%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP566-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n021.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 10:56:19 EDT 2022 % Result : Unsatisfiable 4.67s 4.74s % Output : Proof 4.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GRP566-1 : TPTP v8.1.0. Released v2.6.0. % 0.12/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n021.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jun 14 01:33:27 EDT 2022 % 0.13/0.35 % CPUTime : % 4.67/4.74 % SZS status Unsatisfiable % 4.67/4.74 % SZS output start Proof % 4.67/4.74 The input problem is unsatisfiable because % 4.67/4.74 % 4.67/4.74 [1] the following set of Horn clauses is unsatisfiable: % 4.67/4.74 % 4.67/4.74 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity, C))), double_divide(identity, identity)) = B % 4.67/4.74 multiply(A, B) = double_divide(double_divide(B, A), identity) % 4.67/4.74 inverse(A) = double_divide(A, identity) % 4.67/4.74 identity = double_divide(A, inverse(A)) % 4.67/4.74 multiply(identity, a2) = a2 ==> \bottom % 4.67/4.74 % 4.67/4.74 This holds because % 4.67/4.74 % 4.67/4.74 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.67/4.74 % 4.67/4.74 E: % 4.67/4.74 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity, C))), double_divide(identity, identity)) = B % 4.67/4.74 f1(a2) = false__ % 4.67/4.74 f1(multiply(identity, a2)) = true__ % 4.67/4.74 identity = double_divide(A, inverse(A)) % 4.67/4.74 inverse(A) = double_divide(A, identity) % 4.67/4.74 multiply(A, B) = double_divide(double_divide(B, A), identity) % 4.67/4.74 G: % 4.67/4.74 true__ = false__ % 4.67/4.74 % 4.67/4.74 This holds because % 4.67/4.74 % 4.67/4.74 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.67/4.74 % 4.67/4.74 double_divide(X1, identity) = double_divide(X0, multiply(double_divide(X0, identity), X1)) % 4.67/4.74 double_divide(identity, X0) = double_divide(X0, identity) % 4.67/4.74 double_divide(identity, Y0) = double_divide(Y1, multiply(double_divide(Y1, identity), Y0)) % 4.67/4.74 multiply(Y0, double_divide(Y0, Y1)) = double_divide(Y1, identity) % 4.67/4.74 double_divide(X0, double_divide(double_divide(X1, identity), X0)) -> double_divide(X1, identity) % 4.67/4.74 double_divide(X0, inverse(double_divide(X1, double_divide(X0, inverse(identity))))) -> double_divide(X1, identity) % 4.67/4.74 double_divide(Y0, double_divide(Y0, identity)) -> identity % 4.67/4.74 double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, double_divide(identity, identity))), identity)) -> double_divide(Y1, identity) % 4.67/4.74 double_divide(Y0, double_divide(identity, Y0)) -> identity % 4.67/4.74 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity, C))), double_divide(identity, identity)) -> B % 4.67/4.74 double_divide(double_divide(B, A), identity) -> multiply(A, B) % 4.67/4.74 double_divide(double_divide(X0, identity), X0) -> identity % 4.67/4.74 double_divide(double_divide(Y0, double_divide(double_divide(Y1, identity), double_divide(identity, double_divide(Y0, identity)))), double_divide(identity, identity)) -> Y1 % 4.67/4.74 double_divide(double_divide(Y0, double_divide(inverse(Y1), double_divide(identity, inverse(Y0)))), inverse(identity)) -> Y1 % 4.67/4.74 double_divide(double_divide(double_divide(X0, double_divide(double_divide(X1, inverse(X0)), inverse(identity))), inverse(double_divide(Y1, X1))), inverse(identity)) -> Y1 % 4.67/4.74 double_divide(double_divide(double_divide(Y0, X0), Y0), double_divide(identity, identity)) -> double_divide(X0, identity) % 4.67/4.74 double_divide(double_divide(double_divide(identity, double_divide(double_divide(X0, identity), identity)), double_divide(double_divide(Y1, X0), identity)), double_divide(identity, identity)) -> Y1 % 4.67/4.74 double_divide(double_divide(identity, Y0), Y0) -> identity % 4.67/4.74 double_divide(double_divide(identity, multiply(identity, Y0)), double_divide(identity, identity)) -> Y0 % 4.67/4.74 double_divide(identity, double_divide(Y0, Y1)) -> multiply(Y1, Y0) % 4.67/4.74 double_divide(identity, double_divide(Y0, identity)) -> Y0 % 4.67/4.74 double_divide(identity, double_divide(identity, Y0)) -> Y0 % 4.67/4.74 double_divide(identity, identity) -> identity % 4.67/4.74 f1(a2) -> false__ % 4.67/4.74 f1(multiply(a2, identity)) -> true__ % 4.67/4.74 f1(multiply(identity, a2)) -> true__ % 4.67/4.74 inverse(A) -> double_divide(A, identity) % 4.67/4.74 multiply(Y0, identity) -> Y0 % 4.67/4.74 multiply(double_divide(Y0, identity), Y0) -> identity % 4.67/4.74 multiply(double_divide(identity, Y0), Y0) -> identity % 4.67/4.74 multiply(identity, Y0) -> Y0 % 4.67/4.74 true__ -> false__ % 4.67/4.74 with the LPO induced by % 4.67/4.74 inverse > double_divide > multiply > identity > a2 > f1 > true__ > false__ % 4.67/4.74 % 4.67/4.74 % SZS output end Proof % 4.67/4.74 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