%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP484-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n024.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 10:55:45 EDT 2022 % Result : Unsatisfiable 0.84s 1.02s % Output : Proof 0.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.07 % Problem : GRP484-1 : TPTP v8.1.0. Released v2.6.0. % 0.00/0.07 % Command : moca.sh %s % 0.07/0.26 % Computer : n024.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 600 % 0.07/0.26 % DateTime : Mon Jun 13 11:35:03 EDT 2022 % 0.07/0.26 % CPUTime : % 0.84/1.02 % SZS status Unsatisfiable % 0.84/1.02 % SZS output start Proof % 0.84/1.02 The input problem is unsatisfiable because % 0.84/1.02 % 0.84/1.02 [1] the following set of Horn clauses is unsatisfiable: % 0.84/1.02 % 0.84/1.02 double_divide(double_divide(A, double_divide(double_divide(double_divide(A, B), C), double_divide(B, identity))), double_divide(identity, identity)) = C % 0.84/1.02 multiply(A, B) = double_divide(double_divide(B, A), identity) % 0.84/1.02 inverse(A) = double_divide(A, identity) % 0.84/1.02 identity = double_divide(A, inverse(A)) % 0.84/1.02 multiply(inverse(a1), a1) = identity ==> \bottom % 0.84/1.02 % 0.84/1.02 This holds because % 0.84/1.02 % 0.84/1.02 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.84/1.02 % 0.84/1.02 E: % 0.84/1.02 double_divide(double_divide(A, double_divide(double_divide(double_divide(A, B), C), double_divide(B, identity))), double_divide(identity, identity)) = C % 0.84/1.02 f1(identity) = false__ % 0.84/1.02 f1(multiply(inverse(a1), a1)) = true__ % 0.84/1.02 identity = double_divide(A, inverse(A)) % 0.84/1.02 inverse(A) = double_divide(A, identity) % 0.84/1.02 multiply(A, B) = double_divide(double_divide(B, A), identity) % 0.84/1.02 G: % 0.84/1.02 true__ = false__ % 0.84/1.02 % 0.84/1.02 This holds because % 0.84/1.02 % 0.84/1.02 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.84/1.02 % 0.84/1.02 % 0.84/1.02 double_divide(A, identity) -> inverse(A) % 0.84/1.02 double_divide(A, inverse(A)) -> identity % 0.84/1.02 double_divide(double_divide(A, double_divide(double_divide(double_divide(A, B), C), double_divide(B, identity))), double_divide(identity, identity)) -> C % 0.84/1.02 double_divide(double_divide(Y0, double_divide(double_divide(double_divide(Y0, Y1), Y2), inverse(Y1))), inverse(identity)) -> Y2 % 0.84/1.02 double_divide(double_divide(Y0, double_divide(double_divide(identity, Y2), inverse(inverse(Y0)))), inverse(identity)) -> Y2 % 0.84/1.02 double_divide(double_divide(Y0, double_divide(double_divide(inverse(Y0), Y2), inverse(identity))), inverse(identity)) -> Y2 % 0.84/1.02 double_divide(double_divide(Y0, double_divide(identity, inverse(Y1))), inverse(identity)) -> inverse(double_divide(Y0, Y1)) % 0.84/1.02 double_divide(double_divide(Y0, double_divide(inverse(double_divide(Y0, Y1)), inverse(Y1))), inverse(identity)) -> identity % 0.84/1.02 double_divide(double_divide(Y0, double_divide(inverse(identity), inverse(inverse(Y0)))), inverse(identity)) -> identity % 0.84/1.02 double_divide(double_divide(Y0, double_divide(inverse(inverse(Y0)), inverse(identity))), inverse(identity)) -> identity % 0.84/1.02 double_divide(double_divide(Y0, inverse(inverse(inverse(Y0)))), inverse(identity)) -> identity % 0.84/1.02 double_divide(double_divide(double_divide(X0, double_divide(double_divide(inverse(X0), X1), inverse(identity))), double_divide(inverse(X1), inverse(inverse(identity)))), inverse(identity)) -> identity % 0.84/1.02 double_divide(double_divide(double_divide(inverse(Y0), X1), X2), inverse(X1)) -> double_divide(double_divide(Y0, X2), inverse(identity)) % 0.84/1.02 double_divide(double_divide(inverse(X0), double_divide(inverse(inverse(inverse(X0))), inverse(inverse(identity)))), inverse(identity)) -> identity % 0.84/1.02 double_divide(double_divide(inverse(inverse(Y0)), Y2), inverse(identity)) -> double_divide(double_divide(Y0, Y2), inverse(identity)) % 0.84/1.02 double_divide(identity, inverse(inverse(inverse(Y0)))) -> inverse(inverse(Y0)) % 0.84/1.02 double_divide(inverse(Y0), inverse(identity)) -> inverse(inverse(Y0)) % 0.84/1.02 double_divide(inverse(double_divide(X0, double_divide(inverse(double_divide(X0, X1)), inverse(X1)))), inverse(identity)) -> identity % 0.84/1.02 double_divide(inverse(double_divide(inverse(Y0), Y1)), inverse(Y1)) -> double_divide(inverse(Y0), inverse(identity)) % 0.84/1.02 double_divide(inverse(identity), inverse(inverse(inverse(Y0)))) -> inverse(inverse(Y0)) % 0.84/1.02 double_divide(inverse(inverse(inverse(X0))), inverse(inverse(X0))) -> identity % 0.84/1.02 f1(identity) -> false__ % 0.84/1.02 f1(inverse(identity)) -> true__ % 0.84/1.02 f1(multiply(inverse(a1), a1)) -> true__ % 0.84/1.02 inverse(double_divide(Y0, double_divide(identity, inverse(inverse(Y0))))) -> identity % 0.84/1.02 inverse(double_divide(Y0, double_divide(inverse(double_divide(Y0, Y1)), inverse(Y1)))) -> identity % 0.84/1.02 inverse(double_divide(Y0, inverse(inverse(inverse(Y0))))) -> identity % 0.84/1.02 inverse(double_divide(identity, inverse(double_divide(identity, Y1)))) -> Y1 % 0.84/1.02 inverse(identity) -> identity % 0.84/1.02 inverse(inverse(double_divide(X0, inverse(inverse(inverse(X0)))))) -> identity % 0.84/1.02 inverse(inverse(identity)) -> identity % 0.84/1.02 inverse(inverse(inverse(inverse(Y0)))) -> inverse(inverse(Y0)) % 0.84/1.02 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 0.84/1.02 true__ -> false__ % 0.84/1.02 with the LPO induced by % 0.84/1.02 a1 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 0.84/1.02 % 0.84/1.02 % SZS output end Proof % 0.84/1.02 %------------------------------------------------------------------------------