%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP582-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n010.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 10:56:26 EDT 2022 % Result : Unsatisfiable 187.17s 187.21s % Output : Proof 187.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP582-1 : TPTP v8.1.0. Released v2.6.0. % 0.11/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n010.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jun 13 09:57:09 EDT 2022 % 0.13/0.34 % CPUTime : % 187.17/187.21 % SZS status Unsatisfiable % 187.17/187.21 % SZS output start Proof % 187.17/187.21 The input problem is unsatisfiable because % 187.17/187.21 % 187.17/187.21 [1] the following set of Horn clauses is unsatisfiable: % 187.17/187.21 % 187.17/187.21 double_divide(double_divide(A, double_divide(double_divide(identity, B), double_divide(C, double_divide(B, A)))), double_divide(identity, identity)) = C % 187.17/187.21 multiply(A, B) = double_divide(double_divide(B, A), identity) % 187.17/187.21 inverse(A) = double_divide(A, identity) % 187.17/187.21 identity = double_divide(A, inverse(A)) % 187.17/187.21 multiply(identity, a2) = a2 ==> \bottom % 187.17/187.21 % 187.17/187.21 This holds because % 187.17/187.21 % 187.17/187.21 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 187.17/187.21 % 187.17/187.21 E: % 187.17/187.21 double_divide(double_divide(A, double_divide(double_divide(identity, B), double_divide(C, double_divide(B, A)))), double_divide(identity, identity)) = C % 187.17/187.21 f1(a2) = false__ % 187.17/187.21 f1(multiply(identity, a2)) = true__ % 187.17/187.21 identity = double_divide(A, inverse(A)) % 187.17/187.21 inverse(A) = double_divide(A, identity) % 187.17/187.21 multiply(A, B) = double_divide(double_divide(B, A), identity) % 187.17/187.21 G: % 187.17/187.21 true__ = false__ % 187.17/187.21 % 187.17/187.21 This holds because % 187.17/187.21 % 187.17/187.21 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 187.17/187.21 % 187.17/187.21 double_divide(Y0, double_divide(inverse(identity), double_divide(identity, double_divide(identity, Y0)))) = double_divide(false__, double_divide(double_divide(identity, false__), double_divide(identity, double_divide(false__, false__)))) % 187.17/187.21 double_divide(double_divide(identity, double_divide(inverse(identity), X2)), inverse(identity)) = double_divide(X0, double_divide(double_divide(identity, X1), double_divide(X2, double_divide(X1, X0)))) % 187.17/187.21 double_divide(double_divide(identity, inverse(inverse(identity))), inverse(identity)) = double_divide(Y1, double_divide(double_divide(identity, Y2), double_divide(identity, double_divide(Y2, Y1)))) % 187.17/187.21 double_divide(identity, double_divide(double_divide(identity, Y1), double_divide(identity, inverse(Y1)))) = double_divide(false__, double_divide(double_divide(identity, false__), double_divide(identity, double_divide(false__, false__)))) % 187.17/187.21 double_divide(A, identity) -> inverse(A) % 187.17/187.21 double_divide(A, inverse(A)) -> identity % 187.17/187.21 double_divide(X0, double_divide(X0, inverse(X1))) -> inverse(X1) % 187.17/187.21 double_divide(X0, inverse(inverse(inverse(X0)))) -> identity % 187.17/187.21 double_divide(double_divide(A, double_divide(double_divide(identity, B), double_divide(C, double_divide(B, A)))), double_divide(identity, identity)) -> C % 187.17/187.21 double_divide(double_divide(X0, double_divide(inverse(inverse(X0)), inverse(X1))), X1) -> identity % 187.17/187.21 double_divide(double_divide(X0, double_divide(inverse(inverse(X0)), inverse(X1))), inverse(inverse(X1))) -> identity % 187.17/187.21 double_divide(double_divide(Y0, double_divide(Y0, inverse(Y1))), Y1) -> identity % 187.17/187.21 double_divide(double_divide(Y0, double_divide(double_divide(identity, Y1), double_divide(Y2, double_divide(Y1, Y0)))), inverse(identity)) -> Y2 % 187.17/187.21 double_divide(double_divide(Y0, double_divide(identity, double_divide(Y2, double_divide(inverse(identity), Y0)))), inverse(identity)) -> Y2 % 187.17/187.21 double_divide(double_divide(Y0, double_divide(inverse(identity), double_divide(Y2, double_divide(identity, Y0)))), inverse(identity)) -> Y2 % 187.17/187.21 double_divide(double_divide(identity, double_divide(double_divide(identity, Y1), double_divide(Y2, inverse(Y1)))), inverse(identity)) -> Y2 % 187.17/187.21 double_divide(double_divide(identity, double_divide(identity, double_divide(Y1, inverse(inverse(identity))))), inverse(identity)) -> Y1 % 187.17/187.21 double_divide(double_divide(identity, inverse(double_divide(identity, Y0))), inverse(identity)) -> Y0 % 187.17/187.21 double_divide(double_divide(inverse(X0), double_divide(inverse(inverse(inverse(X0))), inverse(X1))), X1) -> identity % 187.17/187.21 double_divide(double_divide(inverse(X0), double_divide(inverse(inverse(inverse(X0))), inverse(X1))), inverse(inverse(X1))) -> identity % 187.17/187.21 double_divide(double_divide(inverse(Y1), double_divide(double_divide(identity, Y1), inverse(Y2))), inverse(identity)) -> Y2 % 187.17/187.21 