%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP007-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 10:51:45 EDT 2022 % Result : Unsatisfiable 1.10s 1.29s % Output : Proof 1.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.08 % Problem : GRP007-1 : TPTP v8.1.0. Released v1.0.0. % 0.02/0.09 % Command : moca.sh %s % 0.09/0.28 % Computer : n007.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 600 % 0.09/0.28 % DateTime : Mon Jun 13 22:43:54 EDT 2022 % 0.09/0.28 % CPUTime : % 1.10/1.29 % SZS status Unsatisfiable % 1.10/1.29 % SZS output start Proof % 1.10/1.29 The input problem is unsatisfiable because % 1.10/1.29 % 1.10/1.29 [1] the following set of Horn clauses is unsatisfiable: % 1.10/1.29 % 1.10/1.29 product(identity, X, X) % 1.10/1.29 product(X, identity, X) % 1.10/1.29 product(inverse(X), X, identity) % 1.10/1.29 product(X, inverse(X), identity) % 1.10/1.29 product(X, Y, multiply(X, Y)) % 1.10/1.29 product(X, Y, Z) & product(X, Y, W) ==> Z = W % 1.10/1.29 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 1.10/1.29 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 1.10/1.29 product(c, A, A) % 1.10/1.29 product(A, c, A) % 1.10/1.29 identity = c ==> \bottom % 1.10/1.29 % 1.10/1.29 This holds because % 1.10/1.29 % 1.10/1.29 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.10/1.29 % 1.10/1.29 E: % 1.10/1.29 f1(true__, Z, W) = Z % 1.10/1.29 f2(product(X, Y, W), X, Y, Z, W) = W % 1.10/1.29 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 1.10/1.29 f3(true__, X, V, W) = product(X, V, W) % 1.10/1.29 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 1.10/1.29 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 1.10/1.29 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 1.10/1.29 f6(true__, U, Z, W) = product(U, Z, W) % 1.10/1.29 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 1.10/1.29 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 1.10/1.29 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 1.10/1.29 f9(c) = false__ % 1.10/1.29 f9(identity) = true__ % 1.10/1.29 product(A, c, A) = true__ % 1.10/1.29 product(X, Y, multiply(X, Y)) = true__ % 1.10/1.29 product(X, identity, X) = true__ % 1.10/1.29 product(X, inverse(X), identity) = true__ % 1.10/1.29 product(c, A, A) = true__ % 1.10/1.29 product(identity, X, X) = true__ % 1.10/1.29 product(inverse(X), X, identity) = true__ % 1.10/1.29 G: % 1.10/1.29 true__ = false__ % 1.10/1.29 % 1.10/1.29 This holds because % 1.10/1.29 % 1.10/1.29 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.10/1.29 % 1.10/1.29 % 1.10/1.29 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1) % 1.10/1.29 f1(f3(true__, Y2, c, Y3), Y3, Y2) -> Y2 % 1.10/1.29 f1(f3(true__, c, Y0, Y1), Y1, Y0) -> Y0 % 1.10/1.29 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> Y2 % 1.10/1.29 f1(f3(true__, inverse(Y0), Y0, Y1), Y1, c) -> c % 1.10/1.29 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> c % 1.10/1.29 f1(true__, Z, W) -> Z % 1.10/1.29 f2(product(X, Y, W), X, Y, Z, W) -> W % 1.10/1.29 f2(true__, X, Y, Z, W) -> f1(f3(true__, X, Y, Z), Z, W) % 1.10/1.29 f3(f3(true__, Y0, c, c), Y0, Y1, Y1) -> true__ % 1.10/1.29 f3(f3(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 1.10/1.29 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 1.10/1.29 f3(true__, Y0, inverse(Y0), c) -> true__ % 1.10/1.29 f3(true__, Y0, inverse(Y0), identity) -> true__ % 1.10/1.29 f3(true__, Y2, c, Y2) -> true__ % 1.10/1.29 f3(true__, c, Y2, Y2) -> true__ % 1.10/1.29 f3(true__, inverse(Y0), Y0, c) -> true__ % 1.10/1.29 f3(true__, inverse(Y1), Y1, identity) -> true__ % 1.10/1.29 f4(f3(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 1.10/1.29 f4(f3(true__, Y3, c, Y4), Y5, Y3, Y2, Y4, Y2) -> true__ % 1.10/1.29 f4(true__, X, Y, U, V, W) -> f3(f3(true__, X, Y, U), X, V, W) % 1.10/1.29 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 1.10/1.29 f5(true__, Y, Z, V, X, U, W) -> f4(f3(true__, Y, Z, V), X, Y, U, V, W) % 1.10/1.29 f6(f3(true__, c, c, Y0), Y0, Y1, Y1) -> true__ % 1.10/1.29 f6(f3(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__ % 1.10/1.29 f6(true__, U, Z, W) -> f3(true__, U, Z, W) % 1.10/1.29 f7(f3(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 1.10/1.29 f7(f3(true__, Y3, Y4, c), Y2, Y3, Y5, Y4, Y2) -> true__ % 1.10/1.29 f7(true__, X, Y, U, Z, W) -> f6(f3(true__, X, Y, U), U, Z, W) % 1.10/1.29 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 1.10/1.29 f8(true__, Y, Z, V, X, U, W) -> f7(f3(true__, Y, Z, V), X, Y, U, Z, W) % 1.10/1.29 f9(c) -> false__ % 1.10/1.29 f9(identity) -> true__ % 1.10/1.29 identity -> c % 1.10/1.29 inverse(c) -> c % 1.10/1.29 product(X, V, W) -> f3(true__, X, V, W) % 1.10/1.29 true__ -> false__ % 1.10/1.29 with the LPO induced by % 1.10/1.29 f9 > f2 > f1 > f8 > f5 > f4 > f7 > f6 > product > f3 > inverse > multiply > identity > c > true__ > false__ % 1.10/1.29 % 1.10/1.29 % SZS output end Proof % 1.10/1.29 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