%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP042-2 : 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 10:52:09 EDT 2022 % Result : Unsatisfiable 5.49s 5.57s % Output : Proof 5.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : GRP042-2 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.11/0.33 % Computer : n021.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Mon Jun 13 12:22:42 EDT 2022 % 0.11/0.33 % CPUTime : % 5.49/5.57 % SZS status Unsatisfiable % 5.49/5.57 % SZS output start Proof % 5.49/5.57 The input problem is unsatisfiable because % 5.49/5.57 % 5.49/5.57 [1] the following set of Horn clauses is unsatisfiable: % 5.49/5.57 % 5.49/5.57 product(identity, X, X) % 5.49/5.57 product(inverse(X), X, identity) % 5.49/5.57 product(X, Y, multiply(X, Y)) % 5.49/5.57 product(X, Y, Z) & product(X, Y, W) ==> equalish(Z, W) % 5.49/5.57 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 5.49/5.57 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 5.49/5.57 equalish(X, Y) & product(W, Z, X) ==> product(W, Z, Y) % 5.49/5.57 equalish(a, b) % 5.49/5.57 equalish(b, a) ==> \bottom % 5.49/5.57 % 5.49/5.57 This holds because % 5.49/5.57 % 5.49/5.57 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.49/5.57 % 5.49/5.57 E: % 5.49/5.57 equalish(a, b) = true__ % 5.49/5.57 f1(true__, Z, W) = equalish(Z, W) % 5.49/5.57 f10(product(W, Z, X), X, Y, W, Z) = true__ % 5.49/5.57 f10(true__, X, Y, W, Z) = f9(equalish(X, Y), W, Z, Y) % 5.49/5.57 f11(equalish(b, a)) = true__ % 5.49/5.57 f11(true__) = false__ % 5.49/5.57 f2(product(X, Y, W), X, Y, Z, W) = true__ % 5.49/5.57 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 5.49/5.57 f3(true__, X, V, W) = product(X, V, W) % 5.49/5.57 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 5.49/5.57 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 5.49/5.57 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 5.49/5.57 f6(true__, U, Z, W) = product(U, Z, W) % 5.49/5.57 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 5.49/5.57 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 5.49/5.57 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 5.49/5.57 f9(true__, W, Z, Y) = product(W, Z, Y) % 5.49/5.57 product(X, Y, multiply(X, Y)) = true__ % 5.49/5.57 product(identity, X, X) = true__ % 5.49/5.57 product(inverse(X), X, identity) = true__ % 5.49/5.57 G: % 5.49/5.57 true__ = false__ % 5.49/5.57 % 5.49/5.57 This holds because % 5.49/5.57 % 5.49/5.57 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.49/5.57 % 5.49/5.57 % 5.49/5.57 equalish(Z, W) -> f1(true__, Z, W) % 5.49/5.57 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> true__ % 5.49/5.57 f1(f3(true__, identity, a, Y3), Y3, b) -> true__ % 5.49/5.57 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> true__ % 5.49/5.57 f1(f9(true__, identity, a, Y3), Y3, b) -> true__ % 5.49/5.57 f1(true__, Y1, Y1) -> true__ % 5.49/5.57 f1(true__, a, b) -> true__ % 5.49/5.57 f1(true__, b, a) -> true__ % 5.49/5.57 f1(true__, multiply(identity, Y0), Y0) -> true__ % 5.49/5.57 f1(true__, multiply(inverse(Y0), Y0), identity) -> true__ % 5.49/5.57 f10(f9(true__, Y0, Y1, Y2), Y2, Y3, Y0, Y1) -> true__ % 5.49/5.57 f10(product(W, Z, X), X, Y, W, Z) -> true__ % 5.49/5.57 f10(true__, X, Y, W, Z) -> f9(f1(true__, X, Y), W, Z, Y) % 5.49/5.57 f11(f1(true__, b, a)) -> true__ % 5.49/5.57 f11(true__) -> false__ % 5.49/5.57 f2(f9(true__, Y0, Y1, Y2), Y0, Y1, Y3, Y2) -> true__ % 5.49/5.57 f2(product(X, Y, W), X, Y, Z, W) -> true__ % 5.49/5.57 f2(true__, X, Y, Z, W) -> f1(f3(true__, X, Y, Z), Z, W) % 5.49/5.57 f3(f3(true__, Y2, identity, identity), Y2, b, b) -> true__ % 5.49/5.57 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 5.49/5.57 f3(true__, identity, Y2, Y2) -> true__ % 5.49/5.57 f3(true__, identity, a, b) -> true__ % 5.49/5.57 f3(true__, identity, b, a) -> true__ % 5.49/5.57 f3(true__, identity, multiply(identity, Y1), Y1) -> true__ % 5.49/5.57 f3(true__, identity, multiply(inverse(X0), X0), identity) -> true__ % 5.49/5.57 f3(true__, inverse(Y1), Y1, identity) -> true__ % 5.49/5.57 f4(f9(true__, Y3, a, Y4), Y5, Y3, identity, Y4, b) -> true__ % 5.49/5.57 f4(true__, X, Y, U, V, W) -> f3(f3(true__, X, Y, U), X, V, W) % 5.49/5.57 f5(f9(true__, Y0, Y1, Y2), Y3, Y1, Y4, Y5, Y0, Y2) -> true__ % 5.49/5.57 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 5.49/5.57 f5(true__, Y, Z, V, X, U, W) -> f4(f3(true__, Y, Z, V), X, Y, U, V, W) % 5.49/5.57 f6(true__, U, Z, W) -> f3(true__, U, Z, W) % 5.49/5.57 f7(f9(true__, Y3, Y4, a), identity, Y3, Y5, Y4, b) -> true__ % 5.49/5.57 f7(true__, X, Y, U, Z, W) -> f6(f3(true__, X, Y, U), U, Z, W) % 5.49/5.57 f8(f9(true__, Y0, Y1, Y2), Y3, Y4, Y1, Y0, Y5, Y2) -> true__ % 5.49/5.57 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 5.49/5.57 f8(true__, Y, Z, V, X, U, W) -> f7(f3(true__, Y, Z, V), X, Y, U, Z, W) % 5.49/5.57 f9(f1(true__, Y2, Y3), identity, Y2, Y3) -> true__ % 5.49/5.57 f9(f1(true__, b, Y3), identity, a, Y3) -> true__ % 5.49/5.57 f9(true__, W, Z, Y) -> f3(true__, W, Z, Y) % 5.49/5.57 f9(true__, identity, a, b) -> true__ % 5.49/5.57 f9(true__, identity, multiply(identity, Y1), Y1) -> true__ % 5.49/5.57 f9(true__, identity, multiply(inverse(X0), X0), identity) -> true__ % 5.49/5.57 false__ -> true__ % 5.49/5.57 product(X, V, W) -> f3(true__, X, V, W) % 5.49/5.57 with the LPO induced by % 5.49/5.57 f5 > f4 > f2 > f8 > f7 > f6 > f10 > equalish > f9 > product > f3 > f1 > multiply > f11 > inverse > identity > b > a > false__ > true__ % 5.49/5.57 % 5.49/5.57 % SZS output end Proof % 5.49/5.57 %------------------------------------------------------------------------------