%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP033-4 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n019.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 10:52:03 EDT 2022 % Result : Unsatisfiable 9.94s 9.96s % Output : Proof 9.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP033-4 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n019.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Mon Jun 13 23:43:39 EDT 2022 % 0.14/0.34 % CPUTime : % 9.94/9.96 % SZS status Unsatisfiable % 9.94/9.96 % SZS output start Proof % 9.94/9.96 The input problem is unsatisfiable because % 9.94/9.96 % 9.94/9.96 [1] the following set of Horn clauses is unsatisfiable: % 9.94/9.96 % 9.94/9.96 product(identity, X, X) % 9.94/9.96 product(X, identity, X) % 9.94/9.96 product(inverse(X), X, identity) % 9.94/9.96 product(X, inverse(X), identity) % 9.94/9.96 product(X, Y, multiply(X, Y)) % 9.94/9.96 product(X, Y, Z) & product(X, Y, W) ==> Z = W % 9.94/9.96 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 9.94/9.96 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 9.94/9.96 subgroup_member(A) & subgroup_member(B) & product(A, inverse(B), C) ==> subgroup_member(C) % 9.94/9.96 subgroup_member(a) % 9.94/9.96 subgroup_member(A) ==> subgroup_member(j(A)) % 9.94/9.96 product(j(A), A, j(A)) & product(A, j(A), j(A)) & subgroup_member(A) ==> \bottom % 9.94/9.96 % 9.94/9.96 This holds because % 9.94/9.96 % 9.94/9.96 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 9.94/9.96 % 9.94/9.96 E: % 9.94/9.96 f1(true__, Z, W) = Z % 9.94/9.96 f10(true__, A, C) = f9(subgroup_member(A), C) % 9.94/9.96 f11(product(A, inverse(B), C), B, A, C) = true__ % 9.94/9.96 f11(true__, B, A, C) = f10(subgroup_member(B), A, C) % 9.94/9.96 f12(subgroup_member(A), A) = true__ % 9.94/9.96 f12(true__, A) = subgroup_member(j(A)) % 9.94/9.96 f13(true__) = false__ % 9.94/9.96 f14(true__, A) = f13(product(j(A), A, j(A))) % 9.94/9.96 f15(subgroup_member(A), A) = true__ % 9.94/9.96 f15(true__, A) = f14(product(A, j(A), j(A)), A) % 9.94/9.96 f2(product(X, Y, W), X, Y, Z, W) = W % 9.94/9.96 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 9.94/9.96 f3(true__, X, V, W) = product(X, V, W) % 9.94/9.96 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 9.94/9.96 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 9.94/9.96 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 9.94/9.96 f6(true__, U, Z, W) = product(U, Z, W) % 9.94/9.96 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 9.94/9.96 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 9.94/9.96 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 9.94/9.96 f9(true__, C) = subgroup_member(C) % 9.94/9.96 product(X, Y, multiply(X, Y)) = true__ % 9.94/9.96 product(X, identity, X) = true__ % 9.94/9.96 product(X, inverse(X), identity) = true__ % 9.94/9.96 product(identity, X, X) = true__ % 9.94/9.96 product(inverse(X), X, identity) = true__ % 9.94/9.96 subgroup_member(a) = true__ % 9.94/9.96 G: % 9.94/9.96 true__ = false__ % 9.94/9.96 % 9.94/9.96 This holds because % 9.94/9.96 % 9.94/9.96 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 9.94/9.96 % 9.94/9.96 % 9.94/9.96 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1) % 9.94/9.96 f1(f3(true__, Y0, inverse(Y0), Y3), Y3, identity) -> identity % 9.94/9.96 f1(f3(true__, Y2, identity, Y3), Y3, Y2) -> Y2 % 9.94/9.96 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> Y2 % 9.94/9.96 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> identity % 9.94/9.96 f1(true__, Z, W) -> Z % 9.94/9.96 f10(f9(true__, Y1), Y1, identity) -> true__ % 9.94/9.96 f10(f9(true__, Y1), identity, inverse(Y1)) -> true__ % 9.94/9.96 f10(f9(true__, Y1), inverse(inverse(Y1)), identity) -> true__ % 9.94/9.96 f10(true__, A, C) -> f9(subgroup_member(A), C) % 9.94/9.96 f11(f3(true__, Y0, identity, Y2), identity, Y0, Y2) -> true__ % 9.94/9.96 f11(product(A, inverse(B), C), B, A, C) -> true__ % 9.94/9.96 f11(true__, B, A, C) -> f10(subgroup_member(B), A, C) % 9.94/9.96 