%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP034-4 : 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 10:52:04 EDT 2022 % Result : Unsatisfiable 6.97s 7.05s % Output : Proof 6.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP034-4 : TPTP v8.1.0. Released v1.0.0. % 0.12/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n021.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 10:18:42 EDT 2022 % 0.12/0.33 % CPUTime : % 6.97/7.05 % SZS status Unsatisfiable % 6.97/7.05 % SZS output start Proof % 6.97/7.05 The input problem is unsatisfiable because % 6.97/7.05 % 6.97/7.05 [1] the following set of Horn clauses is unsatisfiable: % 6.97/7.05 % 6.97/7.05 product(X, Y, multiply(X, Y)) % 6.97/7.05 product(identity, X, X) % 6.97/7.05 product(X, identity, X) % 6.97/7.05 product(X, inverse(X), identity) % 6.97/7.05 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 6.97/7.05 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 6.97/7.05 subgroup_member(A) & subgroup_member(B) & product(B, inverse(A), C) ==> subgroup_member(C) % 6.97/7.05 subgroup_member(a) % 6.97/7.05 subgroup_member(inverse(a)) ==> \bottom % 6.97/7.05 % 6.97/7.05 This holds because % 6.97/7.05 % 6.97/7.05 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.97/7.05 % 6.97/7.05 E: % 6.97/7.05 f1(true__, X, V, W) = product(X, V, W) % 6.97/7.05 f10(subgroup_member(inverse(a))) = true__ % 6.97/7.05 f10(true__) = false__ % 6.97/7.05 f2(true__, X, Y, U, V, W) = f1(product(X, Y, U), X, V, W) % 6.97/7.05 f3(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 6.97/7.05 f3(true__, Y, Z, V, X, U, W) = f2(product(Y, Z, V), X, Y, U, V, W) % 6.97/7.05 f4(true__, U, Z, W) = product(U, Z, W) % 6.97/7.05 f5(true__, X, Y, U, Z, W) = f4(product(X, Y, U), U, Z, W) % 6.97/7.05 f6(product(X, V, W), Y, Z, V, X, U, W) = true__ % 6.97/7.05 f6(true__, Y, Z, V, X, U, W) = f5(product(Y, Z, V), X, Y, U, Z, W) % 6.97/7.05 f7(true__, C) = subgroup_member(C) % 6.97/7.05 f8(true__, A, C) = f7(subgroup_member(A), C) % 6.97/7.05 f9(product(B, inverse(A), C), B, A, C) = true__ % 6.97/7.05 f9(true__, B, A, C) = f8(subgroup_member(B), A, C) % 6.97/7.05 product(X, Y, multiply(X, Y)) = true__ % 6.97/7.05 product(X, identity, X) = true__ % 6.97/7.05 product(X, inverse(X), identity) = true__ % 6.97/7.05 product(identity, X, X) = true__ % 6.97/7.05 subgroup_member(a) = true__ % 6.97/7.05 G: % 6.97/7.05 true__ = false__ % 6.97/7.05 % 6.97/7.05 This holds because % 6.97/7.05 % 6.97/7.05 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.97/7.05 % 6.97/7.05 % 6.97/7.05 f1(f1(true__, Y3, Y0, identity), Y3, identity, inverse(Y0)) -> true__ % 6.97/7.05 f1(f1(true__, Y3, Y0, identity), Y3, multiply(Y0, Y1), Y1) -> true__ % 6.97/7.05 f1(f1(true__, Y3, Y2, Y4), Y3, Y2, multiply(Y4, identity)) -> true__ % 6.97/7.05 f1(f1(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__ % 6.97/7.05 f1(f1(true__, Y3, identity, Y4), Y3, Y2, multiply(Y4, Y2)) -> true__ % 6.97/7.05 f1(f1(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 6.97/7.05 f1(f1(true__, Y3, identity, identity), Y3, inverse(identity), identity) -> true__ % 6.97/7.05 f1(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 6.97/7.05 f1(true__, Y0, identity, inverse(inverse(Y0))) -> true__ % 6.97/7.05 f1(true__, Y0, inverse(Y0), identity) -> true__ % 6.97/7.05 f1(true__, Y2, identity, Y2) -> true__ % 6.97/7.05 f1(true__, Y2, identity, multiply(identity, Y2)) -> true__ % 6.97/7.05 