%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO012-4 : 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 23:46:24 EDT 2022 % Result : Unsatisfiable 3.68s 3.86s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : BOO012-4 : TPTP v8.1.0. Released v1.1.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n023.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 17:52:41 EDT 2022 % 0.13/0.34 % CPUTime : % 3.68/3.86 % SZS status Unsatisfiable % 3.68/3.86 % SZS output start Proof % 3.68/3.86 The input problem is unsatisfiable because % 3.68/3.86 % 3.68/3.86 [1] the following set of Horn clauses is unsatisfiable: % 3.68/3.86 % 3.68/3.86 add(X, Y) = add(Y, X) % 3.68/3.86 multiply(X, Y) = multiply(Y, X) % 3.68/3.86 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 3.68/3.86 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 3.68/3.86 add(X, additive_identity) = X % 3.68/3.86 multiply(X, multiplicative_identity) = X % 3.68/3.86 add(X, inverse(X)) = multiplicative_identity % 3.68/3.86 multiply(X, inverse(X)) = additive_identity % 3.68/3.86 inverse(inverse(x)) = x ==> \bottom % 3.68/3.86 % 3.68/3.86 This holds because % 3.68/3.86 % 3.68/3.86 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.68/3.86 % 3.68/3.86 E: % 3.68/3.86 add(X, Y) = add(Y, X) % 3.68/3.86 add(X, additive_identity) = X % 3.68/3.86 add(X, inverse(X)) = multiplicative_identity % 3.68/3.86 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 3.68/3.86 f1(inverse(inverse(x))) = true__ % 3.68/3.86 f1(x) = false__ % 3.68/3.86 multiply(X, Y) = multiply(Y, X) % 3.68/3.86 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 3.68/3.86 multiply(X, inverse(X)) = additive_identity % 3.68/3.86 multiply(X, multiplicative_identity) = X % 3.68/3.86 G: % 3.68/3.86 true__ = false__ % 3.68/3.86 % 3.68/3.86 This holds because % 3.68/3.86 % 3.68/3.86 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.68/3.86 % 3.68/3.86 add(X, Y) = add(Y, X) % 3.68/3.86 multiply(X, Y) = multiply(Y, X) % 3.68/3.86 add(X, additive_identity) -> X % 3.68/3.86 add(X, inverse(X)) -> inverse(additive_identity) % 3.68/3.86 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z)) % 3.68/3.86 add(Y0, add(Y0, Y1)) -> add(Y0, Y1) % 3.68/3.86 add(Y0, add(Y1, Y0)) -> add(Y0, Y1) % 3.68/3.86 add(Y0, inverse(additive_identity)) -> inverse(additive_identity) % 3.68/3.86 add(Y0, multiply(Y0, Y1)) -> Y0 % 3.68/3.86 add(Y0, multiply(inverse(Y1), Y0)) -> Y0 % 3.68/3.86 add(Y1, Y1) -> Y1 % 3.68/3.86 add(Y2, multiply(Y1, Y2)) -> Y2 % 3.68/3.86 add(additive_identity, Y0) -> Y0 % 3.68/3.86 add(inverse(additive_identity), Y0) -> inverse(additive_identity) % 3.68/3.86 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 3.68/3.86 add(multiply(Y0, Y0), multiply(Y0, Y2)) -> Y0 % 3.68/3.86 add(multiply(Y0, Y1), multiply(Y0, Y0)) -> Y0 % 3.68/3.86 add(multiply(Y0, Y1), multiply(Y0, Y2)) -> multiply(add(Y1, Y2), Y0) % 3.68/3.86 add(multiply(Y0, Y1), multiply(Y0, inverse(Y1))) -> Y0 % 3.68/3.86 add(multiply(Y0, Y1), multiply(inverse(Y1), Y0)) -> Y0 % 3.68/3.86 add(multiply(Y1, Y0), multiply(Y0, inverse(Y1))) -> Y0 % 3.68/3.86 f1(inverse(inverse(x))) -> true__ % 3.68/3.86 f1(x) -> false__ % 3.68/3.86 inverse(inverse(Y1)) -> Y1 % 3.68/3.86 multiplicative_identity -> inverse(additive_identity) % 3.68/3.86 multiply(X, inverse(X)) -> additive_identity % 3.68/3.86 multiply(X0, multiply(X0, X1)) -> multiply(X0, X1) % 3.68/3.86 multiply(Y0, Y0) -> Y0 % 3.68/3.86 multiply(Y0, add(Y0, Y2)) -> Y0 % 3.68/3.86 multiply(Y0, add(Y1, Y0)) -> Y0 % 3.68/3.86 multiply(Y0, add(Y1, inverse(Y0))) -> multiply(Y0, Y1) % 3.68/3.86 multiply(Y0, add(inverse(Y0), Y2)) -> multiply(Y0, Y2) % 3.68/3.86 multiply(Y0, inverse(additive_identity)) -> Y0 % 3.68/3.86 multiply(Y1, additive_identity) -> additive_identity % 3.68/3.86 multiply(Y1, multiply(X1, Y1)) -> multiply(X1, Y1) % 3.68/3.86 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0 % 3.68/3.86 multiply(add(Y0, Y1), add(inverse(Y1), Y0)) -> Y0 % 3.68/3.86 multiply(add(Y1, Y0), add(Y0, inverse(Y1))) -> Y0 % 3.68/3.86 multiply(additive_identity, Y0) -> additive_identity % 3.68/3.86 multiply(inverse(X0), add(X0, Y1)) -> multiply(inverse(X0), Y1) % 3.68/3.86 multiply(inverse(additive_identity), Y0) -> Y0 % 3.68/3.86 true__ -> false__ % 3.68/3.86 with the LPO induced by % 3.68/3.86 x > f1 > add > multiply > multiplicative_identity > inverse > additive_identity > true__ > false__ % 3.68/3.86 % 3.68/3.86 % SZS output end Proof % 3.68/3.86 %------------------------------------------------------------------------------