%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP004-2 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 12.81s 12.77s % Output : Proof 12.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : GRP004-2 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n020.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jun 13 06:40:50 EDT 2022 % 0.13/0.33 % CPUTime : % 12.81/12.77 % SZS status Unsatisfiable % 12.81/12.77 % SZS output start Proof % 12.81/12.77 The input problem is unsatisfiable because % 12.81/12.77 % 12.81/12.77 [1] the following set of Horn clauses is unsatisfiable: % 12.81/12.77 % 12.81/12.77 product(identity, X, X) % 12.81/12.77 product(inverse(X), X, identity) % 12.81/12.77 product(X, Y, multiply(X, Y)) % 12.81/12.77 product(X, Y, Z) & product(X, Y, W) ==> equalish(Z, W) % 12.81/12.77 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 12.81/12.77 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 12.81/12.77 equalish(X, Y) & product(W, Z, X) ==> product(W, Z, Y) % 12.81/12.77 product(a, inverse(a), identity) ==> \bottom % 12.81/12.77 % 12.81/12.77 This holds because % 12.81/12.77 % 12.81/12.77 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 12.81/12.77 % 12.81/12.77 E: % 12.81/12.77 f1(true__, Z, W) = equalish(Z, W) % 12.81/12.77 f10(product(W, Z, X), X, Y, W, Z) = true__ % 12.81/12.77 f10(true__, X, Y, W, Z) = f9(equalish(X, Y), W, Z, Y) % 12.81/12.77 f11(product(a, inverse(a), identity)) = true__ % 12.81/12.77 f11(true__) = false__ % 12.81/12.77 f2(product(X, Y, W), X, Y, Z, W) = true__ % 12.81/12.77 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 12.81/12.77 f3(true__, X, V, W) = product(X, V, W) % 12.81/12.77 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 12.81/12.77 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 12.81/12.77 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 12.81/12.77 f6(true__, U, Z, W) = product(U, Z, W) % 12.81/12.77 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 12.81/12.77 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 12.81/12.77 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 12.81/12.77 f9(true__, W, Z, Y) = product(W, Z, Y) % 12.81/12.77 product(X, Y, multiply(X, Y)) = true__ % 12.81/12.77 product(identity, X, X) = true__ % 12.81/12.77 product(inverse(X), X, identity) = true__ % 12.81/12.77 G: % 12.81/12.77 true__ = false__ % 12.81/12.77 % 12.81/12.77 This holds because % 12.81/12.77 % 12.81/12.77 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 12.81/12.77 % 12.81/12.77 % 12.81/12.77 equalish(Z, W) -> f1(true__, Z, W) % 12.81/12.77 f1(f6(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> true__ % 12.81/12.77 f1(f6(true__, Y0, inverse(Y0), Y3), Y3, identity) -> true__ % 12.81/12.77 f1(f6(true__, identity, Y2, Y3), Y3, Y2) -> true__ % 12.81/12.77 f1(f6(true__, identity, identity, Y3), Y3, inverse(identity)) -> true__ % 12.81/12.77 f1(f6(true__, identity, inverse(identity), Y3), Y3, identity) -> true__ % 12.81/12.77 f1(f6(true__, identity, multiply(identity, Y2), Y3), Y3, Y2) -> true__ % 12.81/12.77 f1(f6(true__, inverse(Y1), Y1, Y3), Y3, identity) -> true__ % 12.81/12.77 f1(f6(true__, inverse(Y1), Y1, Y3), Y3, inverse(identity)) -> true__ % 12.81/12.77 f1(f6(true__, inverse(identity), Y2, Y3), Y3, Y2) -> true__ % 12.81/12.77 f1(f6(true__, inverse(identity), inverse(identity), Y3), Y3, identity) -> true__ % 12.81/12.77 f1(f6(true__, inverse(inverse(Y2)), identity, Y3), Y3, Y2) -> true__ % 12.81/12.77 f1(f6(true__, inverse(inverse(identity)), Y2, Y3), Y3, Y2) -> true__ % 12.81/12.77 f1(f6(true__, multiply(identity, identity), Y2, Y3), Y3, Y2) -> true__ % 12.81/12.77 f1(true__, Y1, Y1) -> true__ % 12.81/12.77 f1(true__, Y2, multiply(identity, Y2)) -> true__ % 12.81/12.77 f1(true__, Y2, multiply(identity, multiply(identity, Y2))) -> true__ % 12.81/12.77 f1(true__, Y2, multiply(inverse(identity), Y2)) -> true__ % 12.81/12.77 