f1(true__, identity, Y2, Y2) -> true__ % 6.97/7.05 f1(true__, identity, Y2, multiply(Y2, identity)) -> true__ % 6.97/7.05 f1(true__, identity, identity, inverse(identity)) -> true__ % 6.97/7.05 f10(f7(true__, inverse(a))) -> true__ % 6.97/7.05 f10(true__) -> false__ % 6.97/7.05 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__ % 6.97/7.05 f2(f1(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 6.97/7.05 f2(true__, X, Y, U, V, W) -> f1(f1(true__, X, Y, U), X, V, W) % 6.97/7.05 f3(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 6.97/7.05 f3(true__, Y, Z, V, X, U, W) -> f2(f1(true__, Y, Z, V), X, Y, U, V, W) % 6.97/7.05 f4(f1(true__, Y3, Y2, Y4), Y4, identity, multiply(Y3, Y2)) -> true__ % 6.97/7.05 f4(f1(true__, Y3, identity, Y4), Y4, Y2, multiply(Y3, Y2)) -> true__ % 6.97/7.05 f4(true__, U, Z, W) -> f1(true__, U, Z, W) % 6.97/7.05 f5(f1(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(Y0, Y1)) -> true__ % 6.97/7.05 f5(true__, X, Y, U, Z, W) -> f4(f1(true__, X, Y, U), U, Z, W) % 6.97/7.05 f6(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 6.97/7.05 f6(true__, Y, Z, V, X, U, W) -> f5(f1(true__, Y, Z, V), X, Y, U, Z, W) % 6.97/7.05 f7(f7(true__, Y0), inverse(Y0)) -> true__ % 6.97/7.05 f7(f7(true__, Y1), multiply(a, inverse(Y1))) -> true__ % 6.97/7.05 f7(f7(true__, Y1), multiply(identity, inverse(Y1))) -> true__ % 6.97/7.05 f7(f7(true__, Y1), multiply(inverse(Y1), identity)) -> true__ % 6.97/7.05 f7(f7(true__, Y1), multiply(multiply(a, inverse(a)), inverse(Y1))) -> true__ % 6.97/7.05 f7(true__, a) -> true__ % 6.97/7.05 f7(true__, identity) -> true__ % 6.97/7.05 f7(true__, inverse(a)) -> true__ % 6.97/7.05 f7(true__, inverse(identity)) -> true__ % 6.97/7.05 f7(true__, inverse(inverse(a))) -> true__ % 6.97/7.05 f7(true__, inverse(inverse(identity))) -> true__ % 6.97/7.05 f7(true__, inverse(multiply(a, inverse(a)))) -> true__ % 6.97/7.05 f7(true__, inverse(multiply(a, inverse(identity)))) -> true__ % 6.97/7.05 f7(true__, inverse(multiply(identity, inverse(a)))) -> true__ % 6.97/7.05 f7(true__, inverse(multiply(identity, inverse(identity)))) -> true__ % 6.97/7.05 f7(true__, inverse(multiply(inverse(identity), identity))) -> true__ % 6.97/7.05 f7(true__, multiply(a, inverse(a))) -> true__ % 6.97/7.05 f7(true__, multiply(a, inverse(identity))) -> true__ % 6.97/7.05 f7(true__, multiply(a, inverse(inverse(identity)))) -> true__ % 6.97/7.05 f7(true__, multiply(a, inverse(multiply(a, inverse(a))))) -> true__ % 6.97/7.05 f7(true__, multiply(identity, inverse(a))) -> true__ % 6.97/7.05 f7(true__, multiply(identity, inverse(identity))) -> true__ % 6.97/7.05 f7(true__, multiply(inverse(identity), identity)) -> true__ % 6.97/7.05 f8(f7(true__, Y0), Y1, multiply(Y0, inverse(Y1))) -> true__ % 6.97/7.05 f8(f7(true__, Y1), Y1, identity) -> true__ % 6.97/7.05 f8(true__, A, C) -> f7(f7(true__, A), C) % 6.97/7.05 f9(f1(true__, Y0, inverse(Y1), Y2), Y0, Y1, Y2) -> true__ % 6.97/7.05 f9(true__, B, A, C) -> f8(f7(true__, B), A, C) % 6.97/7.05 false__ -> true__ % 6.97/7.05 product(X, V, W) -> f1(true__, X, V, W) % 6.97/7.05 subgroup_member(C) -> f7(true__, C) % 6.97/7.05 with the LPO induced by % 6.97/7.05 f6 > f5 > f4 > f3 > f2 > product > f1 > f9 > f8 > subgroup_member > f7 > multiply > inverse > identity > f10 > a > false__ > true__ % 6.97/7.05 % 6.97/7.05 % SZS output end Proof % 6.97/7.05 %------------------------------------------------------------------------------