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(Y1))), inverse(identity)) -> Y1 % 187.17/187.21 double_divide(double_divide(inverse(inverse(double_divide(identity, X0))), X0), inverse(identity)) -> identity % 187.17/187.21 double_divide(double_divide(inverse(inverse(identity)), double_divide(identity, inverse(Y1))), inverse(identity)) -> Y1 % 187.17/187.21 double_divide(false__, double_divide(double_divide(identity, false__), double_divide(X0, double_divide(false__, false__)))) -> double_divide(identity, inverse(double_divide(identity, X0))) % 187.17/187.21 double_divide(false__, double_divide(double_divide(identity, false__), double_divide(double_divide(Y1, inverse(identity)), double_divide(false__, false__)))) -> Y1 % 187.17/187.21 double_divide(false__, double_divide(double_divide(identity, false__), double_divide(double_divide(identity, X0), double_divide(false__, false__)))) -> inverse(inverse(X0)) % 187.17/187.21 double_divide(false__, double_divide(double_divide(identity, false__), double_divide(identity, double_divide(false__, false__)))) -> identity % 187.17/187.21 double_divide(identity, Y0) -> inverse(inverse(inverse(Y0))) % 187.17/187.21 double_divide(identity, inverse(double_divide(identity, inverse(Y0)))) -> Y0 % 187.17/187.21 double_divide(inverse(X0), X0) -> identity % 187.17/187.21 double_divide(inverse(X0), double_divide(inverse(X0), inverse(X1))) -> inverse(X1) % 187.17/187.21 double_divide(inverse(X0), inverse(inverse(inverse(inverse(X0))))) -> identity % 187.17/187.21 double_divide(inverse(inverse(X0)), inverse(X0)) -> identity % 187.17/187.21 double_divide(inverse(inverse(Y0)), inverse(identity)) -> double_divide(identity, Y0) % 187.17/187.21 double_divide(inverse(inverse(inverse(X0))), inverse(inverse(X0))) -> identity % 187.17/187.21 double_divide(inverse(inverse(inverse(Y0))), Y0) -> identity % 187.17/187.21 double_divide(inverse(inverse(inverse(inverse(X0)))), inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0)))))))) -> identity % 187.17/187.21 double_divide(inverse(inverse(inverse(inverse(inverse(X0))))), X0) -> identity % 187.17/187.21 double_divide(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))), X0) -> identity % 187.17/187.21 f1(a2) -> false__ % 187.17/187.21 f1(inverse(inverse(a2))) -> true__ % 187.17/187.21 f1(multiply(identity, a2)) -> true__ % 187.17/187.21 inverse(double_divide(X0, double_divide(inverse(inverse(X0)), inverse(Y1)))) -> Y1 % 187.17/187.21 inverse(double_divide(X0, inverse(inverse(inverse(X0))))) -> identity % 187.17/187.21 inverse(double_divide(Y0, double_divide(Y0, inverse(Y1)))) -> Y1 % 187.17/187.21 inverse(double_divide(Y0, double_divide(inverse(inverse(Y0)), X0))) -> inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))) % 187.17/187.21 inverse(double_divide(Y0, inverse(inverse(inverse(double_divide(Y1, inverse(inverse(inverse(Y0))))))))) -> Y1 % 187.17/187.21 inverse(double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0 % 187.17/187.21 inverse(double_divide(identity, inverse(double_divide(identity, Y0)))) -> Y0 % 187.17/187.21 inverse(double_divide(inverse(X0), double_divide(inverse(X0), inverse(Y1)))) -> Y1 % 187.17/187.21 inverse(double_divide(inverse(Y0), double_divide(double_divide(identity, Y0), inverse(Y1)))) -> Y1 % 187.17/187.21 inverse(double_divide(inverse(Y0), double_divide(inverse(inverse(inverse(Y0))), X0))) -> inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))) % 187.17/187.21 inverse(double_divide(inverse(Y0), double_divide(inverse(inverse(inverse(Y0))), inverse(Y1)))) -> Y1 % 187.17/187.21 inverse(double_divide(inverse(Y0), inverse(double_divide(identity, Y0)))) -> identity % 187.17/187.21 inverse(double_divide(inverse(Y0), inverse(inverse(inverse(inverse(Y0)))))) -> identity % 187.17/187.21 inverse(double_divide(inverse(inverse(double_divide(identity, Y0))), Y0)) -> identity % 187.17/187.21 inverse(double_divide(inverse(inverse(inverse(X0))), double_divide(inverse(X0), inverse(Y1)))) -> Y1 % 187.17/187.21 inverse(double_divide(inverse(inverse(inverse(X0))), inverse(inverse(X0)))) -> identity % 187.17/187.21 inverse(double_divide(inverse(inverse(inverse(inverse(inverse(Y0))))), Y0)) -> identity % 187.17/187.21 inverse(double_divide(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))), double_divide(inverse(X0), inverse(Y1)))) -> Y1 % 187.17/187.21 inverse(identity) -> identity % 187.17/187.21 inverse(inverse(Y0)) -> Y0 % 187.17/187.21 inverse(inverse(inverse(X0))) -> inverse(X0) % 187.17/187.21 inverse(inverse(inverse(inverse(Y0)))) -> inverse(inverse(Y0)) % 187.17/187.21 inverse(inverse(inverse(inverse(inverse(Y0))))) -> inverse(inverse(inverse(Y0))) % 187.17/187.21 inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(Y0)))))))) -> Y0 % 187.17/187.21 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 187.17/187.21 true__ -> false__ % 187.17/187.21 with the LPO induced by % 187.17/187.21 a2 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 187.17/187.21 % 187.17/187.21 % SZS output end Proof % 187.17/187.21 %------------------------------------------------------------------------------