%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP573-1 : 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 10:56:22 EDT 2022 % Result : Unsatisfiable 5.18s 5.18s % Output : Proof 5.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GRP573-1 : TPTP v8.1.0. Released v2.6.0. % 0.12/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n022.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % 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 23:15:18 EDT 2022 % 0.12/0.34 % CPUTime : % 5.18/5.18 % SZS status Unsatisfiable % 5.18/5.18 % SZS output start Proof % 5.18/5.18 The input problem is unsatisfiable because % 5.18/5.18 % 5.18/5.18 [1] the following set of Horn clauses is unsatisfiable: % 5.18/5.18 % 5.18/5.18 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) = B % 5.18/5.18 multiply(A, B) = double_divide(double_divide(B, A), identity) % 5.18/5.18 inverse(A) = double_divide(A, identity) % 5.18/5.18 identity = double_divide(A, inverse(A)) % 5.18/5.18 multiply(inverse(a1), a1) = identity ==> \bottom % 5.18/5.18 % 5.18/5.18 This holds because % 5.18/5.18 % 5.18/5.18 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.18/5.18 % 5.18/5.18 E: % 5.18/5.18 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) = B % 5.18/5.18 f1(identity) = false__ % 5.18/5.18 f1(multiply(inverse(a1), a1)) = true__ % 5.18/5.18 identity = double_divide(A, inverse(A)) % 5.18/5.18 inverse(A) = double_divide(A, identity) % 5.18/5.18 multiply(A, B) = double_divide(double_divide(B, A), identity) % 5.18/5.18 G: % 5.18/5.18 true__ = false__ % 5.18/5.18 % 5.18/5.18 This holds because % 5.18/5.18 % 5.18/5.18 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.18/5.18 % 5.18/5.18 double_divide(double_divide(Y0, identity), identity) = double_divide(double_divide(identity, Y0), identity) % 5.18/5.18 double_divide(double_divide(Y2, identity), double_divide(double_divide(Y1, identity), double_divide(Y2, identity))) = double_divide(double_divide(identity, double_divide(Y1, identity)), identity) % 5.18/5.18 double_divide(double_divide(identity, double_divide(X1, identity)), identity) = double_divide(X0, double_divide(double_divide(X1, double_divide(X2, X0)), double_divide(X2, identity))) % 5.18/5.18 double_divide(double_divide(identity, double_divide(identity, X0)), identity) = double_divide(double_divide(true__, identity), double_divide(double_divide(X0, identity), double_divide(true__, identity))) % 5.18/5.18 double_divide(identity, double_divide(double_divide(Y1, double_divide(Y2, identity)), double_divide(Y2, identity))) = double_divide(double_divide(identity, double_divide(Y1, identity)), identity) % 5.18/5.18 double_divide(Y0, double_divide(Y0, identity)) -> identity % 5.18/5.18 double_divide(Y1, double_divide(double_divide(identity, double_divide(Y2, Y1)), double_divide(Y2, identity))) -> identity % 5.18/5.18 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) -> B % 5.18/5.18 double_divide(double_divide(X0, identity), double_divide(double_divide(identity, X0), identity)) -> identity % 5.18/5.18 double_divide(double_divide(Y1, identity), double_divide(identity, double_divide(Y1, identity))) -> identity % 5.18/5.18 double_divide(double_divide(double_divide(X0, identity), identity), double_divide(identity, double_divide(identity, double_divide(X0, identity)))) -> identity % 5.18/5.18 double_divide(double_divide(double_divide(Y0, identity), double_divide(double_divide(Y1, identity), double_divide(Y0, identity))), double_divide(identity, identity)) -> Y1 % 5.18/5.18 double_divide(double_divide(double_divide(Y0, identity), identity), identity) -> double_divide(identity, double_divide(identity, double_divide(Y0, identity))) % 5.18/5.18 double_divide(double_divide(double_divide(identity, identity), X0), identity) -> double_divide(identity, double_divide(X0, identity)) % 5.18/5.18 double_divide(double_divide(identity, double_divide(identity, double_divide(Y0, identity))), double_divide(identity, identity)) -> Y0 % 5.18/5.18 double_divide(double_divide(identity, double_divide(identity, double_divide(double_divide(Y0, identity), identity))), identity) -> double_divide(identity, Y0) % 5.18/5.18 double_divide(double_divide(identity, double_divide(identity, double_divide(double_divide(identity, Y0), identity))), identity) -> double_divide(identity, Y0) % 5.18/5.18 double_divide(double_divide(inverse(identity), double_divide(double_divide(Y1, X0), inverse(inverse(inverse(inverse(X0)))))), inverse(identity)) -> Y1 % 5.18/5.18 double_divide(double_divide(true__, identity), double_divide(double_divide(double_divide(identity, double_divide(identity, Y0)), identity), double_divide(true__, identity))) -> double_divide(identity, Y0) % 5.18/5.18 double_divide(double_divide(true__, identity), double_divide(double_divide(identity, double_divide(identity, double_divide(Y0, identity))), double_divide(true__, identity))) -> double_divide(identity, Y0) % 5.18/5.18 double_divide(false__, double_divide(double_divide(Y1, double_divide(false__, false__)), double_divide(false__, identity))) -> double_divide(identity, double_divide(identity, double_divide(Y1, identity))) % 5.18/5.18 double_divide(identity, identity) -> identity % 5.18/5.18 double_divide(true__, double_divide(double_divide(Y0, double_divide(true__, true__)), double_divide(true__, identity))) -> double_divide(identity, double_divide(identity, double_divide(Y0, identity))) % 5.18/5.18 f1(double_divide(identity, identity)) -> true__ % 5.18/5.18 f1(identity) -> false__ % 5.18/5.18 false__ -> true__ % 5.18/5.18 inverse(A) -> double_divide(A, identity) % 5.18/5.18 inverse(inverse(X0)) -> double_divide(double_divide(identity, X0), identity) % 5.18/5.18 inverse(inverse(inverse(X0))) -> double_divide(double_divide(identity, double_divide(X0, identity)), identity) % 5.18/5.18 inverse(inverse(inverse(inverse(inverse(X0))))) -> double_divide(identity, X0) % 5.18/5.18 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 5.18/5.18 with the LPO induced by % 5.18/5.18 f1 > a1 > multiply > inverse > double_divide > identity > false__ > true__ % 5.18/5.18 % 5.18/5.18 % SZS output end Proof % 5.18/5.18 %------------------------------------------------------------------------------