%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP461-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n021.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 : Sat Jul 16 10:55:36 EDT 2022 % Result : Unsatisfiable 0.82s 0.97s % Output : Proof 0.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP461-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n021.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 : Mon Jun 13 09:18:27 EDT 2022 % 0.13/0.34 % CPUTime : % 0.82/0.97 % SZS status Unsatisfiable % 0.82/0.97 % SZS output start Proof % 0.82/0.97 The input problem is unsatisfiable because % 0.82/0.97 % 0.82/0.97 [1] the following set of Horn clauses is unsatisfiable: % 0.82/0.97 % 0.82/0.97 divide(A, divide(divide(divide(identity, B), C), divide(divide(divide(A, A), A), C))) = B % 0.82/0.97 multiply(A, B) = divide(A, divide(identity, B)) % 0.82/0.97 inverse(A) = divide(identity, A) % 0.82/0.97 identity = divide(A, A) % 0.82/0.97 multiply(identity, a2) = a2 ==> \bottom % 0.82/0.97 % 0.82/0.97 This holds because % 0.82/0.97 % 0.82/0.97 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.82/0.97 % 0.82/0.97 E: % 0.82/0.97 divide(A, divide(divide(divide(identity, B), C), divide(divide(divide(A, A), A), C))) = B % 0.82/0.97 f1(a2) = false__ % 0.82/0.97 f1(multiply(identity, a2)) = true__ % 0.82/0.97 identity = divide(A, A) % 0.82/0.97 inverse(A) = divide(identity, A) % 0.82/0.97 multiply(A, B) = divide(A, divide(identity, B)) % 0.82/0.97 G: % 0.82/0.97 true__ = false__ % 0.82/0.97 % 0.82/0.97 This holds because % 0.82/0.97 % 0.82/0.97 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.82/0.97 % 0.82/0.97 % 0.82/0.97 divide(A, A) -> identity % 0.82/0.97 divide(A, divide(divide(divide(identity, B), C), divide(divide(divide(A, A), A), C))) -> B % 0.82/0.97 divide(Y0, divide(X0, inverse(Y0))) -> inverse(X0) % 0.82/0.97 divide(Y0, divide(divide(inverse(Y1), Y2), divide(inverse(Y0), Y2))) -> Y1 % 0.82/0.97 divide(Y0, divide(divide(inverse(Y1), inverse(Y0)), identity)) -> Y1 % 0.82/0.97 divide(Y0, divide(inverse(Y1), inverse(Y0))) -> Y1 % 0.82/0.97 divide(Y0, divide(inverse(Y2), divide(inverse(Y0), Y2))) -> identity % 0.82/0.97 divide(Y0, divide(inverse(inverse(Y0)), identity)) -> identity % 0.82/0.97 divide(Y0, inverse(divide(inverse(Y0), X0))) -> inverse(inverse(inverse(X0))) % 0.82/0.97 divide(Y0, inverse(divide(inverse(Y0), identity))) -> identity % 0.82/0.97 divide(Y0, inverse(divide(inverse(Y0), inverse(Y1)))) -> Y1 % 0.82/0.97 divide(Y0, inverse(inverse(Y0))) -> identity % 0.82/0.97 divide(Y1, identity) -> Y1 % 0.82/0.97 divide(divide(inverse(X0), X1), inverse(X1)) -> inverse(X0) % 0.82/0.97 divide(identity, A) -> inverse(A) % 0.82/0.97 divide(inverse(X0), divide(inverse(Y1), X0)) -> Y1 % 0.82/0.97 divide(inverse(X0), inverse(divide(X0, inverse(Y1)))) -> Y1 % 0.82/0.97 divide(inverse(Y0), inverse(divide(Y0, X0))) -> inverse(X0) % 0.82/0.97 divide(inverse(inverse(X0)), X0) -> identity % 0.82/0.97 divide(inverse(inverse(Y0)), inverse(X1)) -> divide(Y0, inverse(X1)) % 0.82/0.97 f1(a2) -> false__ % 0.82/0.97 f1(inverse(inverse(a2))) -> true__ % 0.82/0.97 f1(multiply(identity, a2)) -> true__ % 0.82/0.97 inverse(divide(X1, inverse(inverse(divide(inverse(inverse(Y0)), inverse(X1)))))) -> Y0 % 0.82/0.97 inverse(divide(divide(X0, Y1), inverse(Y1))) -> inverse(X0) % 0.82/0.97 inverse(divide(divide(inverse(Y0), identity), identity)) -> Y0 % 0.82/0.97 inverse(divide(divide(inverse(Y0), inverse(X0)), X0)) -> Y0 % 0.82/0.97 inverse(divide(divide(inverse(Y1), Y2), inverse(Y2))) -> Y1 % 0.82/0.97 inverse(identity) -> identity % 0.82/0.97 inverse(inverse(Y0)) -> Y0 % 0.82/0.97 inverse(inverse(inverse(X0))) -> inverse(X0) % 0.82/0.97 inverse(inverse(inverse(inverse(Y1)))) -> Y1 % 0.82/0.97 multiply(A, B) -> divide(A, divide(identity, B)) % 0.82/0.97 true__ -> false__ % 0.82/0.97 with the LPO induced by % 0.82/0.97 a2 > f1 > multiply > divide > identity > inverse > true__ > false__ % 0.82/0.97 % 0.82/0.97 % SZS output end Proof % 0.82/0.97 %------------------------------------------------------------------------------