%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP569-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 10:56:20 EDT 2022 % Result : Unsatisfiable 3.79s 3.87s % Output : Proof 3.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP569-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.34 % Computer : n022.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 : Mon Jun 13 18:05:03 EDT 2022 % 0.12/0.34 % CPUTime : % 3.79/3.87 % SZS status Unsatisfiable % 3.79/3.87 % SZS output start Proof % 3.79/3.87 The input problem is unsatisfiable because % 3.79/3.87 % 3.79/3.87 [1] the following set of Horn clauses is unsatisfiable: % 3.79/3.87 % 3.79/3.87 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B % 3.79/3.87 multiply(A, B) = double_divide(double_divide(B, A), identity) % 3.79/3.87 inverse(A) = double_divide(A, identity) % 3.79/3.87 identity = double_divide(A, inverse(A)) % 3.79/3.87 multiply(inverse(a1), a1) = identity ==> \bottom % 3.79/3.87 % 3.79/3.87 This holds because % 3.79/3.87 % 3.79/3.87 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.79/3.87 % 3.79/3.87 E: % 3.79/3.87 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B % 3.79/3.87 f1(identity) = false__ % 3.79/3.87 f1(multiply(inverse(a1), a1)) = true__ % 3.79/3.87 identity = double_divide(A, inverse(A)) % 3.79/3.87 inverse(A) = double_divide(A, identity) % 3.79/3.87 multiply(A, B) = double_divide(double_divide(B, A), identity) % 3.79/3.87 G: % 3.79/3.87 true__ = false__ % 3.79/3.87 % 3.79/3.87 This holds because % 3.79/3.87 % 3.79/3.87 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.79/3.87 % 3.79/3.87 % 3.79/3.87 double_divide(A, inverse(A)) -> identity % 3.79/3.87 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) -> B % 3.79/3.87 double_divide(double_divide(Y0, double_divide(inverse(Y1), inverse(inverse(Y0)))), inverse(identity)) -> Y1 % 3.79/3.87 double_divide(double_divide(identity, double_divide(X0, double_divide(identity, identity))), double_divide(identity, identity)) -> double_divide(X0, identity) % 3.79/3.87 double_divide(identity, identity) -> identity % 3.79/3.87 double_divide(inverse(Y0), inverse(identity)) -> Y0 % 3.79/3.87 f1(identity) -> false__ % 3.79/3.87 f1(inverse(identity)) -> true__ % 3.79/3.87 f1(multiply(inverse(a1), a1)) -> true__ % 3.79/3.87 inverse(A) -> double_divide(A, identity) % 3.79/3.87 inverse(identity) -> identity % 3.79/3.87 inverse(inverse(X0)) -> double_divide(double_divide(identity, X0), double_divide(identity, identity)) % 3.79/3.87 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 3.79/3.87 true__ -> false__ % 3.79/3.87 with the LPO induced by % 3.79/3.87 a1 > multiply > inverse > double_divide > f1 > identity > true__ > false__ % 3.79/3.87 % 3.79/3.87 % SZS output end Proof % 3.79/3.87 %------------------------------------------------------------------------------