%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP570-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 10:56:20 EDT 2022 % Result : Unsatisfiable 4.03s 4.14s % Output : Proof 4.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP570-1 : TPTP v8.1.0. Released v2.6.0. % 0.12/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n020.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 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jun 13 22:02:05 EDT 2022 % 0.12/0.34 % CPUTime : % 4.03/4.14 % SZS status Unsatisfiable % 4.03/4.14 % SZS output start Proof % 4.03/4.14 The input problem is unsatisfiable because % 4.03/4.14 % 4.03/4.14 [1] the following set of Horn clauses is unsatisfiable: % 4.03/4.14 % 4.03/4.14 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B % 4.03/4.14 multiply(A, B) = double_divide(double_divide(B, A), identity) % 4.03/4.14 inverse(A) = double_divide(A, identity) % 4.03/4.14 identity = double_divide(A, inverse(A)) % 4.03/4.14 multiply(identity, a2) = a2 ==> \bottom % 4.03/4.14 % 4.03/4.14 This holds because % 4.03/4.14 % 4.03/4.14 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.03/4.14 % 4.03/4.14 E: % 4.03/4.14 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B % 4.03/4.14 f1(a2) = false__ % 4.03/4.14 f1(multiply(identity, a2)) = true__ % 4.03/4.14 identity = double_divide(A, inverse(A)) % 4.03/4.14 inverse(A) = double_divide(A, identity) % 4.03/4.14 multiply(A, B) = double_divide(double_divide(B, A), identity) % 4.03/4.14 G: % 4.03/4.14 true__ = false__ % 4.03/4.14 % 4.03/4.14 This holds because % 4.03/4.14 % 4.03/4.14 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.03/4.14 % 4.03/4.14 double_divide(identity, Y1) = double_divide(Y1, identity) % 4.03/4.14 double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), double_divide(X2, identity))) -> double_divide(X1, identity) % 4.03/4.14 double_divide(Y0, double_divide(Y0, identity)) -> identity % 4.03/4.14 double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, identity)), identity)) -> double_divide(Y1, identity) % 4.03/4.14 double_divide(Y0, double_divide(double_divide(Y1, identity), double_divide(double_divide(Y0, identity), identity))) -> double_divide(Y1, identity) % 4.03/4.14 double_divide(Y0, double_divide(identity, Y0)) -> identity % 4.03/4.14 double_divide(Y0, double_divide(identity, double_divide(Y1, double_divide(Y0, identity)))) -> double_divide(identity, Y1) % 4.03/4.14 double_divide(Y1, double_divide(double_divide(identity, double_divide(Y1, Y2)), double_divide(Y2, identity))) -> identity % 4.03/4.14 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) -> B % 4.03/4.14 double_divide(double_divide(X0, identity), X0) -> identity % 4.03/4.14 double_divide(double_divide(X0, identity), double_divide(double_divide(identity, X0), double_divide(double_divide(identity, identity), identity))) -> identity % 4.03/4.14 double_divide(double_divide(Y0, double_divide(double_divide(Y1, identity), double_divide(double_divide(Y0, identity), identity))), double_divide(identity, identity)) -> Y1 % 4.03/4.14 double_divide(double_divide(Y0, identity), double_divide(identity, identity)) -> Y0 % 4.03/4.14 double_divide(double_divide(Y0, identity), identity) -> Y0 % 4.03/4.14 double_divide(double_divide(double_divide(X1, identity), identity), double_divide(X1, identity)) -> identity % 4.03/4.14 double_divide(double_divide(double_divide(Y0, identity), double_divide(double_divide(Y1, Y0), double_divide(double_divide(identity, identity), identity))), double_divide(identity, identity)) -> Y1 % 4.03/4.14 double_divide(double_divide(identity, Y0), double_divide(identity, identity)) -> Y0 % 4.03/4.14 double_divide(double_divide(identity, Y0), identity) -> Y0 % 4.03/4.14 double_divide(double_divide(inverse(X0), double_divide(double_divide(Y1, X0), inverse(inverse(identity)))), inverse(identity)) -> Y1 % 4.03/4.14 double_divide(identity, double_divide(Y0, identity)) -> Y0 % 4.03/4.14 double_divide(identity, double_divide(double_divide(identity, X0), double_divide(double_divide(X0, identity), identity))) -> identity % 4.03/4.14 double_divide(identity, identity) -> identity % 4.03/4.14 f1(a2) -> false__ % 4.03/4.14 f1(double_divide(double_divide(a2, identity), identity)) -> true__ % 4.03/4.14 f1(double_divide(identity, double_divide(a2, identity))) -> true__ % 4.03/4.14 inverse(A) -> double_divide(A, identity) % 4.03/4.14 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 4.03/4.14 true__ -> false__ % 4.03/4.14 with the LPO induced by % 4.03/4.14 multiply > inverse > double_divide > identity > a2 > f1 > true__ > false__ % 4.03/4.14 % 4.03/4.14 % SZS output end Proof % 4.03/4.14 %------------------------------------------------------------------------------