%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP023-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 10:51:54 EDT 2022 % Result : Unsatisfiable 0.96s 1.10s % Output : Proof 0.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP023-1 : TPTP v8.1.0. Released v1.0.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n022.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 08:26:03 EDT 2022 % 0.12/0.34 % CPUTime : % 0.96/1.10 % SZS status Unsatisfiable % 0.96/1.10 % SZS output start Proof % 0.96/1.10 The input problem is unsatisfiable because % 0.96/1.10 % 0.96/1.10 [1] the following set of Horn clauses is unsatisfiable: % 0.96/1.10 % 0.96/1.10 product(identity, X, X) % 0.96/1.10 product(X, identity, X) % 0.96/1.10 product(inverse(X), X, identity) % 0.96/1.10 product(X, inverse(X), identity) % 0.96/1.10 product(X, Y, multiply(X, Y)) % 0.96/1.10 product(X, Y, Z) & product(X, Y, W) ==> Z = W % 0.96/1.10 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 0.96/1.10 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 0.96/1.10 inverse(identity) = identity ==> \bottom % 0.96/1.10 % 0.96/1.10 This holds because % 0.96/1.10 % 0.96/1.10 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.96/1.10 % 0.96/1.10 E: % 0.96/1.10 f1(true__, Z, W) = Z % 0.96/1.10 f2(product(X, Y, W), X, Y, Z, W) = W % 0.96/1.10 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 0.96/1.10 f3(true__, X, V, W) = product(X, V, W) % 0.96/1.10 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 0.96/1.10 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 0.96/1.10 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 0.96/1.10 f6(true__, U, Z, W) = product(U, Z, W) % 0.96/1.10 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 0.96/1.10 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 0.96/1.10 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 0.96/1.10 f9(identity) = false__ % 0.96/1.10 f9(inverse(identity)) = true__ % 0.96/1.10 product(X, Y, multiply(X, Y)) = true__ % 0.96/1.10 product(X, identity, X) = true__ % 0.96/1.10 product(X, inverse(X), identity) = true__ % 0.96/1.10 product(identity, X, X) = true__ % 0.96/1.10 product(inverse(X), X, identity) = true__ % 0.96/1.10 G: % 0.96/1.10 true__ = false__ % 0.96/1.10 % 0.96/1.10 This holds because % 0.96/1.10 % 0.96/1.10 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.96/1.10 % 0.96/1.10 % 0.96/1.10 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1) % 0.96/1.10 f1(f3(true__, Y0, inverse(Y0), Y3), Y3, identity) -> identity % 0.96/1.10 f1(f3(true__, Y2, identity, Y3), Y3, Y2) -> Y2 % 0.96/1.10 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> Y2 % 0.96/1.10 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> identity % 0.96/1.10 f1(true__, Z, W) -> Z % 0.96/1.10 f2(product(X, Y, W), X, Y, Z, W) -> W % 0.96/1.10 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W) % 0.96/1.10 f3(f3(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__ % 0.96/1.10 f3(f3(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 0.96/1.10 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 0.96/1.10 f3(true__, Y0, inverse(Y0), identity) -> true__ % 0.96/1.10 f3(true__, Y2, identity, Y2) -> true__ % 0.96/1.10 f3(true__, identity, Y2, Y2) -> true__ % 0.96/1.10 f3(true__, inverse(Y1), Y1, identity) -> true__ % 0.96/1.10 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__ % 0.96/1.10 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__ % 0.96/1.10 f4(f3(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 0.96/1.10 f4(f3(true__, Y3, identity, Y4), Y5, Y3, Y2, Y4, Y2) -> true__ % 0.96/1.10 f4(f3(true__, Y3, inverse(Y0), Y4), Y5, Y3, Y0, Y4, identity) -> true__ % 0.96/1.10 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W) % 0.96/1.10 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 0.96/1.10 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W) % 0.96/1.10 f6(f3(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__ % 0.96/1.10 f6(true__, U, Z, W) -> product(U, Z, W) % 0.96/1.10 f7(f3(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(Y0, Y1)) -> true__ % 0.96/1.10 f7(f3(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__ % 0.96/1.10 f7(f3(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 0.96/1.10 f7(f3(true__, Y3, Y4, identity), Y2, Y3, Y5, Y4, Y2) -> true__ % 0.96/1.10 f7(f3(true__, Y3, Y4, inverse(Y0)), Y0, Y3, Y5, Y4, identity) -> true__ % 0.96/1.10 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W) % 0.96/1.10 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 0.96/1.10 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W) % 0.96/1.10 f9(identity) -> false__ % 0.96/1.10 f9(inverse(identity)) -> true__ % 0.96/1.10 false__ -> true__ % 0.96/1.10 inverse(identity) -> identity % 0.96/1.10 multiply(Y0, identity) -> Y0 % 0.96/1.10 multiply(identity, Y0) -> Y0 % 0.96/1.10 multiply(inverse(Y0), Y0) -> identity % 0.96/1.10 product(X, V, W) -> f3(true__, X, V, W) % 0.96/1.10 product(X, Y, multiply(X, Y)) -> true__ % 0.96/1.10 product(X, identity, X) -> true__ % 0.96/1.10 product(X, inverse(X), identity) -> true__ % 0.96/1.10 product(identity, X, X) -> true__ % 0.96/1.10 product(inverse(X), X, identity) -> true__ % 0.96/1.10 with the LPO induced by % 0.96/1.10 f9 > f5 > f4 > f2 > f1 > f8 > f7 > f6 > product > f3 > multiply > inverse > identity > false__ > true__ % 0.96/1.10 % 0.96/1.10 % SZS output end Proof % 0.96/1.10 %------------------------------------------------------------------------------