f1(true__, Y2, multiply(inverse(inverse(Y2)), identity)) -> true__ % 12.81/12.77 f1(true__, Y2, multiply(inverse(inverse(identity)), Y2)) -> true__ % 12.81/12.77 f1(true__, Y2, multiply(multiply(identity, identity), Y2)) -> true__ % 12.81/12.77 f1(true__, identity, inverse(identity)) -> true__ % 12.81/12.77 f1(true__, identity, inverse(inverse(identity))) -> true__ % 12.81/12.77 f1(true__, identity, inverse(multiply(identity, identity))) -> true__ % 12.81/12.77 f1(true__, identity, multiply(Y0, inverse(Y0))) -> true__ % 12.81/12.77 f1(true__, identity, multiply(identity, inverse(identity))) -> true__ % 12.81/12.77 f1(true__, identity, multiply(inverse(Y1), Y1)) -> true__ % 12.81/12.77 f1(true__, identity, multiply(inverse(identity), inverse(identity))) -> true__ % 12.81/12.77 f1(true__, inverse(identity), identity) -> true__ % 12.81/12.77 f1(true__, inverse(identity), multiply(identity, identity)) -> true__ % 12.81/12.77 f1(true__, inverse(identity), multiply(inverse(Y1), Y1)) -> true__ % 12.81/12.77 f1(true__, inverse(identity), multiply(inverse(identity), identity)) -> true__ % 12.81/12.77 f1(true__, multiply(identity, Y0), Y0) -> true__ % 12.81/12.77 f1(true__, multiply(identity, identity), inverse(identity)) -> true__ % 12.81/12.77 f1(true__, multiply(identity, inverse(identity)), identity) -> true__ % 12.81/12.77 f1(true__, multiply(identity, multiply(identity, Y0)), Y0) -> true__ % 12.81/12.77 f1(true__, multiply(inverse(X0), X0), inverse(identity)) -> true__ % 12.81/12.77 f1(true__, multiply(inverse(Y0), Y0), identity) -> true__ % 12.81/12.77 f1(true__, multiply(inverse(identity), Y0), Y0) -> true__ % 12.81/12.77 f1(true__, multiply(inverse(identity), identity), inverse(identity)) -> true__ % 12.81/12.77 f1(true__, multiply(inverse(identity), inverse(identity)), identity) -> true__ % 12.81/12.77 f1(true__, multiply(inverse(inverse(Y0)), identity), Y0) -> true__ % 12.81/12.77 f1(true__, multiply(multiply(identity, identity), Y0), Y0) -> true__ % 12.81/12.77 f10(f6(true__, Y0, Y1, Y2), Y2, Y3, Y0, Y1) -> true__ % 12.81/12.77 f10(product(W, Z, X), X, Y, W, Z) -> true__ % 12.81/12.77 f10(true__, X, Y, W, Z) -> f9(equalish(X, Y), W, Z, Y) % 12.81/12.77 f11(f6(true__, a, inverse(a), identity)) -> true__ % 12.81/12.77 f11(product(a, inverse(a), identity)) -> true__ % 12.81/12.77 f11(true__) -> false__ % 12.81/12.77 f2(f6(true__, Y0, Y1, Y2), Y0, Y1, Y3, Y2) -> true__ % 12.81/12.77 f2(product(X, Y, W), X, Y, Z, W) -> true__ % 12.81/12.77 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W) % 12.81/12.77 f3(f6(true__, Y3, identity, Y4), Y3, Y2, multiply(Y4, Y2)) -> true__ % 12.81/12.77 f3(f6(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 12.81/12.77 f3(f6(true__, Y3, identity, inverse(Y2)), Y3, Y2, identity) -> true__ % 12.81/12.77 f3(f6(true__, Y3, inverse(Y1), identity), Y3, identity, Y1) -> true__ % 12.81/12.77 f3(true__, X, V, W) -> product(X, V, W) % 12.81/12.77 f4(f6(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__ % 12.81/12.77 f4(f6(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__ % 12.81/12.77 f4(f6(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 12.81/12.77 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W) % 12.81/12.77 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 12.81/12.77 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W) % 12.81/12.77 f6(f6(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__ % 12.81/12.77 f6(f6(true__, identity, inverse(Y1), Y3), Y3, Y1, identity) -> true__ % 12.81/12.77 f6(f6(true__, inverse(Y2), identity, Y3), Y3, Y2, identity) -> true__ % 12.81/12.77 f6(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 12.81/12.77 f6(true__, Y0, Y1, multiply(identity, multiply(Y0, Y1))) -> true__ % 12.81/12.77 f6(true__, Y0, Y1, multiply(inverse(identity), multiply(Y0, Y1))) -> true__ % 12.81/12.77 f6(true__, Y1, identity, Y1) -> true__ % 12.81/12.77 