%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP494-1 : 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 10:55:49 EDT 2022 % Result : Unsatisfiable 4.06s 4.13s % Output : Proof 4.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GRP494-1 : TPTP v8.1.0. Released v2.6.0. % 0.07/0.13 % Command : moca.sh %s % 0.14/0.35 % Computer : n022.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Mon Jun 13 04:46:48 EDT 2022 % 0.14/0.35 % CPUTime : % 4.06/4.13 % SZS status Unsatisfiable % 4.06/4.13 % SZS output start Proof % 4.06/4.13 The input problem is unsatisfiable because % 4.06/4.13 % 4.06/4.13 [1] the following set of Horn clauses is unsatisfiable: % 4.06/4.13 % 4.06/4.13 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B % 4.06/4.13 multiply(A, B) = double_divide(double_divide(B, A), identity) % 4.06/4.13 inverse(A) = double_divide(A, identity) % 4.06/4.13 identity = double_divide(A, inverse(A)) % 4.06/4.13 multiply(identity, a2) = a2 ==> \bottom % 4.06/4.13 % 4.06/4.13 This holds because % 4.06/4.13 % 4.06/4.13 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.06/4.13 % 4.06/4.13 E: % 4.06/4.13 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B % 4.06/4.13 f1(a2) = false__ % 4.06/4.13 f1(multiply(identity, a2)) = true__ % 4.06/4.13 identity = double_divide(A, inverse(A)) % 4.06/4.13 inverse(A) = double_divide(A, identity) % 4.06/4.13 multiply(A, B) = double_divide(double_divide(B, A), identity) % 4.06/4.13 G: % 4.06/4.13 true__ = false__ % 4.06/4.13 % 4.06/4.13 This holds because % 4.06/4.13 % 4.06/4.13 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.06/4.13 % 4.06/4.13 double_divide(X0, identity) = double_divide(identity, X0) % 4.06/4.13 double_divide(X0, double_divide(identity, X0)) -> identity % 4.06/4.13 double_divide(Y0, double_divide(Y0, identity)) -> identity % 4.06/4.13 double_divide(double_divide(X0, identity), X0) -> identity % 4.06/4.13 double_divide(double_divide(Y0, identity), identity) -> Y0 % 4.06/4.13 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) -> B % 4.06/4.13 double_divide(double_divide(identity, X0), X0) -> identity % 4.06/4.13 double_divide(double_divide(identity, Y0), double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(Y0))) -> Y1 % 4.06/4.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, double_divide(Y1, identity)))) -> Y1 % 4.06/4.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, identity))) -> identity % 4.06/4.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, inverse(Y1)))) -> Y1 % 4.06/4.13 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(Y0))) -> identity % 4.06/4.13 double_divide(double_divide(identity, Y0), identity) -> Y0 % 4.06/4.13 double_divide(double_divide(identity, Y0), inverse(double_divide(double_divide(Y1, inverse(Y0)), inverse(identity)))) -> Y1 % 4.06/4.13 double_divide(identity, double_divide(Y0, identity)) -> Y0 % 4.06/4.13 double_divide(identity, double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(inverse(identity), Y2))) -> Y1 % 4.06/4.13 double_divide(identity, double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(inverse(identity)))) -> Y1 % 4.06/4.13 double_divide(identity, double_divide(identity, X0)) -> X0 % 4.06/4.13 double_divide(identity, double_divide(identity, double_divide(inverse(identity), inverse(Y1)))) -> Y1 % 4.06/4.13 double_divide(identity, identity) -> identity % 4.06/4.13 double_divide(identity, inverse(inverse(inverse(Y0)))) -> Y0 % 4.06/4.13 f1(a2) -> false__ % 4.06/4.13 f1(double_divide(double_divide(a2, identity), identity)) -> true__ % 4.06/4.13 inverse(A) -> double_divide(A, identity) % 4.06/4.13 inverse(double_divide(identity, double_divide(X0, inverse(identity)))) -> double_divide(identity, X0) % 4.06/4.13 inverse(inverse(X0)) -> double_divide(identity, double_divide(X0, identity)) % 4.06/4.13 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 4.06/4.13 true__ -> false__ % 4.06/4.13 with the LPO induced by % 4.06/4.13 a2 > f1 > multiply > inverse > double_divide > identity > true__ > false__ % 4.06/4.13 % 4.06/4.13 % SZS output end Proof % 4.06/4.13 %------------------------------------------------------------------------------