%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP482-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n017.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 4.71s 4.73s % Output : Proof 4.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP482-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n017.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jun 13 05:45:22 EDT 2022 % 0.12/0.34 % CPUTime : % 4.71/4.73 % SZS status Unsatisfiable % 4.71/4.73 % SZS output start Proof % 4.71/4.73 The input problem is unsatisfiable because % 4.71/4.73 % 4.71/4.73 [1] the following set of Horn clauses is unsatisfiable: % 4.71/4.73 % 4.71/4.73 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 % 4.71/4.73 multiply(A, B) = double_divide(double_divide(B, A), identity) % 4.71/4.73 inverse(A) = double_divide(A, identity) % 4.71/4.73 identity = double_divide(A, inverse(A)) % 4.71/4.73 multiply(identity, a2) = a2 ==> \bottom % 4.71/4.73 % 4.71/4.73 This holds because % 4.71/4.73 % 4.71/4.73 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.71/4.73 % 4.71/4.73 E: % 4.71/4.73 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 % 4.71/4.73 f1(a2) = false__ % 4.71/4.73 f1(multiply(identity, a2)) = true__ % 4.71/4.73 identity = double_divide(A, inverse(A)) % 4.71/4.73 inverse(A) = double_divide(A, identity) % 4.71/4.73 multiply(A, B) = double_divide(double_divide(B, A), identity) % 4.71/4.73 G: % 4.71/4.73 true__ = false__ % 4.71/4.73 % 4.71/4.73 This holds because % 4.71/4.73 % 4.71/4.73 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.71/4.73 % 4.71/4.73 double_divide(double_divide(double_divide(Y0, double_divide(Y1, identity)), X2), Y1) = double_divide(double_divide(X2, identity), Y0) % 4.71/4.73 double_divide(double_divide(double_divide(Y0, identity), Y2), identity) = double_divide(double_divide(Y2, identity), Y0) % 4.71/4.73 double_divide(identity, Y1) = double_divide(Y1, identity) % 4.71/4.73 double_divide(Y0, double_divide(Y0, identity)) -> identity % 4.71/4.73 double_divide(Y0, double_divide(identity, Y0)) -> identity % 4.71/4.73 double_divide(double_divide(Y0, identity), Y0) -> identity % 4.71/4.73 double_divide(double_divide(Y0, identity), identity) -> Y0 % 4.71/4.73 double_divide(double_divide(double_divide(X0, inverse(identity)), double_divide(inverse(X1), inverse(X0))), X1) -> identity % 4.71/4.73 double_divide(double_divide(double_divide(Y0, double_divide(Y1, identity)), double_divide(double_divide(Y2, identity), double_divide(Y0, identity))), Y1) -> Y2 % 4.71/4.73 double_divide(double_divide(double_divide(Y0, double_divide(Y1, identity)), identity), Y1) -> double_divide(identity, Y0) % 4.71/4.73 double_divide(double_divide(double_divide(Y0, double_divide(identity, identity)), double_divide(double_divide(Y1, identity), double_divide(Y0, identity))), Y1) -> identity % 4.71/4.73 double_divide(double_divide(double_divide(double_divide(Y0, identity), double_divide(identity, identity)), identity), Y0) -> identity % 4.71/4.73 double_divide(double_divide(identity, X0), X0) -> identity % 4.71/4.73 double_divide(double_divide(identity, double_divide(double_divide(Y0, identity), double_divide(Y1, identity))), Y1) -> Y0 % 4.71/4.73 double_divide(double_divide(identity, identity), double_divide(Y0, identity)) -> Y0 % 4.71/4.73 double_divide(double_divide(identity, identity), multiply(identity, double_divide(Y0, identity))) -> Y0 % 4.71/4.73 double_divide(identity, double_divide(Y0, identity)) -> Y0 % 4.71/4.73 double_divide(identity, double_divide(identity, Y0)) -> Y0 % 4.71/4.73 double_divide(identity, double_divide(identity, double_divide(identity, double_divide(Y0, identity)))) -> Y0 % 4.71/4.73 double_divide(identity, identity) -> identity % 4.71/4.73 double_divide(inverse(identity), inverse(inverse(inverse(Y2)))) -> Y2 % 4.71/4.73 f1(a2) -> false__ % 4.71/4.73 f1(double_divide(double_divide(a2, identity), identity)) -> true__ % 4.71/4.73 f1(double_divide(identity, double_divide(a2, identity))) -> true__ % 4.71/4.73 inverse(A) -> double_divide(A, identity) % 4.71/4.73 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 4.71/4.73 true__ -> false__ % 4.71/4.73 with the LPO induced by % 4.71/4.73 multiply > inverse > double_divide > identity > a2 > f1 > true__ > false__ % 4.71/4.73 % 4.71/4.73 % SZS output end Proof % 4.71/4.73 %------------------------------------------------------------------------------