%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP490-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n015.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 10:55:47 EDT 2022 % Result : Unsatisfiable 6.52s 6.58s % Output : Proof 6.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP490-1 : TPTP v8.1.0. Released v2.6.0. % 0.11/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n015.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 : Tue Jun 14 11:27:54 EDT 2022 % 0.13/0.34 % CPUTime : % 6.52/6.58 % SZS status Unsatisfiable % 6.52/6.58 % SZS output start Proof % 6.52/6.58 The input problem is unsatisfiable because % 6.52/6.58 % 6.52/6.58 [1] the following set of Horn clauses is unsatisfiable: % 6.52/6.58 % 6.52/6.58 double_divide(double_divide(identity, A), double_divide(identity, double_divide(double_divide(double_divide(A, B), identity), double_divide(C, B)))) = C % 6.52/6.58 multiply(A, B) = double_divide(double_divide(B, A), identity) % 6.52/6.58 inverse(A) = double_divide(A, identity) % 6.52/6.58 identity = double_divide(A, inverse(A)) % 6.52/6.58 multiply(inverse(a1), a1) = identity ==> \bottom % 6.52/6.58 % 6.52/6.58 This holds because % 6.52/6.58 % 6.52/6.58 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.52/6.58 % 6.52/6.58 E: % 6.52/6.58 double_divide(double_divide(identity, A), double_divide(identity, double_divide(double_divide(double_divide(A, B), identity), double_divide(C, B)))) = C % 6.52/6.58 f1(identity) = false__ % 6.52/6.58 f1(multiply(inverse(a1), a1)) = true__ % 6.52/6.58 identity = double_divide(A, inverse(A)) % 6.52/6.58 inverse(A) = double_divide(A, identity) % 6.52/6.58 multiply(A, B) = double_divide(double_divide(B, A), identity) % 6.52/6.58 G: % 6.52/6.58 true__ = false__ % 6.52/6.58 % 6.52/6.58 This holds because % 6.52/6.58 % 6.52/6.58 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.52/6.58 % 6.52/6.58 double_divide(X0, double_divide(identity, inverse(inverse(identity)))) = double_divide(identity, double_divide(inverse(inverse(inverse(identity))), inverse(X0))) % 6.52/6.58 double_divide(X0, inverse(identity)) = inverse(inverse(double_divide(identity, double_divide(inverse(inverse(inverse(identity))), inverse(X0))))) % 6.52/6.58 double_divide(X0, inverse(identity)) = inverse(inverse(double_divide(identity, inverse(inverse(double_divide(inverse(identity), inverse(X0))))))) % 6.52/6.58 double_divide(A, identity) -> inverse(A) % 6.52/6.58 double_divide(A, inverse(A)) -> identity % 6.52/6.58 double_divide(double_divide(identity, A), double_divide(identity, double_divide(double_divide(double_divide(A, B), identity), double_divide(C, B)))) -> C % 6.52/6.58 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(identity, double_divide(Y1, inverse(Y0))))) -> Y1 % 6.52/6.58 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(inverse(double_divide(Y0, Y1)), double_divide(Y2, Y1)))) -> Y2 % 6.52/6.58 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(inverse(identity), double_divide(Y2, inverse(Y0))))) -> Y2 % 6.52/6.58 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(inverse(inverse(Y0)), inverse(Y2)))) -> Y2 % 6.52/6.58 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(inverse(double_divide(Y0, inverse(Y2)))))) -> Y2 % 6.52/6.58 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(inverse(inverse(Y0))))) -> inverse(inverse(identity)) % 6.52/6.58 double_divide(double_divide(identity, Y0), inverse(identity)) -> inverse(inverse(Y0)) % 6.52/6.58 double_divide(double_divide(identity, Y1), double_divide(identity, inverse(inverse(identity)))) -> Y1 % 6.52/6.58 double_divide(double_divide(identity, inverse(inverse(identity))), double_divide(identity, double_divide(inverse(identity), inverse(Y1)))) -> Y1 % 6.52/6.58 double_divide(identity, double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0 % 6.52/6.58 double_divide(identity, double_divide(identity, double_divide(inverse(double_divide(identity, Y0)), double_divide(Y1, Y0)))) -> Y1 % 6.52/6.58 double_divide(identity, double_divide(identity, double_divide(inverse(double_divide(inverse(identity), Y1)), double_divide(Y2, Y1)))) -> Y2 % 6.52/6.58 double_divide(identity, double_divide(identity, double_divide(inverse(inverse(inverse(identity))), inverse(Y1)))) -> Y1 % 6.52/6.58 double_divide(identity, double_divide(identity, inverse(inverse(double_divide(identity, inverse(Y0)))))) -> Y0 % 6.52/6.58 double_divide(identity, double_divide(identity, inverse(inverse(double_divide(inverse(identity), inverse(Y1)))))) -> Y1 % 6.52/6.58 double_divide(identity, double_divide(identity, inverse(inverse(identity)))) -> inverse(identity) % 6.52/6.58 double_divide(identity, inverse(inverse(identity))) -> identity % 6.52/6.58 double_divide(inverse(identity), double_divide(identity, double_divide(inverse(double_divide(identity, Y1)), double_divide(Y2, Y1)))) -> Y2 % 6.52/6.58 double_divide(inverse(identity), double_divide(identity, double_divide(inverse(identity), double_divide(Y1, inverse(identity))))) -> Y1 % 6.52/6.58 double_divide(inverse(identity), double_divide(identity, double_divide(inverse(inverse(identity)), inverse(Y1)))) -> Y1 % 6.52/6.58 double_divide(inverse(identity), double_divide(identity, inverse(inverse(double_divide(identity, inverse(Y1)))))) -> Y1 % 6.52/6.58 double_divide(inverse(identity), double_divide(identity, inverse(inverse(identity)))) -> identity % 6.52/6.58 double_divide(inverse(identity), inverse(identity)) -> inverse(inverse(identity)) % 6.52/6.58 f1(identity) -> false__ % 6.52/6.58 f1(inverse(identity)) -> true__ % 6.52/6.58 f1(multiply(inverse(a1), a1)) -> true__ % 6.52/6.58 inverse(double_divide(identity, Y0)) -> Y0 % 6.52/6.58 inverse(double_divide(identity, Y0)) -> inverse(inverse(Y0)) % 6.52/6.58 inverse(identity) -> identity % 6.52/6.58 inverse(inverse(double_divide(identity, double_divide(identity, inverse(X0))))) -> inverse(X0) % 6.52/6.58 inverse(inverse(double_divide(identity, inverse(inverse(identity))))) -> inverse(inverse(identity)) % 6.52/6.58 inverse(inverse(identity)) -> inverse(identity) % 6.52/6.58 inverse(inverse(inverse(identity))) -> identity % 6.52/6.58 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 6.52/6.58 true__ -> false__ % 6.52/6.58 with the LPO induced by % 6.52/6.58 a1 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 6.52/6.58 % 6.52/6.58 % SZS output end Proof % 6.52/6.58 %------------------------------------------------------------------------------