f6(true__, Y1, inverse(Y1), identity) -> true__ % 12.81/12.77 f6(true__, identity, Y0, multiply(inverse(identity), Y0)) -> true__ % 12.81/12.77 f6(true__, identity, Y0, multiply(inverse(inverse(Y0)), identity)) -> true__ % 12.81/12.77 f6(true__, identity, Y0, multiply(inverse(inverse(identity)), Y0)) -> true__ % 12.81/12.77 f6(true__, identity, Y0, multiply(multiply(identity, identity), Y0)) -> true__ % 12.81/12.77 f6(true__, identity, Y2, Y2) -> true__ % 12.81/12.77 f6(true__, identity, identity, inverse(identity)) -> true__ % 12.81/12.77 f6(true__, identity, identity, multiply(identity, inverse(identity))) -> true__ % 12.81/12.77 f6(true__, identity, identity, multiply(identity, multiply(identity, inverse(identity)))) -> true__ % 12.81/12.77 f6(true__, identity, identity, multiply(inverse(X0), X0)) -> true__ % 12.81/12.77 f6(true__, identity, identity, multiply(inverse(identity), inverse(identity))) -> true__ % 12.81/12.77 f6(true__, identity, inverse(identity), identity) -> true__ % 12.81/12.77 f6(true__, identity, inverse(identity), multiply(identity, identity)) -> true__ % 12.81/12.77 f6(true__, identity, inverse(identity), multiply(identity, multiply(identity, identity))) -> true__ % 12.81/12.77 f6(true__, identity, inverse(identity), multiply(inverse(X0), X0)) -> true__ % 12.81/12.77 f6(true__, identity, inverse(identity), multiply(inverse(identity), identity)) -> true__ % 12.81/12.77 f6(true__, identity, inverse(identity), multiply(multiply(identity, identity), identity)) -> true__ % 12.81/12.77 f6(true__, identity, multiply(identity, Y1), Y1) -> true__ % 12.81/12.77 f6(true__, identity, multiply(identity, identity), inverse(identity)) -> true__ % 12.81/12.77 f6(true__, identity, multiply(identity, identity), multiply(inverse(X0), X0)) -> true__ % 12.81/12.77 f6(true__, identity, multiply(identity, inverse(identity)), identity) -> true__ % 12.81/12.77 f6(true__, identity, multiply(identity, multiply(identity, Y1)), Y1) -> true__ % 12.81/12.77 f6(true__, identity, multiply(identity, multiply(inverse(X0), X0)), identity) -> true__ % 12.81/12.77 f6(true__, identity, multiply(inverse(X0), X0), identity) -> true__ % 12.81/12.77 f6(true__, identity, multiply(inverse(X0), X0), inverse(identity)) -> true__ % 12.81/12.77 f6(true__, identity, multiply(inverse(identity), Y1), Y1) -> true__ % 12.81/12.77 f6(true__, identity, multiply(inverse(identity), identity), inverse(identity)) -> true__ % 12.81/12.78 f6(true__, identity, multiply(inverse(identity), inverse(identity)), identity) -> true__ % 12.81/12.78 f6(true__, identity, multiply(inverse(inverse(Y1)), identity), Y1) -> true__ % 12.81/12.78 f6(true__, identity, multiply(multiply(identity, identity), Y1), Y1) -> true__ % 12.81/12.78 f6(true__, inverse(Y1), Y1, identity) -> true__ % 12.81/12.78 f6(true__, inverse(Y1), Y1, inverse(identity)) -> true__ % 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(identity, identity)) -> true__ % 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(identity, inverse(identity))) -> true__ % 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(identity, multiply(identity, identity))) -> true__ % 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(inverse(X0), X0)) -> true__ % 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(inverse(identity), identity)) -> true__ % 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(inverse(identity), inverse(identity))) -> true__ % 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(inverse(inverse(identity)), identity)) -> true__ % 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(multiply(identity, identity), identity)) -> true__ % 12.81/12.78 f6(true__, inverse(identity), Y0, multiply(identity, Y0)) -> true__ % 12.81/12.78 f6(true__, inverse(identity), Y0, multiply(identity, multiply(identity, Y0))) -> true__ % 12.81/12.78 f6(true__, inverse(identity), Y0, multiply(multiply(identity, identity), Y0)) -> true__ % 12.81/12.78 f6(true__, inverse(identity), Y1, Y1) -> true__ % 12.81/12.78 f6(true__, inverse(identity), identity, inverse(identity)) -> true__ % 12.81/12.78 f6(true__, inverse(identity), inverse(identity), identity) -> true__ % 12.81/12.78 f6(true__, inverse(identity), inverse(identity), multiply(identity, identity)) -> true__ % 12.81/12.78 f6(true__, inverse(identity), multiply(identity, Y1), Y1) -> true__ % 12.81/12.78 f6(true__, inverse(identity), multiply(identity, identity), inverse(identity)) -> true__ % 12.81/12.78 f6(true__, inverse(identity), multiply(identity, inverse(identity)), identity) -> true__ % 12.81/12.78 f6(true__, inverse(identity), multiply(identity, multiply(identity, Y1)), Y1) -> true__ % 12.81/12.78 f6(true__, inverse(identity), multiply(inverse(X0), X0), identity) -> true__ % 12.81/12.78 f6(true__, inverse(identity), multiply(inverse(identity), Y1), Y1) -> true__ % 12.81/12.78 f6(true__, inverse(inverse(Y1)), identity, Y1) -> true__ % 12.81/12.78 f6(true__, inverse(inverse(identity)), Y1, Y1) -> true__ % 12.81/12.78 f6(true__, inverse(inverse(inverse(Y1))), Y1, identity) -> true__ % 12.81/12.78 f6(true__, inverse(inverse(inverse(identity))), Y1, Y1) -> true__ % 12.81/12.78 f6(true__, multiply(identity, identity), Y0, multiply(identity, Y0)) -> true__ % 12.81/12.78 f6(true__, multiply(identity, identity), Y1, Y1) -> true__ % 12.81/12.78 f6(true__, multiply(identity, identity), identity, inverse(identity)) -> true__ % 12.81/12.78 f6(true__, multiply(identity, identity), inverse(identity), identity) -> true__ % 12.81/12.78 f6(true__, multiply(identity, identity), multiply(identity, Y1), Y1) -> true__ % 12.81/12.78 f6(true__, multiply(identity, inverse(Y0)), Y0, identity) -> true__ % 12.81/12.78 f6(true__, multiply(identity, inverse(identity)), Y1, Y1) -> true__ % 12.81/12.78 f6(true__, multiply(inverse(X0), X0), Y1, Y1) -> true__ % 12.81/12.78 f6(true__, multiply(inverse(Y0), identity), Y0, identity) -> true__ % 12.81/12.78 f7(f6(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(Y0, Y1)) -> true__ % 12.81/12.78 f7(f6(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__ % 12.81/12.78 f7(f6(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 12.81/12.78 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W) % 12.81/12.78 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 12.81/12.78 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W) % 12.81/12.78 f9(f1(true__, Y2, Y3), identity, Y2, Y3) -> true__ % 12.81/12.78 f9(f1(true__, Y2, Y3), identity, multiply(identity, Y2), Y3) -> true__ % 12.81/12.78 f9(f1(true__, Y2, Y3), inverse(identity), Y2, Y3) -> true__ % 12.81/12.78 f9(f1(true__, Y2, Y3), inverse(inverse(Y2)), identity, Y3) -> true__ % 12.81/12.78 f9(f1(true__, Y2, Y3), inverse(inverse(identity)), Y2, Y3) -> true__ % 12.81/12.78 f9(f1(true__, Y2, Y3), multiply(identity, identity), Y2, Y3) -> true__ % 12.81/12.78 f9(f1(true__, identity, Y3), Y0, inverse(Y0), Y3) -> true__ % 12.81/12.78 f9(f1(true__, identity, Y3), identity, inverse(identity), Y3) -> true__ % 12.81/12.78 f9(f1(true__, identity, Y3), inverse(Y1), Y1, Y3) -> true__ % 12.81/12.78 f9(f1(true__, inverse(identity), Y3), identity, identity, Y3) -> true__ % 12.81/12.78 f9(f1(true__, multiply(Y0, Y1), Y3), Y0, Y1, Y3) -> true__ % 12.81/12.78 f9(true__, W, Z, Y) -> product(W, Z, Y) % 12.81/12.78 false__ -> true__ % 12.81/12.78 product(U, Z, W) -> f6(true__, U, Z, W) % 12.81/12.78 product(X, Y, multiply(X, Y)) -> true__ % 12.81/12.78 product(identity, X, X) -> true__ % 12.81/12.78 product(inverse(X), X, identity) -> true__ % 12.81/12.78 with the LPO induced by % 12.81/12.78 a > f11 > f10 > f2 > f8 > f7 > f9 > f5 > f4 > f3 > equalish > f1 > product > f6 > multiply > inverse > identity > false__ > true__ % 12.81/12.78 % 12.81/12.78 % SZS output end Proof % 12.81/12.78 %------------------------------------------------------------------------------