%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP006-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 6.54s 6.65s % Output : Proof 6.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP006-1 : TPTP v8.1.0. Released v1.0.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n025.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 : Tue Jun 14 03:18:24 EDT 2022 % 0.12/0.34 % CPUTime : % 6.54/6.65 % SZS status Unsatisfiable % 6.54/6.65 % SZS output start Proof % 6.54/6.65 The input problem is unsatisfiable because % 6.54/6.65 % 6.54/6.65 [1] the following set of Horn clauses is unsatisfiable: % 6.54/6.65 % 6.54/6.65 product(identity, X, X) % 6.54/6.65 product(X, identity, X) % 6.54/6.65 product(X, inverse(X), identity) % 6.54/6.65 product(inverse(X), X, identity) % 6.54/6.65 an_element(X) & an_element(Y) & product(X, inverse(Y), Z) ==> an_element(Z) % 6.54/6.65 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 6.54/6.65 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 6.54/6.65 an_element(the_element) % 6.54/6.65 an_element(inverse(the_element)) ==> \bottom % 6.54/6.65 % 6.54/6.65 This holds because % 6.54/6.65 % 6.54/6.65 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.54/6.65 % 6.54/6.65 E: % 6.54/6.65 an_element(the_element) = true__ % 6.54/6.65 f1(true__, Z) = an_element(Z) % 6.54/6.65 f10(an_element(inverse(the_element))) = true__ % 6.54/6.65 f10(true__) = false__ % 6.54/6.65 f2(true__, X, Z) = f1(an_element(X), Z) % 6.54/6.65 f3(product(X, inverse(Y), Z), Y, X, Z) = true__ % 6.54/6.65 f3(true__, Y, X, Z) = f2(an_element(Y), X, Z) % 6.54/6.65 f4(true__, X, V, W) = product(X, V, W) % 6.54/6.65 f5(true__, X, Y, U, V, W) = f4(product(X, Y, U), X, V, W) % 6.54/6.65 f6(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 6.54/6.65 f6(true__, Y, Z, V, X, U, W) = f5(product(Y, Z, V), X, Y, U, V, W) % 6.54/6.65 f7(true__, U, Z, W) = product(U, Z, W) % 6.54/6.65 f8(true__, X, Y, U, Z, W) = f7(product(X, Y, U), U, Z, W) % 6.54/6.65 f9(product(X, V, W), Y, Z, V, X, U, W) = true__ % 6.54/6.65 f9(true__, Y, Z, V, X, U, W) = f8(product(Y, Z, V), X, Y, U, Z, W) % 6.54/6.65 product(X, identity, X) = true__ % 6.54/6.65 product(X, inverse(X), identity) = true__ % 6.54/6.65 product(identity, X, X) = true__ % 6.54/6.65 product(inverse(X), X, identity) = true__ % 6.54/6.65 G: % 6.54/6.65 true__ = false__ % 6.54/6.65 % 6.54/6.65 This holds because % 6.54/6.65 % 6.54/6.65 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.54/6.65 % 6.54/6.65 % 6.54/6.65 an_element(Z) -> f1(true__, Z) % 6.54/6.65 f1(f1(true__, inverse(inverse(identity))), identity) -> true__ % 6.54/6.65 f1(f1(true__, inverse(inverse(inverse(identity)))), identity) -> true__ % 6.54/6.65 f1(f1(true__, inverse(inverse(inverse(the_element)))), identity) -> true__ % 6.54/6.65 f1(f1(true__, inverse(inverse(the_element))), identity) -> true__ % 6.54/6.65 f1(true__, identity) -> true__ % 6.54/6.65 f1(true__, inverse(identity)) -> true__ % 6.54/6.65 f1(true__, inverse(inverse(identity))) -> true__ % 6.54/6.65 f1(true__, inverse(inverse(the_element))) -> true__ % 6.54/6.65 f1(true__, inverse(the_element)) -> true__ % 6.54/6.65 f1(true__, the_element) -> true__ % 6.54/6.65 f10(f1(true__, inverse(the_element))) -> true__ % 6.54/6.65 f10(true__) -> false__ % 6.54/6.65 f2(f1(true__, Y1), Y1, identity) -> true__ % 6.54/6.65 f2(f1(true__, Y1), identity, inverse(Y1)) -> true__ % 6.54/6.65 f2(f1(true__, Y1), inverse(identity), inverse(Y1)) -> true__ % 6.54/6.65 f2(f1(true__, Y1), inverse(inverse(Y1)), identity) -> true__ % 6.54/6.65 f2(f1(true__, Y1), inverse(inverse(identity)), inverse(Y1)) -> true__ % 6.54/6.65 f2(true__, X, Z) -> f1(f1(true__, X), Z) % 6.54/6.65 f3(f4(true__, Y0, inverse(Y1), Y2), Y1, Y0, Y2) -> true__ % 6.54/6.65 f3(true__, Y, X, Z) -> f2(f1(true__, Y), X, Z) % 6.54/6.65 f4(f4(true__, Y3, Y0, identity), Y3, identity, inverse(Y0)) -> true__ % 6.54/6.65 f4(f4(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__ % 6.54/6.65 f4(f4(true__, Y3, Y2, inverse(identity)), Y3, Y2, identity) -> true__ % 6.54/6.65 f4(f4(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 6.54/6.65 f4(f4(true__, Y3, identity, identity), Y3, inverse(identity), identity) -> true__ % 6.54/6.65 f4(f4(true__, Y3, identity, inverse(Y2)), Y3, Y2, identity) -> true__ % 6.54/6.65 f4(f4(true__, Y3, inverse(Y1), identity), Y3, identity, Y1) -> true__ % 6.54/6.65 f4(f4(true__, Y3, inverse(identity), identity), Y3, Y2, Y2) -> true__ % 6.54/6.65 f4(f4(true__, Y3, inverse(identity), inverse(Y2)), Y3, Y2, identity) -> true__ % 6.54/6.65 f4(true__, Y0, identity, inverse(inverse(Y0))) -> true__ % 6.54/6.65 f4(true__, Y0, inverse(Y0), identity) -> true__ % 6.54/6.65 f4(true__, Y2, identity, Y2) -> true__ % 6.54/6.65 f4(true__, identity, Y2, Y2) -> true__ % 6.54/6.65 f4(true__, identity, identity, inverse(identity)) -> true__ % 6.54/6.65 f4(true__, inverse(Y1), Y1, identity) -> true__ % 6.54/6.65 f4(true__, inverse(identity), Y1, Y1) -> true__ % 6.54/6.65 f4(true__, inverse(identity), inverse(identity), identity) -> true__ % 6.54/6.65 f4(true__, inverse(inverse(Y1)), identity, Y1) -> true__ % 6.54/6.65 f4(true__, inverse(inverse(identity)), Y1, Y1) -> true__ % 6.54/6.65 f4(true__, inverse(inverse(inverse(Y0))), Y0, identity) -> true__ % 6.54/6.65 f5(f4(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__ % 6.54/6.65 f5(f4(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 6.54/6.65 f5(true__, X, Y, U, V, W) -> f4(f4(true__, X, Y, U), X, V, W) % 6.54/6.65 f6(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 6.54/6.65 f6(true__, Y, Z, V, X, U, W) -> f5(f4(true__, Y, Z, V), X, Y, U, V, W) % 6.54/6.65 f7(f4(true__, inverse(Y2), Y2, Y3), Y3, identity, identity) -> true__ % 6.54/6.65 f7(f4(true__, inverse(Y2), identity, Y3), Y3, Y2, identity) -> true__ % 6.54/6.65 f7(f4(true__, inverse(Y2), inverse(identity), Y3), Y3, Y2, identity) -> true__ % 6.54/6.65 f7(true__, U, Z, W) -> f4(true__, U, Z, W) % 6.54/6.65 f8(f4(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__ % 6.54/6.65 f8(true__, X, Y, U, Z, W) -> f7(f4(true__, X, Y, U), U, Z, W) % 6.54/6.65 f9(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 6.54/6.65 f9(true__, Y, Z, V, X, U, W) -> f8(f4(true__, Y, Z, V), X, Y, U, Z, W) % 6.54/6.65 false__ -> true__ % 6.54/6.65 product(X, V, W) -> f4(true__, X, V, W) % 6.54/6.65 with the LPO induced by % 6.54/6.65 f9 > f8 > f7 > f6 > f5 > product > f4 > f3 > f2 > an_element > f1 > inverse > identity > f10 > the_element > false__ > true__ % 6.54/6.65 % 6.54/6.65 % SZS output end Proof % 6.54/6.65 %------------------------------------------------------------------------------