%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO017-2 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 23:46:30 EDT 2022 % Result : Unsatisfiable 7.72s 7.71s % Output : Proof 7.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : BOO017-2 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n025.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 : Wed Jun 1 20:36:29 EDT 2022 % 0.12/0.34 % CPUTime : % 7.72/7.71 % SZS status Unsatisfiable % 7.72/7.71 % SZS output start Proof % 7.72/7.71 The input problem is unsatisfiable because % 7.72/7.71 % 7.72/7.71 [1] the following set of Horn clauses is unsatisfiable: % 7.72/7.71 % 7.72/7.71 add(X, Y) = add(Y, X) % 7.72/7.71 multiply(X, Y) = multiply(Y, X) % 7.72/7.71 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)) % 7.72/7.71 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 7.72/7.71 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 7.72/7.71 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 7.72/7.71 add(X, inverse(X)) = multiplicative_identity % 7.72/7.71 add(inverse(X), X) = multiplicative_identity % 7.72/7.71 multiply(X, inverse(X)) = additive_identity % 7.72/7.71 multiply(inverse(X), X) = additive_identity % 7.72/7.71 multiply(X, multiplicative_identity) = X % 7.72/7.71 multiply(multiplicative_identity, X) = X % 7.72/7.71 add(X, additive_identity) = X % 7.72/7.71 add(additive_identity, X) = X % 7.72/7.71 add(x, y) = z % 7.72/7.71 multiply(x, z) = x ==> \bottom % 7.72/7.71 % 7.72/7.71 This holds because % 7.72/7.71 % 7.72/7.71 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 7.72/7.71 % 7.72/7.71 E: % 7.72/7.71 add(X, Y) = add(Y, X) % 7.72/7.71 add(X, additive_identity) = X % 7.72/7.71 add(X, inverse(X)) = multiplicative_identity % 7.72/7.71 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 7.72/7.71 add(additive_identity, X) = X % 7.72/7.71 add(inverse(X), X) = multiplicative_identity % 7.72/7.71 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)) % 7.72/7.71 add(x, y) = z % 7.72/7.71 f1(multiply(x, z)) = true__ % 7.72/7.71 f1(x) = false__ % 7.72/7.71 multiply(X, Y) = multiply(Y, X) % 7.72/7.71 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 7.72/7.71 multiply(X, inverse(X)) = additive_identity % 7.72/7.71 multiply(X, multiplicative_identity) = X % 7.72/7.71 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 7.72/7.71 multiply(inverse(X), X) = additive_identity % 7.72/7.71 multiply(multiplicative_identity, X) = X % 7.72/7.71 G: % 7.72/7.71 true__ = false__ % 7.72/7.71 % 7.72/7.71 This holds because % 7.72/7.71 % 7.72/7.71 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 7.72/7.71 % 7.72/7.71 add(X, Y) = add(Y, X) % 7.72/7.71 multiply(X, Y) = multiply(Y, X) % 7.72/7.71 add(X, additive_identity) -> X % 7.72/7.71 add(X, inverse(X)) -> inverse(additive_identity) % 7.72/7.71 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z)) % 7.72/7.71 add(Y0, Y0) -> Y0 % 7.72/7.71 add(Y0, inverse(additive_identity)) -> inverse(additive_identity) % 7.72/7.71 add(add(Y0, multiply(Y0, Y0)), add(Y1, multiply(Y1, Y0))) -> add(Y1, Y0) % 7.72/7.71 add(additive_identity, X) -> X % 7.72/7.71 add(inverse(X), X) -> inverse(additive_identity) % 7.72/7.71 add(inverse(additive_identity), Y0) -> inverse(additive_identity) % 7.72/7.71 add(multiply(X, Y), Z) -> multiply(add(X, Z), add(Y, Z)) % 7.72/7.71 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 7.72/7.71 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z) % 7.72/7.71 add(multiply(Y0, additive_identity), multiply(Y0, additive_identity)) -> additive_identity % 7.72/7.71 add(multiply(Y0, additive_identity), multiply(additive_identity, additive_identity)) -> additive_identity % 7.72/7.71 add(multiply(Y0, inverse(multiplicative_identity)), multiply(Y0, inverse(multiplicative_identity))) -> additive_identity % 7.72/7.71 add(multiply(Y0, inverse(multiplicative_identity)), multiply(inverse(multiplicative_identity), inverse(multiplicative_identity))) -> additive_identity % 7.72/7.71 add(multiply(additive_identity, Y1), multiply(additive_identity, Y1)) -> additive_identity % 7.72/7.71 add(multiply(additive_identity, Y1), multiply(additive_identity, additive_identity)) -> additive_identity % 7.72/7.71 add(multiply(inverse(multiplicative_identity), Y0), multiply(inverse(multiplicative_identity), Y0)) -> additive_identity % 7.72/7.71 add(multiply(inverse(multiplicative_identity), Y0), multiply(inverse(multiplicative_identity), inverse(multiplicative_identity))) -> additive_identity % 7.72/7.71 add(multiply(inverse(multiplicative_identity), inverse(multiplicative_identity)), multiply(inverse(multiplicative_identity), Y0)) -> additive_identity % 7.72/7.71 f1(multiply(x, add(x, y))) -> true__ % 7.72/7.71 f1(multiply(x, add(y, x))) -> true__ % 7.72/7.71 f1(x) -> false__ % 7.72/7.71 inverse(inverse(additive_identity)) -> additive_identity % 7.72/7.71 multiplicative_identity -> inverse(additive_identity) % 7.72/7.71 multiply(X, inverse(X)) -> additive_identity % 7.72/7.71 multiply(Y0, Y0) -> Y0 % 7.72/7.71 multiply(Y0, add(Y0, Y2)) -> Y0 % 7.72/7.71 multiply(Y0, add(Y1, Y0)) -> Y0 % 7.72/7.71 multiply(Y0, inverse(additive_identity)) -> Y0 % 7.72/7.71 multiply(Y0, multiply(Y0, additive_identity)) -> additive_identity % 7.72/7.71 multiply(Y1, additive_identity) -> additive_identity % 7.72/7.71 multiply(add(Y0, Y0), add(Y1, Y0)) -> Y0 % 7.72/7.71 multiply(add(Y0, Y1), add(Y1, Y1)) -> Y1 % 7.72/7.71 multiply(add(Y0, inverse(multiply(Y0, Y1))), add(Y1, inverse(multiply(Y0, Y1)))) -> inverse(additive_identity) % 7.72/7.71 multiply(add(Y1, Y2), Y1) -> Y1 % 7.72/7.71 multiply(additive_identity, Y1) -> additive_identity % 7.72/7.71 multiply(additive_identity, additive_identity) -> additive_identity % 7.72/7.71 multiply(inverse(X), X) -> additive_identity % 7.72/7.71 multiply(inverse(additive_identity), Y0) -> Y0 % 7.72/7.71 multiply(inverse(multiplicative_identity), inverse(multiplicative_identity)) -> additive_identity % 7.72/7.71 true__ -> false__ % 7.72/7.71 z -> add(x, y) % 7.72/7.71 with the LPO induced by % 7.72/7.71 z > add > multiply > y > x > multiplicative_identity > additive_identity > inverse > f1 > true__ > false__ % 7.72/7.71 % 7.72/7.71 % SZS output end Proof % 7.72/7.71 %------------------------------------------------------------------------------