%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP481-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.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 10:55:44 EDT 2022 % Result : Unsatisfiable 3.91s 3.95s % Output : Proof 3.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP481-1 : TPTP v8.1.0. Released v2.6.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.32 % Computer : n011.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Mon Jun 13 09:42:33 EDT 2022 % 0.12/0.32 % CPUTime : % 3.91/3.95 % SZS status Unsatisfiable % 3.91/3.95 % SZS output start Proof % 3.91/3.95 The input problem is unsatisfiable because % 3.91/3.95 % 3.91/3.95 [1] the following set of Horn clauses is unsatisfiable: % 3.91/3.95 % 3.91/3.95 double_divide(double_divide(double_divide(A, double_divide(B, identity)), double_divide(double_divide(C, double_divide(D, double_divide(D, identity))), double_divide(A, identity))), B) = C % 3.91/3.95 multiply(A, B) = double_divide(double_divide(B, A), identity) % 3.91/3.95 inverse(A) = double_divide(A, identity) % 3.91/3.95 identity = double_divide(A, inverse(A)) % 3.91/3.95 multiply(inverse(a1), a1) = identity ==> \bottom % 3.91/3.95 % 3.91/3.95 This holds because % 3.91/3.95 % 3.91/3.95 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.91/3.95 % 3.91/3.95 E: % 3.91/3.95 double_divide(double_divide(double_divide(A, double_divide(B, identity)), double_divide(double_divide(C, double_divide(D, double_divide(D, identity))), double_divide(A, identity))), B) = C % 3.91/3.95 f1(identity) = false__ % 3.91/3.95 f1(multiply(inverse(a1), a1)) = true__ % 3.91/3.95 identity = double_divide(A, inverse(A)) % 3.91/3.95 inverse(A) = double_divide(A, identity) % 3.91/3.95 multiply(A, B) = double_divide(double_divide(B, A), identity) % 3.91/3.95 G: % 3.91/3.95 true__ = false__ % 3.91/3.95 % 3.91/3.95 This holds because % 3.91/3.95 % 3.91/3.95 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.91/3.95 % 3.91/3.95 double_divide(double_divide(double_divide(Y0, double_divide(Y1, identity)), X2), Y1) = double_divide(double_divide(X2, identity), Y0) % 3.91/3.95 double_divide(double_divide(double_divide(Y0, identity), Y2), identity) = double_divide(double_divide(Y2, identity), Y0) % 3.91/3.95 double_divide(identity, Y1) = double_divide(Y1, identity) % 3.91/3.95 double_divide(Y0, double_divide(Y0, identity)) -> identity % 3.91/3.95 double_divide(Y0, double_divide(identity, Y0)) -> identity % 3.91/3.95 double_divide(double_divide(X0, identity), X0) -> identity % 3.91/3.95 double_divide(double_divide(Y0, identity), identity) -> Y0 % 3.91/3.95 double_divide(double_divide(double_divide(X0, inverse(identity)), double_divide(inverse(X1), inverse(X0))), X1) -> identity % 3.91/3.95 double_divide(double_divide(double_divide(Y0, double_divide(Y1, identity)), double_divide(double_divide(Y2, identity), double_divide(Y0, identity))), Y1) -> Y2 % 3.91/3.95 double_divide(double_divide(double_divide(Y0, double_divide(Y1, identity)), identity), Y1) -> double_divide(identity, Y0) % 3.91/3.95 double_divide(double_divide(double_divide(Y0, double_divide(identity, identity)), double_divide(double_divide(Y1, identity), double_divide(Y0, identity))), Y1) -> identity % 3.91/3.95 double_divide(double_divide(double_divide(double_divide(Y0, identity), double_divide(identity, identity)), identity), Y0) -> identity % 3.91/3.95 double_divide(double_divide(identity, double_divide(double_divide(Y0, identity), double_divide(Y1, identity))), Y1) -> Y0 % 3.91/3.95 double_divide(double_divide(identity, double_divide(identity, double_divide(Y1, identity))), Y1) -> identity % 3.91/3.95 double_divide(double_divide(identity, identity), double_divide(Y0, identity)) -> Y0 % 3.91/3.95 double_divide(double_divide(identity, identity), multiply(identity, double_divide(Y0, identity))) -> Y0 % 3.91/3.95 double_divide(identity, double_divide(Y0, identity)) -> Y0 % 3.91/3.95 double_divide(identity, double_divide(identity, Y0)) -> Y0 % 3.91/3.95 double_divide(identity, double_divide(identity, double_divide(identity, double_divide(Y0, identity)))) -> Y0 % 3.91/3.95 double_divide(identity, identity) -> identity % 3.91/3.95 double_divide(inverse(identity), inverse(inverse(inverse(Y2)))) -> Y2 % 3.91/3.95 f1(double_divide(identity, identity)) -> true__ % 3.91/3.95 f1(identity) -> false__ % 3.91/3.95 inverse(A) -> double_divide(A, identity) % 3.91/3.95 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 3.91/3.95 true__ -> false__ % 3.91/3.95 with the LPO induced by % 3.91/3.95 a1 > multiply > inverse > double_divide > identity > f1 > true__ > false__ % 3.91/3.95 % 3.91/3.95 % SZS output end Proof % 3.91/3.95 %------------------------------------------------------------------------------