%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP012-3 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.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 10:51:48 EDT 2022 % Result : Unsatisfiable 7.52s 7.50s % Output : Proof 7.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP012-3 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n011.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Tue Jun 14 01:55:51 EDT 2022 % 0.12/0.34 % CPUTime : % 7.52/7.50 % SZS status Unsatisfiable % 7.52/7.50 % SZS output start Proof % 7.52/7.50 The input problem is unsatisfiable because % 7.52/7.50 % 7.52/7.50 [1] the following set of Horn clauses is unsatisfiable: % 7.52/7.50 % 7.52/7.50 product(identity, X, X) % 7.52/7.50 product(X, identity, X) % 7.52/7.50 product(inverse(X), X, identity) % 7.52/7.50 product(X, inverse(X), identity) % 7.52/7.50 product(X, Y, multiply(X, Y)) % 7.52/7.50 product(X, Y, Z) & product(X, Y, W) ==> Z = W % 7.52/7.50 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 7.52/7.50 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 7.52/7.50 inverse(multiply(a, b)) = multiply(inverse(b), inverse(a)) ==> \bottom % 7.52/7.50 % 7.52/7.50 This holds because % 7.52/7.50 % 7.52/7.50 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 7.52/7.50 % 7.52/7.50 E: % 7.52/7.50 f1(true__, Z, W) = Z % 7.52/7.50 f2(product(X, Y, W), X, Y, Z, W) = W % 7.52/7.50 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 7.52/7.50 f3(true__, X, V, W) = product(X, V, W) % 7.52/7.50 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 7.52/7.50 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 7.52/7.50 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 7.52/7.50 f6(true__, U, Z, W) = product(U, Z, W) % 7.52/7.50 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 7.52/7.50 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 7.52/7.50 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 7.52/7.50 f9(inverse(multiply(a, b))) = true__ % 7.52/7.50 f9(multiply(inverse(b), inverse(a))) = false__ % 7.52/7.50 product(X, Y, multiply(X, Y)) = true__ % 7.52/7.50 product(X, identity, X) = true__ % 7.52/7.50 product(X, inverse(X), identity) = true__ % 7.52/7.50 product(identity, X, X) = true__ % 7.52/7.50 product(inverse(X), X, identity) = true__ % 7.52/7.50 G: % 7.52/7.50 true__ = false__ % 7.52/7.50 % 7.52/7.50 This holds because % 7.52/7.50 % 7.52/7.50 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 7.52/7.50 % 7.52/7.50 inverse(multiply(X1, X0)) = multiply(inverse(X0), inverse(X1)) % 7.52/7.50 multiply(X1, Y1) = inverse(multiply(inverse(Y1), inverse(X1))) % 7.52/7.50 multiply(X1, inverse(Y1)) = inverse(multiply(Y1, inverse(X1))) % 7.52/7.50 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1) % 7.52/7.50 f1(f3(true__, Y0, inverse(Y0), Y3), Y3, identity) -> identity % 7.52/7.50 f1(f3(true__, Y0, multiply(inverse(Y0), Y2), Y3), Y3, Y2) -> Y2 % 7.52/7.50 f1(f3(true__, Y2, identity, Y3), Y3, Y2) -> Y2 % 7.52/7.50 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> Y2 % 7.52/7.50 f1(f3(true__, inverse(X0), multiply(X0, Y2), Y3), Y3, Y2) -> Y2 % 7.52/7.50 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> identity % 7.52/7.50 f1(f3(true__, inverse(inverse(Y2)), identity, Y3), Y3, Y2) -> Y2 % 7.52/7.50 f1(f3(true__, multiply(Y0, X0), inverse(X0), Y2), Y2, Y0) -> Y0 % 7.52/7.50 f1(f3(true__, multiply(Y2, inverse(Y1)), Y1, Y3), Y3, Y2) -> Y2 % 7.52/7.50 f1(true__, Z, W) -> Z % 7.52/7.50 f2(f3(true__, Y0, Y1, Y2), Y0, Y1, Y3, Y2) -> Y2 % 7.52/7.50 f2(product(X, Y, W), X, Y, Z, W) -> W % 7.52/7.50 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W) % 7.52/7.50 f3(f3(true__, Y0, X0, X0), Y0, identity, identity) -> true__ % 7.52/7.50 f3(f3(true__, Y0, identity, X0), Y0, inverse(X0), identity) -> true__ % 7.52/7.50 f3(f3(true__, Y0, multiply(Y1, X0), identity), Y0, Y1, inverse(X0)) -> true__ % 7.52/7.50 f3(f3(true__, Y2, Y1, Y3), Y2, Y1, Y3) -> true__ % 7.52/7.50 f3(f3(true__, Y2, identity, Y3), Y2, identity, Y3) -> true__ % 7.52/7.50 f3(f3(true__, Y3, Y0, identity), Y3, identity, inverse(Y0)) -> true__ % 7.52/7.50 f3(f3(true__, Y3, Y0, identity), Y3, multiply(Y0, Y1), Y1) -> true__ % 7.52/7.50 f3(f3(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__ % 7.52/7.50 f3(f3(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 7.52/7.50 f3(f3(true__, Y3, identity, inverse(Y2)), Y3, Y2, identity) -> true__ % 7.52/7.50 f3(f3(true__, Y3, inverse(Y1), identity), Y3, identity, Y1) -> true__ % 7.52/7.50 f3(f3(true__, Y3, inverse(Y1), inverse(Y1)), Y3, identity, identity) -> true__ % 7.52/7.50 f3(f3(true__, Y3, inverse(inverse(Y2)), identity), Y3, Y2, identity) -> true__ % 7.52/7.50 f3(f3(true__, Y3, multiply(Y2, inverse(Y1)), identity), Y3, Y2, Y1) -> true__ % 7.52/7.50 f3(true__, Y0, Y1, inverse(multiply(inverse(Y1), inverse(Y0)))) -> true__ % 7.52/7.50 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 7.52/7.50 f3(true__, Y0, inverse(X0), inverse(multiply(X0, inverse(Y0)))) -> true__ % 7.52/7.50 f3(true__, Y0, inverse(Y0), identity) -> true__ % 7.52/7.50 f3(true__, Y0, multiply(inverse(Y0), Y2), Y2) -> true__ % 7.52/7.50 f3(true__, Y1, identity, inverse(inverse(Y1))) -> true__ % 7.52/7.50 f3(true__, Y2, identity, Y2) -> true__ % 7.52/7.50 f3(true__, Y2, inverse(multiply(X0, Y2)), inverse(X0)) -> true__ % 7.52/7.50 f3(true__, Y2, inverse(multiply(inverse(Y0), Y2)), Y0) -> true__ % 7.52/7.50 f3(true__, identity, Y2, Y2) -> true__ % 7.52/7.50 f3(true__, inverse(Y1), Y1, identity) -> true__ % 7.52/7.50 f3(true__, inverse(Y1), multiply(Y1, Y2), Y2) -> true__ % 7.52/7.50 f3(true__, inverse(inverse(Y1)), identity, Y1) -> true__ % 7.52/7.50 f3(true__, inverse(inverse(inverse(Y1))), Y1, identity) -> true__ % 7.52/7.50 f3(true__, inverse(multiply(X0, inverse(Y1))), X0, Y1) -> true__ % 7.52/7.50 f3(true__, inverse(multiply(Y0, X0)), Y0, inverse(X0)) -> true__ % 7.52/7.50 f3(true__, multiply(X1, X0), multiply(inverse(X0), inverse(X1)), identity) -> true__ % 7.52/7.50 f3(true__, multiply(Y0, X0), inverse(X0), Y0) -> true__ % 7.52/7.50 f3(true__, multiply(Y0, inverse(Y1)), Y1, Y0) -> true__ % 7.52/7.50 f3(true__, multiply(inverse(X0), inverse(X1)), multiply(X1, X0), identity) -> true__ % 7.52/7.50 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__ % 7.52/7.50 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__ % 7.52/7.50 f4(f3(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 7.52/7.50 f4(f3(true__, Y3, identity, Y4), Y5, Y3, Y2, Y4, Y2) -> true__ % 7.52/7.50 f4(f3(true__, Y3, inverse(Y0), Y4), Y5, Y3, Y0, Y4, identity) -> true__ % 7.52/7.50 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W) % 7.52/7.50 f5(f3(true__, Y0, Y1, Y2), Y3, Y1, Y4, Y5, Y0, Y2) -> true__ % 7.52/7.50 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 7.52/7.50 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W) % 7.52/7.50 f6(f3(true__, X0, identity, Y1), Y1, inverse(X0), identity) -> true__ % 7.52/7.50 f6(f3(true__, Y0, X0, Y2), Y2, inverse(X0), Y0) -> true__ % 7.52/7.50 f6(f3(true__, Y2, identity, Y3), Y3, identity, Y2) -> true__ % 7.52/7.50 f6(f3(true__, Y2, inverse(Y1), Y3), Y3, Y1, Y2) -> true__ % 7.52/7.50 f6(f3(true__, Y2, inverse(Y2), Y3), Y3, identity, identity) -> true__ % 7.52/7.50 f6(f3(true__, identity, Y0, Y3), Y3, Y1, multiply(Y0, Y1)) -> true__ % 7.52/7.50 f6(f3(true__, identity, Y0, Y3), Y3, inverse(Y0), identity) -> true__ % 7.52/7.50 f6(f3(true__, identity, Y2, Y3), Y3, identity, Y2) -> true__ % 7.52/7.50 f6(f3(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__ % 7.52/7.50 f6(f3(true__, identity, inverse(Y1), Y3), Y3, Y1, identity) -> true__ % 7.52/7.50 f6(f3(true__, identity, multiply(X0, inverse(Y2)), Y1), Y1, Y2, X0) -> true__ % 7.52/7.50 f6(f3(true__, inverse(Y2), Y2, Y3), Y3, identity, identity) -> true__ % 7.52/7.50 f6(f3(true__, inverse(Y2), identity, Y3), Y3, Y2, identity) -> true__ % 7.52/7.50 f6(true__, U, Z, W) -> product(U, Z, W) % 7.52/7.50 f7(f3(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(Y0, Y1)) -> true__ % 7.52/7.50 f7(f3(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__ % 7.52/7.50 f7(f3(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 7.52/7.50 f7(f3(true__, Y3, Y4, identity), Y2, Y3, Y5, Y4, Y2) -> true__ % 7.52/7.50 f7(f3(true__, Y3, Y4, inverse(Y0)), Y0, Y3, Y5, Y4, identity) -> true__ % 7.52/7.50 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W) % 7.52/7.50 f8(f3(true__, Y0, Y1, Y2), Y3, Y4, Y1, Y0, Y5, Y2) -> true__ % 7.52/7.50 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 7.52/7.50 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W) % 7.52/7.50 f9(inverse(multiply(a, b))) -> true__ % 7.52/7.50 f9(multiply(inverse(b), inverse(a))) -> false__ % 7.52/7.50 false__ -> true__ % 7.52/7.50 inverse(identity) -> identity % 7.52/7.50 inverse(inverse(Y1)) -> Y1 % 7.52/7.50 multiply(X0, multiply(inverse(X0), Y1)) -> Y1 % 7.52/7.50 multiply(X1, inverse(multiply(X0, X1))) -> inverse(X0) % 7.52/7.50 multiply(X1, inverse(multiply(inverse(Y0), X1))) -> Y0 % 7.52/7.50 multiply(Y0, identity) -> Y0 % 7.52/7.50 multiply(Y0, inverse(Y0)) -> identity % 7.52/7.50 multiply(identity, Y0) -> Y0 % 7.52/7.50 multiply(inverse(X1), inverse(multiply(inverse(Y1), inverse(X1)))) -> Y1 % 7.52/7.50 multiply(inverse(Y0), Y0) -> identity % 7.52/7.50 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1 % 7.52/7.50 multiply(inverse(multiply(X0, inverse(Y1))), X0) -> Y1 % 7.52/7.50 multiply(inverse(multiply(Y0, X0)), Y0) -> inverse(X0) % 7.52/7.50 multiply(multiply(X1, X0), multiply(inverse(X0), inverse(X1))) -> identity % 7.52/7.50 multiply(multiply(Y0, X0), inverse(X0)) -> Y0 % 7.52/7.50 multiply(multiply(Y0, inverse(Y1)), Y1) -> Y0 % 7.52/7.50 multiply(multiply(inverse(X0), inverse(X1)), multiply(X1, X0)) -> identity % 7.52/7.50 product(X, V, W) -> f3(true__, X, V, W) % 7.52/7.50 product(X, Y, multiply(X, Y)) -> true__ % 7.52/7.50 product(X, identity, X) -> true__ % 7.52/7.50 product(X, inverse(X), identity) -> true__ % 7.52/7.50 product(identity, X, X) -> true__ % 7.52/7.50 product(inverse(X), X, identity) -> true__ % 7.52/7.50 with the LPO induced by % 7.52/7.50 a > b > f9 > f5 > f4 > f8 > f7 > f6 > f2 > f1 > product > f3 > multiply > inverse > identity > false__ > true__ % 7.52/7.50 % 7.52/7.50 % SZS output end Proof % 7.52/7.50 %------------------------------------------------------------------------------