%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO010-4 : TPTP v8.1.0. Released v1.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n018.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 23:46:21 EDT 2022 % Result : Unsatisfiable 4.35s 4.50s % Output : Proof 4.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : BOO010-4 : TPTP v8.1.0. Released v1.1.0. % 0.10/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n018.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 : Thu Jun 2 00:21:44 EDT 2022 % 0.13/0.34 % CPUTime : % 4.35/4.50 % SZS status Unsatisfiable % 4.35/4.50 % SZS output start Proof % 4.35/4.50 The input problem is unsatisfiable because % 4.35/4.50 % 4.35/4.50 [1] the following set of Horn clauses is unsatisfiable: % 4.35/4.50 % 4.35/4.50 add(X, Y) = add(Y, X) % 4.35/4.50 multiply(X, Y) = multiply(Y, X) % 4.35/4.50 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 4.35/4.50 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 4.35/4.50 add(X, additive_identity) = X % 4.35/4.50 multiply(X, multiplicative_identity) = X % 4.35/4.50 add(X, inverse(X)) = multiplicative_identity % 4.35/4.50 multiply(X, inverse(X)) = additive_identity % 4.35/4.50 add(a, multiply(a, b)) = a ==> \bottom % 4.35/4.50 % 4.35/4.50 This holds because % 4.35/4.50 % 4.35/4.50 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.35/4.50 % 4.35/4.50 E: % 4.35/4.50 add(X, Y) = add(Y, X) % 4.35/4.50 add(X, additive_identity) = X % 4.35/4.50 add(X, inverse(X)) = multiplicative_identity % 4.35/4.50 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 4.35/4.50 f1(a) = false__ % 4.35/4.50 f1(add(a, multiply(a, b))) = true__ % 4.35/4.50 multiply(X, Y) = multiply(Y, X) % 4.35/4.50 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 4.35/4.50 multiply(X, inverse(X)) = additive_identity % 4.35/4.50 multiply(X, multiplicative_identity) = X % 4.35/4.50 G: % 4.35/4.50 true__ = false__ % 4.35/4.50 % 4.35/4.50 This holds because % 4.35/4.50 % 4.35/4.50 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.35/4.50 % 4.35/4.50 add(X, Y) = add(Y, X) % 4.35/4.50 multiply(X, Y) = multiply(Y, X) % 4.35/4.50 add(X, additive_identity) -> X % 4.35/4.50 add(X, inverse(X)) -> inverse(additive_identity) % 4.35/4.50 add(Y0, add(Y1, Y0)) -> add(Y0, Y1) % 4.35/4.50 add(Y0, inverse(additive_identity)) -> inverse(additive_identity) % 4.35/4.50 add(Y0, inverse(inverse(Y0))) -> Y0 % 4.35/4.50 add(Y0, multiply(Y0, Y1)) -> Y0 % 4.35/4.50 add(Y0, multiply(Y1, Y0)) -> Y0 % 4.35/4.50 add(Y1, Y1) -> Y1 % 4.35/4.50 add(add(Y0, multiply(Y0, Y1)), multiply(inverse(Y1), Y0)) -> Y0 % 4.35/4.50 add(add(Y0, multiply(Y1, Y0)), multiply(inverse(Y1), Y0)) -> Y0 % 4.35/4.50 add(additive_identity, Y0) -> Y0 % 4.35/4.50 add(inverse(additive_identity), Y0) -> inverse(additive_identity) % 4.35/4.50 add(multiply(Y0, Y1), multiply(Y0, inverse(Y1))) -> Y0 % 4.35/4.50 add(multiply(Y0, Y1), multiply(inverse(Y1), Y0)) -> Y0 % 4.35/4.50 add(multiply(Y1, Y0), multiply(Y0, inverse(Y1))) -> Y0 % 4.35/4.50 add(multiply(inverse(Y1), Y0), add(Y0, multiply(Y0, Y1))) -> Y0 % 4.35/4.50 f1(a) -> false__ % 4.35/4.50 f1(add(a, multiply(a, b))) -> true__ % 4.35/4.50 inverse(inverse(Y0)) -> Y0 % 4.35/4.50 inverse(inverse(additive_identity)) -> additive_identity % 4.35/4.50 multiplicative_identity -> inverse(additive_identity) % 4.35/4.50 multiply(X, add(Y, Z)) -> add(multiply(X, Y), multiply(X, Z)) % 4.35/4.50 multiply(X, inverse(X)) -> additive_identity % 4.35/4.50 multiply(X0, multiply(X0, X1)) -> multiply(X0, X1) % 4.35/4.50 multiply(Y0, Y0) -> Y0 % 4.35/4.50 multiply(Y0, add(Y1, Y0)) -> Y0 % 4.35/4.50 multiply(Y0, additive_identity) -> additive_identity % 4.35/4.50 multiply(Y0, inverse(additive_identity)) -> Y0 % 4.35/4.50 multiply(Y0, inverse(inverse(Y0))) -> Y0 % 4.35/4.50 multiply(Y0, multiply(Y1, Y0)) -> multiply(Y0, Y1) % 4.35/4.50 multiply(Y1, inverse(inverse(Y1))) -> inverse(inverse(Y1)) % 4.35/4.50 multiply(add(X, Y), add(X, Z)) -> add(X, multiply(Y, Z)) % 4.35/4.50 multiply(add(Y0, Y0), add(Y0, Y1)) -> add(multiply(Y0, Y1), Y0) % 4.35/4.50 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0 % 4.35/4.50 multiply(add(Y0, Y1), add(Y0, multiplicative_identity)) -> add(Y0, Y1) % 4.35/4.50 multiply(add(Y0, Y1), add(inverse(Y1), Y0)) -> Y0 % 4.35/4.50 multiply(add(Y1, Y0), add(Y0, inverse(Y1))) -> Y0 % 4.35/4.50 multiply(additive_identity, Y1) -> additive_identity % 4.35/4.50 multiply(inverse(additive_identity), Y0) -> Y0 % 4.35/4.50 true__ -> false__ % 4.35/4.50 with the LPO induced by % 4.35/4.50 b > multiply > add > multiplicative_identity > additive_identity > inverse > a > f1 > true__ > false__ % 4.35/4.50 % 4.35/4.50 % SZS output end Proof % 4.35/4.50 %------------------------------------------------------------------------------