%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP005-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n012.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 10:51:44 EDT 2022 % Result : Unsatisfiable 1.10s 1.26s % Output : Proof 1.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP005-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n012.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jun 13 11:44:40 EDT 2022 % 0.12/0.34 % CPUTime : % 1.10/1.26 % SZS status Unsatisfiable % 1.10/1.26 % SZS output start Proof % 1.10/1.26 The input problem is unsatisfiable because % 1.10/1.26 % 1.10/1.26 [1] the following set of Horn clauses is unsatisfiable: % 1.10/1.26 % 1.10/1.26 product(identity, X, X) % 1.10/1.26 product(X, identity, X) % 1.10/1.26 product(X, inverse(X), identity) % 1.10/1.26 product(inverse(X), X, identity) % 1.10/1.26 an_element(a) % 1.10/1.26 an_element(X) & an_element(Y) & product(X, inverse(Y), Z) ==> an_element(Z) % 1.10/1.26 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 1.10/1.26 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 1.10/1.26 an_element(identity) ==> \bottom % 1.10/1.26 % 1.10/1.26 This holds because % 1.10/1.26 % 1.10/1.26 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.10/1.26 % 1.10/1.26 E: % 1.10/1.26 an_element(a) = true__ % 1.10/1.26 f1(true__, Z) = an_element(Z) % 1.10/1.26 f10(an_element(identity)) = true__ % 1.10/1.26 f10(true__) = false__ % 1.10/1.26 f2(true__, X, Z) = f1(an_element(X), Z) % 1.10/1.26 f3(product(X, inverse(Y), Z), Y, X, Z) = true__ % 1.10/1.26 f3(true__, Y, X, Z) = f2(an_element(Y), X, Z) % 1.10/1.26 f4(true__, X, V, W) = product(X, V, W) % 1.10/1.26 f5(true__, X, Y, U, V, W) = f4(product(X, Y, U), X, V, W) % 1.10/1.26 f6(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 1.10/1.26 f6(true__, Y, Z, V, X, U, W) = f5(product(Y, Z, V), X, Y, U, V, W) % 1.10/1.26 f7(true__, U, Z, W) = product(U, Z, W) % 1.10/1.26 f8(true__, X, Y, U, Z, W) = f7(product(X, Y, U), U, Z, W) % 1.10/1.26 f9(product(X, V, W), Y, Z, V, X, U, W) = true__ % 1.10/1.26 f9(true__, Y, Z, V, X, U, W) = f8(product(Y, Z, V), X, Y, U, Z, W) % 1.10/1.26 product(X, identity, X) = true__ % 1.10/1.26 product(X, inverse(X), identity) = true__ % 1.10/1.26 product(identity, X, X) = true__ % 1.10/1.26 product(inverse(X), X, identity) = true__ % 1.10/1.26 G: % 1.10/1.26 true__ = false__ % 1.10/1.26 % 1.10/1.26 This holds because % 1.10/1.26 % 1.10/1.26 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.10/1.26 % 1.10/1.26 % 1.10/1.26 an_element(Z) -> f1(true__, Z) % 1.10/1.26 an_element(a) -> true__ % 1.10/1.26 f1(f1(true__, identity), inverse(a)) -> true__ % 1.10/1.26 f1(f1(true__, inverse(inverse(a))), identity) -> true__ % 1.10/1.26 f1(f1(true__, inverse(inverse(identity))), identity) -> true__ % 1.10/1.26 f1(true__, a) -> true__ % 1.10/1.26 f1(true__, identity) -> true__ % 1.10/1.26 f1(true__, inverse(a)) -> true__ % 1.10/1.26 f1(true__, inverse(identity)) -> true__ % 1.10/1.26 f10(an_element(identity)) -> true__ % 1.10/1.26 f10(f1(true__, identity)) -> true__ % 1.10/1.26 f10(true__) -> false__ % 1.10/1.26 f2(f1(true__, Y1), Y1, identity) -> true__ % 1.10/1.26 f2(f1(true__, Y1), identity, inverse(Y1)) -> true__ % 1.10/1.26 f2(f1(true__, Y1), inverse(inverse(Y1)), identity) -> true__ % 1.10/1.26 f2(true__, X, Z) -> f1(an_element(X), Z) % 1.10/1.26 f3(product(X, inverse(Y), Z), Y, X, Z) -> true__ % 1.10/1.26 f3(true__, Y, X, Z) -> f2(an_element(Y), X, Z) % 1.10/1.26 f4(f7(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__ % 1.10/1.26 f4(f7(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 1.10/1.26 f4(true__, X, V, W) -> product(X, V, W) % 1.10/1.26 f5(f7(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__ % 1.10/1.26 f5(f7(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 1.10/1.26 f5(f7(true__, Y3, identity, Y4), Y5, Y3, Y2, Y4, Y2) -> true__ % 1.10/1.26 f5(f7(true__, Y3, inverse(Y0), Y4), Y5, Y3, Y0, Y4, identity) -> true__ % 1.10/1.26 f5(true__, X, Y, U, V, W) -> f4(product(X, Y, U), X, V, W) % 1.10/1.26 f6(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 1.10/1.26 f6(true__, Y, Z, V, X, U, W) -> f5(product(Y, Z, V), X, Y, U, V, W) % 1.10/1.26 f7(f7(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__ % 1.10/1.26 f7(true__, Y0, inverse(Y0), identity) -> true__ % 1.10/1.26 f7(true__, Y2, identity, Y2) -> true__ % 1.10/1.26 f7(true__, identity, Y2, Y2) -> true__ % 1.10/1.26 f7(true__, inverse(Y1), Y1, identity) -> true__ % 1.10/1.26 f7(true__, inverse(identity), Y1, Y1) -> true__ % 1.10/1.26 f8(f7(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__ % 1.10/1.26 f8(f7(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 1.10/1.26 f8(f7(true__, Y3, Y4, identity), Y2, Y3, Y5, Y4, Y2) -> true__ % 1.10/1.26 f8(f7(true__, Y3, Y4, inverse(Y0)), Y0, Y3, Y5, Y4, identity) -> true__ % 1.10/1.26 f8(true__, X, Y, U, Z, W) -> f7(product(X, Y, U), U, Z, W) % 1.10/1.26 f9(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 1.10/1.26 f9(true__, Y, Z, V, X, U, W) -> f8(product(Y, Z, V), X, Y, U, Z, W) % 1.10/1.26 false__ -> true__ % 1.10/1.26 product(U, Z, W) -> f7(true__, U, Z, W) % 1.10/1.26 product(X, identity, X) -> true__ % 1.10/1.26 product(X, inverse(X), identity) -> true__ % 1.10/1.26 product(identity, X, X) -> true__ % 1.10/1.26 product(inverse(X), X, identity) -> true__ % 1.10/1.26 with the LPO induced by % 1.10/1.26 f10 > f6 > f5 > f4 > f9 > f8 > product > f7 > f3 > f2 > an_element > f1 > a > inverse > identity > false__ > true__ % 1.10/1.26 % 1.10/1.26 % SZS output end Proof % 1.10/1.26 %------------------------------------------------------------------------------