%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP493-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n016.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 10:55:49 EDT 2022 % Result : Unsatisfiable 0.94s 1.14s % Output : Proof 0.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GRP493-1 : TPTP v8.1.0. Released v2.6.0. % 0.08/0.14 % Command : moca.sh %s % 0.13/0.35 % Computer : n016.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Tue Jun 14 13:40:31 EDT 2022 % 0.13/0.35 % CPUTime : % 0.94/1.14 % SZS status Unsatisfiable % 0.94/1.14 % SZS output start Proof % 0.94/1.14 The input problem is unsatisfiable because % 0.94/1.14 % 0.94/1.14 [1] the following set of Horn clauses is unsatisfiable: % 0.94/1.14 % 0.94/1.14 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B % 0.94/1.14 multiply(A, B) = double_divide(double_divide(B, A), identity) % 0.94/1.14 inverse(A) = double_divide(A, identity) % 0.94/1.14 identity = double_divide(A, inverse(A)) % 0.94/1.14 multiply(inverse(a1), a1) = identity ==> \bottom % 0.94/1.14 % 0.94/1.14 This holds because % 0.94/1.14 % 0.94/1.14 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.94/1.14 % 0.94/1.14 E: % 0.94/1.14 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B % 0.94/1.14 f1(identity) = false__ % 0.94/1.14 f1(multiply(inverse(a1), a1)) = true__ % 0.94/1.14 identity = double_divide(A, inverse(A)) % 0.94/1.14 inverse(A) = double_divide(A, identity) % 0.94/1.14 multiply(A, B) = double_divide(double_divide(B, A), identity) % 0.94/1.14 G: % 0.94/1.14 true__ = false__ % 0.94/1.14 % 0.94/1.14 This holds because % 0.94/1.14 % 0.94/1.14 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.94/1.14 % 0.94/1.14 double_divide(X0, inverse(identity)) = double_divide(identity, double_divide(inverse(identity), inverse(X0))) % 0.94/1.14 double_divide(inverse(identity), double_divide(identity, double_divide(identity, X0))) = double_divide(identity, double_divide(inverse(X0), inverse(identity))) % 0.94/1.14 double_divide(A, identity) -> inverse(A) % 0.94/1.14 double_divide(A, inverse(A)) -> identity % 0.94/1.14 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) -> B % 0.94/1.14 double_divide(double_divide(identity, Y0), double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(Y0, Y2))) -> Y1 % 0.94/1.14 double_divide(double_divide(identity, Y0), double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(Y0))) -> Y1 % 0.94/1.14 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, inverse(Y1)))) -> Y1 % 0.94/1.14 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(Y0))) -> identity % 0.94/1.14 double_divide(double_divide(identity, Y0), inverse(double_divide(double_divide(Y1, inverse(Y0)), inverse(identity)))) -> Y1 % 0.94/1.14 double_divide(double_divide(identity, Y1), inverse(identity)) -> Y1 % 0.94/1.14 double_divide(double_divide(identity, double_divide(identity, X0)), double_divide(identity, X0)) -> identity % 0.94/1.14 double_divide(double_divide(identity, double_divide(inverse(X0), inverse(identity))), X0) -> identity % 0.94/1.14 double_divide(double_divide(identity, inverse(inverse(Y0))), Y0) -> identity % 0.94/1.14 double_divide(identity, double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(inverse(identity), Y2))) -> Y1 % 0.94/1.14 double_divide(identity, double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(inverse(identity)))) -> Y1 % 0.94/1.14 double_divide(identity, double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0 % 0.94/1.14 double_divide(identity, double_divide(identity, double_divide(inverse(identity), inverse(Y1)))) -> Y1 % 0.94/1.14 double_divide(identity, double_divide(identity, inverse(Y0))) -> inverse(Y0) % 0.94/1.14 double_divide(identity, double_divide(inverse(X0), inverse(identity))) -> inverse(double_divide(identity, double_divide(X0, inverse(identity)))) % 0.94/1.14 double_divide(inverse(identity), double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(identity, Y2))) -> Y1 % 0.94/1.14 double_divide(inverse(identity), double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(identity))) -> Y1 % 0.94/1.14 double_divide(inverse(identity), double_divide(identity, double_divide(identity, inverse(Y1)))) -> Y1 % 0.94/1.14 double_divide(inverse(identity), inverse(double_divide(double_divide(Y1, inverse(identity)), inverse(identity)))) -> Y1 % 0.94/1.14 double_divide(inverse(identity), inverse(identity)) -> identity % 0.94/1.14 f1(identity) -> false__ % 0.94/1.14 f1(inverse(identity)) -> true__ % 0.94/1.14 f1(multiply(inverse(a1), a1)) -> true__ % 0.94/1.14 inverse(double_divide(identity, Y0)) -> Y0 % 0.94/1.14 inverse(double_divide(identity, double_divide(inverse(Y1), inverse(identity)))) -> Y1 % 0.94/1.14 inverse(double_divide(identity, inverse(inverse(Y0)))) -> Y0 % 0.94/1.14 inverse(identity) -> identity % 0.94/1.14 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 0.94/1.14 true__ -> false__ % 0.94/1.14 with the LPO induced by % 0.94/1.14 a1 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 0.94/1.14 % 0.94/1.14 % SZS output end Proof % 0.94/1.14 %------------------------------------------------------------------------------