%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP577-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 10:56:24 EDT 2022 % Result : Unsatisfiable 11.74s 11.74s % Output : Proof 11.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : GRP577-1 : TPTP v8.1.0. Released v2.6.0. % 0.15/0.14 % Command : moca.sh %s % 0.15/0.35 % Computer : n020.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 600 % 0.15/0.35 % DateTime : Mon Jun 13 06:21:05 EDT 2022 % 0.15/0.35 % CPUTime : % 11.74/11.74 % SZS status Unsatisfiable % 11.74/11.74 % SZS output start Proof % 11.74/11.74 The input problem is unsatisfiable because % 11.74/11.74 % 11.74/11.74 [1] the following set of Horn clauses is unsatisfiable: % 11.74/11.74 % 11.74/11.74 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) = C % 11.74/11.74 multiply(A, B) = double_divide(double_divide(B, A), identity) % 11.74/11.74 inverse(A) = double_divide(A, identity) % 11.74/11.74 identity = double_divide(A, inverse(A)) % 11.74/11.74 multiply(inverse(a1), a1) = identity ==> \bottom % 11.74/11.74 % 11.74/11.74 This holds because % 11.74/11.74 % 11.74/11.74 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 11.74/11.74 % 11.74/11.74 E: % 11.74/11.74 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) = C % 11.74/11.74 f1(identity) = false__ % 11.74/11.74 f1(multiply(inverse(a1), a1)) = true__ % 11.74/11.74 identity = double_divide(A, inverse(A)) % 11.74/11.74 inverse(A) = double_divide(A, identity) % 11.74/11.74 multiply(A, B) = double_divide(double_divide(B, A), identity) % 11.74/11.74 G: % 11.74/11.74 true__ = false__ % 11.74/11.74 % 11.74/11.74 This holds because % 11.74/11.74 % 11.74/11.74 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 11.74/11.74 % 11.74/11.74 double_divide(X0, inverse(identity)) = inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0))))) % 11.74/11.74 double_divide(A, identity) -> inverse(A) % 11.74/11.74 double_divide(A, inverse(A)) -> identity % 11.74/11.74 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) -> C % 11.74/11.74 double_divide(double_divide(X0, double_divide(inverse(identity), X0)), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(Y0, double_divide(double_divide(double_divide(Y1, Y0), Y2), inverse(Y1))), inverse(identity)) -> Y2 % 11.74/11.74 double_divide(double_divide(Y0, double_divide(identity, inverse(Y1))), inverse(identity)) -> inverse(double_divide(Y1, Y0)) % 11.74/11.74 double_divide(double_divide(Y0, double_divide(inverse(double_divide(Y1, Y0)), inverse(Y1))), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(Y0, inverse(double_divide(identity, double_divide(identity, Y0)))), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(Y0, inverse(inverse(double_divide(double_divide(identity, inverse(inverse(identity))), Y0)))), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(double_divide(X1, double_divide(identity, Y0)), X2), inverse(X1)) -> double_divide(double_divide(Y0, X2), inverse(identity)) % 11.74/11.74 double_divide(double_divide(identity, double_divide(X0, inverse(inverse(double_divide(identity, X0))))), inverse(identity)) -> inverse(identity) % 11.74/11.74 double_divide(double_divide(identity, double_divide(double_divide(inverse(Y1), Y2), inverse(Y1))), inverse(identity)) -> Y2 % 11.74/11.74 double_divide(double_divide(identity, double_divide(inverse(X0), X0)), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(identity, double_divide(inverse(double_divide(identity, Y0)), inverse(Y0))), inverse(identity)) -> inverse(identity) % 11.74/11.74 double_divide(double_divide(identity, double_divide(inverse(inverse(Y1)), inverse(Y1))), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(identity, inverse(double_divide(identity, X0))), X0) -> identity % 11.74/11.74 double_divide(double_divide(identity, inverse(inverse(identity))), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(inverse(Y1), double_divide(double_divide(identity, Y2), inverse(Y1))), inverse(identity)) -> Y2 % 11.74/11.74 double_divide(double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1))), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(inverse(identity), double_divide(inverse(X0), inverse(inverse(inverse(double_divide(identity, X0)))))), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(inverse(identity), double_divide(inverse(X1), inverse(double_divide(identity, double_divide(double_divide(inverse(X0), X1), inverse(X0)))))), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(X0, double_divide(inverse(double_divide(X1, X0)), inverse(X1)))))), inverse(identity)) -> identity % 11.74/11.74 double_divide(double_divide(inverse(identity), double_divide(inverse(inverse(double_divide(identity, X0))), inverse(inverse(X0)))), inverse(identity)) -> identity % 11.74/11.74 double_divide(identity, inverse(inverse(identity))) -> inverse(inverse(identity)) % 11.74/11.74 double_divide(inverse(Y0), inverse(identity)) -> inverse(double_divide(identity, Y0)) % 11.74/11.74 double_divide(inverse(double_divide(X1, inverse(identity))), inverse(X1)) -> double_divide(inverse(identity), inverse(identity)) % 11.74/11.74 double_divide(inverse(identity), double_divide(identity, inverse(inverse(identity)))) -> identity % 11.74/11.74 double_divide(inverse(inverse(double_divide(identity, Y1))), inverse(identity)) -> Y1 % 11.74/11.74 f1(identity) -> false__ % 11.74/11.74 f1(inverse(identity)) -> true__ % 11.74/11.74 f1(multiply(inverse(a1), a1)) -> true__ % 11.74/11.74 inverse(double_divide(Y0, double_divide(identity, Y0))) -> identity % 11.74/11.74 inverse(double_divide(identity, Y0)) -> inverse(inverse(Y0)) % 11.74/11.74 inverse(double_divide(identity, double_divide(identity, double_divide(identity, inverse(inverse(identity)))))) -> identity % 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0))))) -> inverse(X0) % 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(Y0, double_divide(identity, Y0))))))) -> identity % 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(identity, double_divide(X0, double_divide(identity, inverse(double_divide(identity, X0)))))))))) -> identity % 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(identity, double_divide(identity, double_divide(identity, inverse(inverse(identity)))))))))) -> identity % 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, inverse(inverse(inverse(identity)))))))) -> identity % 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(inverse(identity))))) -> identity % 11.74/11.74 inverse(double_divide(identity, double_divide(inverse(Y0), Y0))) -> identity % 11.74/11.74 inverse(double_divide(identity, inverse(double_divide(identity, Y0)))) -> Y0 % 11.74/11.74 inverse(double_divide(identity, inverse(inverse(identity)))) -> identity % 11.74/11.74 inverse(identity) -> identity % 11.74/11.74 inverse(inverse(inverse(double_divide(identity, Y0)))) -> Y0 % 11.74/11.74 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 11.74/11.74 true__ -> false__ % 11.74/11.74 with the LPO induced by % 11.74/11.74 a1 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 11.74/11.74 % 11.74/11.74 % SZS output end Proof % 11.74/11.74 %------------------------------------------------------------------------------