%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO009-4 : TPTP v8.1.0. Released v1.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n023.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 23:46:20 EDT 2022 % Result : Unsatisfiable 4.07s 4.15s % Output : Proof 4.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : BOO009-4 : TPTP v8.1.0. Released v1.1.0. % 0.11/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n023.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 : Thu Jun 2 00:09:41 EDT 2022 % 0.12/0.34 % CPUTime : % 4.07/4.15 % SZS status Unsatisfiable % 4.07/4.15 % SZS output start Proof % 4.07/4.15 The input problem is unsatisfiable because % 4.07/4.15 % 4.07/4.15 [1] the following set of Horn clauses is unsatisfiable: % 4.07/4.15 % 4.07/4.15 add(X, Y) = add(Y, X) % 4.07/4.15 multiply(X, Y) = multiply(Y, X) % 4.07/4.15 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 4.07/4.15 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 4.07/4.15 add(X, additive_identity) = X % 4.07/4.15 multiply(X, multiplicative_identity) = X % 4.07/4.15 add(X, inverse(X)) = multiplicative_identity % 4.07/4.15 multiply(X, inverse(X)) = additive_identity % 4.07/4.15 multiply(a, add(a, b)) = a ==> \bottom % 4.07/4.15 % 4.07/4.15 This holds because % 4.07/4.15 % 4.07/4.15 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.07/4.15 % 4.07/4.15 E: % 4.07/4.15 add(X, Y) = add(Y, X) % 4.07/4.15 add(X, additive_identity) = X % 4.07/4.15 add(X, inverse(X)) = multiplicative_identity % 4.07/4.15 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 4.07/4.15 f1(a) = false__ % 4.07/4.15 f1(multiply(a, add(a, b))) = true__ % 4.07/4.15 multiply(X, Y) = multiply(Y, X) % 4.07/4.15 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 4.07/4.15 multiply(X, inverse(X)) = additive_identity % 4.07/4.15 multiply(X, multiplicative_identity) = X % 4.07/4.15 G: % 4.07/4.15 true__ = false__ % 4.07/4.15 % 4.07/4.15 This holds because % 4.07/4.15 % 4.07/4.15 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.07/4.15 % 4.07/4.15 add(X, Y) = add(Y, X) % 4.07/4.15 multiply(X, Y) = multiply(Y, X) % 4.07/4.15 add(X, additive_identity) -> X % 4.07/4.15 add(X, inverse(X)) -> inverse(additive_identity) % 4.07/4.15 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z)) % 4.07/4.15 add(Y0, inverse(additive_identity)) -> inverse(additive_identity) % 4.07/4.15 add(Y0, inverse(inverse(Y0))) -> Y0 % 4.07/4.15 add(Y0, multiply(Y0, Y1)) -> Y0 % 4.07/4.15 add(Y1, Y1) -> Y1 % 4.07/4.15 add(add(Y0, multiply(Y0, Y1)), multiply(inverse(Y1), Y0)) -> Y0 % 4.07/4.15 add(add(Y1, multiply(Y1, Y2)), add(Y2, multiply(Y2, Y1))) -> add(Y1, Y2) % 4.07/4.15 add(additive_identity, Y0) -> Y0 % 4.07/4.15 add(inverse(additive_identity), Y0) -> inverse(additive_identity) % 4.07/4.15 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 4.07/4.15 add(multiply(Y0, Y1), multiply(Y0, additive_identity)) -> multiply(Y0, Y1) % 4.07/4.15 add(multiply(Y0, Y1), multiply(Y0, inverse(Y1))) -> Y0 % 4.07/4.15 add(multiply(Y0, Y1), multiply(Y0, inverse(multiplicative_identity))) -> multiply(Y0, Y1) % 4.07/4.15 add(multiply(inverse(Y1), Y0), add(Y0, multiply(Y0, Y1))) -> Y0 % 4.07/4.15 f1(a) -> false__ % 4.07/4.15 f1(multiply(a, add(a, b))) -> true__ % 4.07/4.15 inverse(inverse(additive_identity)) -> additive_identity % 4.07/4.15 multiplicative_identity -> inverse(additive_identity) % 4.07/4.15 multiply(X, inverse(X)) -> additive_identity % 4.07/4.15 multiply(X0, multiply(X0, X1)) -> multiply(X0, X1) % 4.07/4.15 multiply(Y0, Y0) -> Y0 % 4.07/4.15 multiply(Y0, add(Y0, Y2)) -> Y0 % 4.07/4.15 multiply(Y0, add(Y1, Y0)) -> Y0 % 4.07/4.15 multiply(Y0, add(Y1, inverse(Y0))) -> multiply(Y0, Y1) % 4.07/4.15 multiply(Y0, add(inverse(Y0), Y2)) -> multiply(Y0, Y2) % 4.07/4.15 multiply(Y0, additive_identity) -> additive_identity % 4.07/4.15 multiply(Y0, inverse(additive_identity)) -> Y0 % 4.07/4.15 multiply(Y0, inverse(inverse(Y0))) -> Y0 % 4.07/4.15 multiply(Y1, inverse(inverse(Y1))) -> inverse(inverse(Y1)) % 4.07/4.15 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0 % 4.07/4.15 multiply(add(Y0, Y1), add(inverse(Y1), Y0)) -> Y0 % 4.07/4.15 multiply(add(Y1, Y0), add(Y0, inverse(Y1))) -> Y0 % 4.07/4.15 multiply(additive_identity, Y1) -> additive_identity % 4.07/4.15 multiply(inverse(additive_identity), Y0) -> Y0 % 4.07/4.15 true__ -> false__ % 4.07/4.15 with the LPO induced by % 4.07/4.15 b > add > multiplicative_identity > multiply > inverse > additive_identity > a > f1 > true__ > false__ % 4.07/4.15 % 4.07/4.15 % SZS output end Proof % 4.07/4.15 %------------------------------------------------------------------------------