__ % 5.65/5.68 f1(true__, Y2, identity, Y2) -> true__ % 5.65/5.68 f1(true__, a, b, c) -> true__ % 5.65/5.68 f1(true__, a, c, b) -> true__ % 5.65/5.68 f1(true__, b, a, c) -> true__ % 5.65/5.68 f1(true__, b, c, a) -> true__ % 5.65/5.68 f1(true__, c, a, b) -> true__ % 5.65/5.68 f1(true__, c, b, a) -> true__ % 5.65/5.68 f1(true__, identity, Y2, Y2) -> true__ % 5.65/5.68 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, Y1, Y4, identity) -> true__ % 5.65/5.68 f2(f1(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 5.65/5.68 f2(f1(true__, Y3, b, Y4), Y5, Y3, a, Y4, c) -> true__ % 5.65/5.68 f2(f1(true__, Y3, identity, Y4), Y5, Y3, Y2, Y4, Y2) -> true__ % 5.65/5.68 f2(true__, X, Y, U, V, W) -> f1(product(X, Y, U), X, V, W) % 5.65/5.68 f3(f1(true__, Y0, Y1, Y2), Y3, Y1, Y4, Y5, Y0, Y2) -> true__ % 5.65/5.68 f3(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 5.65/5.68 f3(true__, Y, Z, V, X, U, W) -> f2(product(Y, Z, V), X, Y, U, V, W) % 5.65/5.68 f4(f1(true__, Y2, Y1, Y3), Y3, Y1, Y2) -> true__ % 5.65/5.68 f4(f1(true__, Y2, Y2, Y3), Y3, identity, identity) -> true__ % 5.65/5.68 f4(f1(true__, Y2, identity, Y3), Y3, Y2, identity) -> true__ % 5.65/5.68 f4(f1(true__, Y2, identity, Y3), Y3, identity, Y2) -> true__ % 5.65/5.68 f4(f1(true__, a, a, Y2), Y2, c, c) -> true__ % 5.65/5.68 f4(f1(true__, a, b, Y2), Y2, identity, c) -> true__ % 5.65/5.68 f4(f1(true__, a, b, Y3), Y3, c, identity) -> true__ % 5.65/5.68 f4(f1(true__, a, c, Y3), Y3, b, identity) -> true__ % 5.65/5.68 f4(f1(true__, a, identity, Y2), Y2, b, c) -> true__ % 5.65/5.68 f4(f1(true__, b, a, Y3), Y3, c, identity) -> true__ % 5.65/5.68 f4(f1(true__, c, a, Y3), Y3, b, identity) -> true__ % 5.65/5.68 f4(f1(true__, identity, Y1, Y3), Y3, Y1, identity) -> true__ % 5.65/5.68 f4(f1(true__, identity, Y2, Y3), Y3, identity, Y2) -> true__ % 5.65/5.68 f4(f1(true__, identity, a, Y3), Y3, b, c) -> true__ % 5.65/5.68 f4(f1(true__, identity, a, Y3), Y3, c, b) -> true__ % 5.65/5.68 f4(f1(true__, identity, b, Y3), Y3, a, c) -> true__ % 5.65/5.68 f4(f1(true__, identity, b, Y3), Y3, c, a) -> true__ % 5.65/5.68 f4(f1(true__, identity, c, Y3), Y3, a, b) -> true__ % 5.65/5.68 f4(f1(true__, identity, c, Y3), Y3, b, a) -> true__ % 5.65/5.68 f4(f1(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__ % 5.65/5.68 f4(true__, U, Z, W) -> product(U, Z, W) % 5.65/5.68 f5(f1(true__, Y3, Y4, Y1), Y1, Y3, Y5, Y4, identity) -> true__ % 5.65/5.68 f5(f1(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 5.65/5.68 f5(f1(true__, Y3, Y4, b), a, Y3, Y5, Y4, c) -> true__ % 5.65/5.68 f5(f1(true__, Y3, Y4, identity), Y2, Y3, Y5, Y4, Y2) -> true__ % 5.65/5.68 f5(true__, X, Y, U, Z, W) -> f4(product(X, Y, U), U, Z, W) % 5.65/5.68 f6(f1(true__, Y0, Y1, Y2), Y3, Y4, Y1, Y0, Y5, Y2) -> true__ % 5.65/5.68 f6(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 5.65/5.68 f6(true__, Y, Z, V, X, U, W) -> f5(product(Y, Z, V), X, Y, U, Z, W) % 5.65/5.68 f7(f1(true__, b, a, c)) -> true__ % 5.65/5.68 f7(product(b, a, c)) -> true__ % 5.65/5.68 f7(true__) -> false__ % 5.65/5.68 false__ -> true__ % 5.65/5.68 product(X, V, W) -> f1(true__, X, V, W) % 5.65/5.68 product(X, X, identity) -> true__ % 5.65/5.68 product(X, identity, X) -> true__ % 5.65/5.68 product(a, b, c) -> true__ % 5.65/5.68 product(identity, X, X) -> true__ % 5.65/5.68 with the LPO induced by % 5.65/5.68 f7 > c > b > a > f3 > f2 > f6 > f5 > f4 > product > f1 > identity > false__ > true__ % 5.65/5.68 % 5.65/5.68 % SZS output end Proof % 5.65/5.68 %------------------------------------------------------------------------------