%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO009-2 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n027.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 : Thu Jul 14 23:46:19 EDT 2022 % Result : Unsatisfiable 5.27s 5.28s % Output : Proof 5.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : BOO009-2 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jun 1 16:06:19 EDT 2022 % 0.13/0.34 % CPUTime : % 5.27/5.28 % SZS status Unsatisfiable % 5.27/5.28 % SZS output start Proof % 5.27/5.28 The input problem is unsatisfiable because % 5.27/5.28 % 5.27/5.28 [1] the following set of Horn clauses is unsatisfiable: % 5.27/5.28 % 5.27/5.28 add(X, Y) = add(Y, X) % 5.27/5.28 multiply(X, Y) = multiply(Y, X) % 5.27/5.28 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)) % 5.27/5.28 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 5.27/5.28 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 5.27/5.28 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 5.27/5.28 add(X, inverse(X)) = multiplicative_identity % 5.27/5.28 add(inverse(X), X) = multiplicative_identity % 5.27/5.28 multiply(X, inverse(X)) = additive_identity % 5.27/5.28 multiply(inverse(X), X) = additive_identity % 5.27/5.28 multiply(X, multiplicative_identity) = X % 5.27/5.28 multiply(multiplicative_identity, X) = X % 5.27/5.28 add(X, additive_identity) = X % 5.27/5.28 add(additive_identity, X) = X % 5.27/5.28 multiply(a, add(a, b)) = a ==> \bottom % 5.27/5.28 % 5.27/5.28 This holds because % 5.27/5.28 % 5.27/5.28 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.27/5.28 % 5.27/5.28 E: % 5.27/5.28 add(X, Y) = add(Y, X) % 5.27/5.28 add(X, additive_identity) = X % 5.27/5.28 add(X, inverse(X)) = multiplicative_identity % 5.27/5.28 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 5.27/5.28 add(additive_identity, X) = X % 5.27/5.28 add(inverse(X), X) = multiplicative_identity % 5.27/5.28 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)) % 5.27/5.28 f1(a) = false__ % 5.27/5.28 f1(multiply(a, add(a, b))) = true__ % 5.27/5.28 multiply(X, Y) = multiply(Y, X) % 5.27/5.28 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 5.27/5.28 multiply(X, inverse(X)) = additive_identity % 5.27/5.28 multiply(X, multiplicative_identity) = X % 5.27/5.28 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 5.27/5.28 multiply(inverse(X), X) = additive_identity % 5.27/5.28 multiply(multiplicative_identity, X) = X % 5.27/5.28 G: % 5.27/5.28 true__ = false__ % 5.27/5.28 % 5.27/5.28 This holds because % 5.27/5.28 % 5.27/5.28 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.27/5.28 % 5.27/5.28 add(X, Y) = add(Y, X) % 5.27/5.28 multiply(X, Y) = multiply(Y, X) % 5.27/5.28 add(X, inverse(X)) -> multiplicative_identity % 5.27/5.28 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z)) % 5.27/5.28 add(Y0, Y0) -> Y0 % 5.27/5.28 add(Y0, add(Y0, X1)) -> add(Y0, X1) % 5.27/5.28 add(Y0, inverse(multiplicative_identity)) -> Y0 % 5.27/5.28 add(Y0, multiplicative_identity) -> multiplicative_identity % 5.27/5.28 add(Y1, add(Y0, multiply(Y0, Y1))) -> add(Y0, Y1) % 5.27/5.28 add(add(Y0, Y0), add(Y1, multiply(Y1, Y0))) -> add(Y0, Y1) % 5.27/5.28 add(add(Y1, Y1), add(Y0, multiply(Y0, Y1))) -> add(Y0, Y1) % 5.27/5.28 add(inverse(X), X) -> multiplicative_identity % 5.27/5.28 add(inverse(multiplicative_identity), Y0) -> Y0 % 5.27/5.28 add(multiplicative_identity, Y1) -> multiplicative_identity % 5.27/5.28 add(multiply(X, Y), Z) -> multiply(add(X, Z), add(Y, Z)) % 5.27/5.28 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 5.27/5.28 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z) % 5.27/5.28 add(multiply(Y0, Y1), multiply(Y0, additive_identity)) -> multiply(Y0, Y1) % 5.27/5.28 add(multiply(Y0, Y1), multiply(Y0, inverse(Y1))) -> Y0 % 5.27/5.28 add(multiply(Y0, Y1), multiply(Y1, inverse(Y0))) -> Y1 % 5.27/5.28 add(multiply(Y0, Y2), multiply(additive_identity, Y2)) -> multiply(Y0, Y2) % 5.27/5.28 add(multiply(Y0, Y2), multiply(inverse(Y0), Y2)) -> Y2 % 5.27/5.28 add(multiply(Y0, additive_identity), multiply(Y0, Y2)) -> multiply(Y0, Y2) % 5.27/5.28 add(multiply(additive_identity, Y2), multiply(Y1, Y2)) -> multiply(Y1, Y2) % 5.27/5.28 additive_identity -> inverse(multiplicative_identity) % 5.27/5.28 f1(a) -> false__ % 5.27/5.28 f1(multiply(a, add(a, b))) -> true__ % 5.27/5.28 inverse(inverse(Y0)) -> Y0 % 5.27/5.28 multiply(X, inverse(X)) -> inverse(multiplicative_identity) % 5.27/5.28 multiply(X, multiplicative_identity) -> X % 5.27/5.28 multiply(Y0, add(Y0, Y2)) -> Y0 % 5.27/5.28 multiply(Y0, add(Y1, Y0)) -> Y0 % 5.27/5.28 multiply(Y0, additive_identity) -> inverse(multiplicative_identity) % 5.27/5.28 multiply(Y0, inverse(multiplicative_identity)) -> inverse(multiplicative_identity) % 5.27/5.28 multiply(Y1, Y1) -> Y1 % 5.27/5.28 multiply(Y1, add(inverse(X0), Y1)) -> Y1 % 5.27/5.28 multiply(additive_identity, Y1) -> inverse(multiplicative_identity) % 5.27/5.28 multiply(inverse(X), X) -> inverse(multiplicative_identity) % 5.27/5.28 multiply(inverse(multiplicative_identity), Y0) -> inverse(multiplicative_identity) % 5.27/5.28 multiply(multiplicative_identity, X) -> X % 5.27/5.28 multiply(multiply(Y1, add(Y2, Y1)), multiply(Y2, add(Y1, Y2))) -> multiply(Y1, Y2) % 5.27/5.28 true__ -> false__ % 5.27/5.28 with the LPO induced by % 5.27/5.28 b > add > multiply > additive_identity > multiplicative_identity > inverse > a > f1 > true__ > false__ % 5.27/5.28 % 5.27/5.28 % SZS output end Proof % 5.27/5.28 %------------------------------------------------------------------------------