f12(f9(true__, Y0), Y0) -> true__ % 9.94/9.96 f12(subgroup_member(A), A) -> true__ % 9.94/9.96 f12(true__, A) -> subgroup_member(j(A)) % 9.94/9.96 f13(true__) -> false__ % 9.94/9.96 f14(f3(true__, a, j(a), j(a)), a) -> true__ % 9.94/9.96 f14(f3(true__, j(a), j(j(a)), j(j(a))), j(a)) -> true__ % 9.94/9.96 f14(f3(true__, j(j(a)), j(j(j(a))), j(j(j(a)))), j(j(a))) -> true__ % 9.94/9.96 f14(f3(true__, j(j(j(a))), j(j(j(j(a)))), j(j(j(j(a))))), j(j(j(a)))) -> true__ % 9.94/9.96 f14(f3(true__, j(j(j(j(a)))), j(j(j(j(j(a))))), j(j(j(j(j(a)))))), j(j(j(j(a))))) -> true__ % 9.94/9.96 f14(f3(true__, j(j(j(j(j(a))))), j(j(j(j(j(j(a)))))), j(j(j(j(j(j(a))))))), j(j(j(j(j(a)))))) -> true__ % 9.94/9.96 f14(true__, A) -> f13(product(j(A), A, j(A))) % 9.94/9.96 f15(f9(true__, Y0), Y0) -> true__ % 9.94/9.96 f15(subgroup_member(A), A) -> true__ % 9.94/9.96 f15(true__, A) -> f14(product(A, j(A), j(A)), A) % 9.94/9.96 f2(product(X, Y, W), X, Y, Z, W) -> W % 9.94/9.96 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W) % 9.94/9.96 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 9.94/9.96 f3(true__, Y0, inverse(Y0), identity) -> true__ % 9.94/9.96 f3(true__, Y2, identity, Y2) -> true__ % 9.94/9.96 f3(true__, identity, Y2, Y2) -> true__ % 9.94/9.96 f3(true__, inverse(Y1), Y1, identity) -> true__ % 9.94/9.96 f4(f3(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 9.94/9.96 f4(f3(true__, Y3, identity, Y4), Y5, Y3, Y2, Y4, Y2) -> true__ % 9.94/9.96 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W) % 9.94/9.96 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 9.94/9.96 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W) % 9.94/9.96 f6(true__, U, Z, W) -> product(U, Z, W) % 9.94/9.96 f7(f3(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 9.94/9.96 f7(f3(true__, Y3, Y4, identity), Y2, Y3, Y5, Y4, Y2) -> true__ % 9.94/9.96 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W) % 9.94/9.96 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 9.94/9.96 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W) % 9.94/9.96 f9(f9(true__, identity), inverse(a)) -> true__ % 9.94/9.96 f9(f9(true__, identity), inverse(j(a))) -> true__ % 9.94/9.96 f9(f9(true__, identity), inverse(j(j(a)))) -> true__ % 9.94/9.96 f9(f9(true__, identity), inverse(j(j(j(a))))) -> true__ % 9.94/9.96 f9(f9(true__, identity), inverse(j(j(j(j(a)))))) -> true__ % 9.94/9.96 f9(f9(true__, inverse(inverse(a))), identity) -> true__ % 9.94/9.96 f9(f9(true__, inverse(inverse(j(a)))), identity) -> true__ % 9.94/9.96 f9(f9(true__, inverse(inverse(j(j(a))))), identity) -> true__ % 9.94/9.96 f9(true__, a) -> true__ % 9.94/9.96 f9(true__, identity) -> true__ % 9.94/9.96 f9(true__, inverse(a)) -> true__ % 9.94/9.96 f9(true__, inverse(j(a))) -> true__ % 9.94/9.96 f9(true__, inverse(j(j(a)))) -> true__ % 9.94/9.96 f9(true__, inverse(j(j(j(a))))) -> true__ % 9.94/9.96 f9(true__, j(a)) -> true__ % 9.94/9.96 f9(true__, j(identity)) -> true__ % 9.94/9.96 f9(true__, j(j(a))) -> true__ % 9.94/9.96 f9(true__, j(j(j(a)))) -> true__ % 9.94/9.96 f9(true__, j(j(j(j(a))))) -> true__ % 9.94/9.96 f9(true__, j(j(j(j(j(a)))))) -> true__ % 9.94/9.96 f9(true__, j(j(j(j(j(j(a))))))) -> true__ % 9.94/9.96 false__ -> true__ % 9.94/9.96 inverse(identity) -> identity % 9.94/9.96 product(X, V, W) -> f3(true__, X, V, W) % 9.94/9.96 product(X, Y, multiply(X, Y)) -> true__ % 9.94/9.96 product(X, identity, X) -> true__ % 9.94/9.96 product(X, inverse(X), identity) -> true__ % 9.94/9.96 product(identity, X, X) -> true__ % 9.94/9.96 product(inverse(X), X, identity) -> true__ % 9.94/9.96 subgroup_member(C) -> f9(true__, C) % 9.94/9.96 subgroup_member(a) -> true__ % 9.94/9.96 with the LPO induced by % 9.94/9.96 f15 > f14 > f13 > inverse > f2 > f1 > identity > f12 > f11 > f5 > f8 > f7 > f6 > f10 > subgroup_member > f4 > product > f3 > a > f9 > j > multiply > false__ > true__ % 9.94/9.96 % 9.94/9.96 % SZS output end Proof % 9.94/9.96 %------------------------------------------------------------------------------