%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 10:56:27 EDT 2022 % Result : Unsatisfiable 6.74s 6.82s % Output : Proof 6.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.11/0.12 % Command : moca.sh %s % 0.13/0.34 % Computer : n025.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 : Mon Jun 13 17:17:24 EDT 2022 % 0.13/0.34 % CPUTime : % 6.74/6.82 % SZS status Unsatisfiable % 6.74/6.82 % SZS output start Proof % 6.74/6.82 The input problem is unsatisfiable because % 6.74/6.82 % 6.74/6.82 [1] the following set of Horn clauses is unsatisfiable: % 6.74/6.82 % 6.74/6.82 double_divide(double_divide(A, double_divide(double_divide(identity, B), double_divide(C, double_divide(B, A)))), double_divide(identity, identity)) = C % 6.74/6.82 multiply(A, B) = double_divide(double_divide(B, A), identity) % 6.74/6.82 inverse(A) = double_divide(A, identity) % 6.74/6.82 identity = double_divide(A, inverse(A)) % 6.74/6.82 multiply(a, b) = multiply(b, a) ==> \bottom % 6.74/6.82 % 6.74/6.82 This holds because % 6.74/6.82 % 6.74/6.82 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.74/6.82 % 6.74/6.82 E: % 6.74/6.82 double_divide(double_divide(A, double_divide(double_divide(identity, B), double_divide(C, double_divide(B, A)))), double_divide(identity, identity)) = C % 6.74/6.82 f1(multiply(a, b)) = true__ % 6.74/6.82 f1(multiply(b, a)) = false__ % 6.74/6.82 identity = double_divide(A, inverse(A)) % 6.74/6.82 inverse(A) = double_divide(A, identity) % 6.74/6.82 multiply(A, B) = double_divide(double_divide(B, A), identity) % 6.74/6.82 G: % 6.74/6.82 true__ = false__ % 6.74/6.82 % 6.74/6.82 This holds because % 6.74/6.82 % 6.74/6.82 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.74/6.82 % 6.74/6.82 double_divide(Y0, X1) = double_divide(X1, Y0) % 6.74/6.82 double_divide(inverse(Y0), X1) = double_divide(X1, inverse(Y0)) % 6.74/6.82 double_divide(inverse(double_divide(X1, X0)), Y1) = double_divide(Y1, inverse(double_divide(X0, X1))) % 6.74/6.82 inverse(double_divide(Y0, X1)) = inverse(double_divide(X1, Y0)) % 6.74/6.82 inverse(double_divide(Y0, double_divide(Y0, X1))) = double_divide(X0, double_divide(X0, inverse(X1))) % 6.74/6.82 double_divide(A, identity) -> inverse(A) % 6.74/6.82 double_divide(A, inverse(A)) -> identity % 6.74/6.82 double_divide(X0, double_divide(X0, X1)) -> X1 % 6.74/6.82 double_divide(X0, double_divide(X0, inverse(X1))) -> inverse(X1) % 6.74/6.82 double_divide(X0, double_divide(Y1, X0)) -> Y1 % 6.74/6.82 double_divide(X0, double_divide(inverse(inverse(X0)), inverse(X1))) -> inverse(inverse(inverse(inverse(inverse(inverse(inverse(X1))))))) % 6.74/6.82 double_divide(X0, inverse(double_divide(X1, inverse(X0)))) -> inverse(X1) % 6.74/6.82 double_divide(X0, inverse(inverse(inverse(X0)))) -> identity % 6.74/6.82 double_divide(X1, double_divide(X0, double_divide(X0, inverse(X1)))) -> identity % 6.74/6.82 double_divide(X1, double_divide(X0, inverse(double_divide(X1, inverse(X0))))) -> identity % 6.74/6.82 double_divide(X1, double_divide(inverse(X0), inverse(double_divide(X1, X0)))) -> identity % 6.74/6.82 double_divide(Y0, inverse(double_divide(inverse(Y0), Y1))) -> inverse(Y1) % 6.74/6.82 double_divide(double_divide(A, double_divide(double_divide(identity, B), double_divide(C, double_divide(B, A)))), double_divide(identity, identity)) -> C % 6.74/6.82 double_divide(double_divide(X0, double_divide(inverse(inverse(X0)), inverse(X1))), X1) -> identity % 6.74/6.82 double_divide(double_divide(X0, inverse(inverse(inverse(double_divide(X1, inverse(inverse(inverse(X0)))))))), X1) -> identity % 6.74/6.82 double_divide(double_divide(X1, Y1), X1) -> Y1 % 6.74/6.82 double_divide(double_divide(Y0, double_divide(Y0, X0)), inverse(X0)) -> identity % 6.74/6.82 double_divide(double_divide(Y0, double_divide(Y0, double_divide(X0, double_divide(X0, X1)))), inverse(X1)) -> identity % 6.74/6.82 double_divide(double_divide(Y0, double_divide(Y0, inverse(Y1))), Y1) -> identity % 6.74/6.82 double_divide(double_divide(Y0, double_divide(double_divide(identity, Y1), double_divide(Y2, double_divide(Y1, Y0)))), inverse(identity)) -> Y2 % 6.74/6.82 double_divide(double_divide(Y0, double_divide(identity, double_divide(Y2, double_divide(inverse(identity), Y0)))), inverse(identity)) -> Y2 % 6.74/6.82 double_divide(double_divide(Y0, double_divide(inverse(identity), double_divide(Y2, double_divide(identity, Y0)))), inverse(identity)) -> Y2 % 6.74/6.82 double_divide(double_divide(Y0, double_divide(inverse(inverse(Y0)), X0)), inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0)))))))) -> identity % 6.74/6.82 double_divide(double_divide(Y1, X1), X1) -> Y1 % 6.74/6.82 double_divide(double_divide(Y1, inverse(X1)), inverse(X1)) -> Y1 % 6.74/6.82 double_divide(double_divide(identity, double_divide(double_divide(identity, Y1), double_divide(Y2, inverse(Y1)))), inverse(identity)) -> Y2 % 6.74/6.82 double_divide(double_divide(identity, double_divide(identity, double_divide(Y1, inverse(inverse(identity))))), inverse(identity)) -> Y1 % 6.74/6.82 double_divide(double_divide(identity, double_divide(inverse(identity), X0)), inverse(identity)) -> double_divide(identity, inverse(double_divide(identity, X0))) % 6.74/6.82 double_divide(double_divide(identity, double_divide(inverse(identity), X0)), inverse(identity)) -> double_divide(inverse(identity), double_divide(inverse(identity), inverse(X0))) % 6.74/6.82 double_divide(double_divide(identity, double_divide(inverse(identity), double_divide(Y1, inverse(identity)))), inverse(identity)) -> Y1 % 6.74/6.82 double_divide(double_divide(identity, double_divide(inverse(identity), double_divide(identity, X0))), inverse(identity)) -> inverse(inverse(X0)) % 6.74/6.82 double_divide(double_divide(identity, inverse(double_divide(identity, Y0))), inverse(identity)) -> Y0 % 6.74/6.82 double_divide(double_divide(identity, inverse(inverse(identity))), inverse(identity)) -> identity % 6.74/6.82 double_divide(double_divide(inverse(X0), X1), X1) -> inverse(X0) % 6.74/6.82 double_divide(double_divide(inverse(X0), double_divide(inverse(X0), inverse(Y1))), Y1) -> identity % 6.74/6.82 double_divide(double_divide(inverse(X0), double_divide(inverse(inverse(inverse(X0))), inverse(X1))), X1) -> identity % 6.74/6.82 double_divide(double_divide(inverse(Y1), double_divide(double_divide(identity, Y1), inverse(Y2))), inverse(identity)) -> Y2 % 6.74/6.82 double_divide(double_divide(inverse(double_divide(inverse(identity), double_divide(X1, inverse(identity)))), X1), inverse(identity)) -> identity % 6.74/6.82 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(Y1))), inverse(identity)) -> Y1 % 6.74/6.82 double_divide(double_divide(inverse(inverse(double_divide(identity, X0))), X0), inverse(identity)) -> identity % 6.74/6.82 double_divide(double_divide(inverse(inverse(identity)), double_divide(identity, inverse(Y1))), inverse(identity)) -> Y1 % 6.74/6.82 double_divide(double_divide(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))), double_divide(inverse(X0), inverse(Y1))), Y1) -> identity % 6.74/6.82 double_divide(identity, Y0) -> inverse(inverse(inverse(Y0))) % 6.74/6.82 double_divide(identity, double_divide(identity, inverse(inverse(Y0)))) -> Y0 % 6.74/6.82 double_divide(identity, inverse(inverse(identity))) -> identity % 6.74/6.82 double_divide(inverse(X0), X0) -> identity % 6.74/6.82 double_divide(inverse(X0), double_divide(inverse(X0), X1)) -> X1 % 6.74/6.82 double_divide(inverse(X0), double_divide(inverse(X0), inverse(X1))) -> inverse(X1) % 6.74/6.82 double_divide(inverse(X0), inverse(double_divide(X1, X0))) -> inverse(X1) % 6.74/6.82 double_divide(inverse(X0), inverse(inverse(inverse(inverse(X0))))) -> identity % 6.74/6.82 double_divide(inverse(X1), double_divide(X0, double_divide(X0, X1))) -> identity % 6.74/6.82 double_divide(inverse(X1), double_divide(inverse(X0), double_divide(inverse(X0), X1))) -> identity % 6.74/6.82 double_divide(inverse(Y0), double_divide(Y1, inverse(Y0))) -> Y1 % 6.74/6.82 double_divide(inverse(inverse(Y0)), inverse(identity)) -> double_divide(identity, Y0) % 6.74/6.82 double_divide(inverse(inverse(inverse(double_divide(inverse(inverse(inverse(X0))), double_divide(X1, inverse(X0)))))), X1) -> identity % 6.74/6.82 double_divide(inverse(inverse(inverse(inverse(inverse(X0))))), X0) -> identity % 6.74/6.82 double_divide(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))), X0) -> identity % 6.74/6.82 f1(inverse(double_divide(a, b))) -> false__ % 6.74/6.82 f1(inverse(double_divide(b, a))) -> true__ % 6.74/6.82 f1(multiply(a, b)) -> true__ % 6.74/6.82 f1(multiply(b, a)) -> false__ % 6.74/6.82 inverse(double_divide(X0, double_divide(inverse(inverse(X0)), inverse(Y1)))) -> Y1 % 6.74/6.82 inverse(double_divide(X0, inverse(inverse(inverse(X0))))) -> identity % 6.74/6.82 inverse(double_divide(X1, double_divide(X0, double_divide(X0, inverse(X1))))) -> identity % 6.74/6.82 inverse(double_divide(Y0, double_divide(Y0, X0))) -> inverse(X0) % 6.74/6.82 inverse(double_divide(Y0, double_divide(Y0, inverse(Y1)))) -> Y1 % 6.74/6.82 inverse(double_divide(Y0, double_divide(inverse(inverse(Y0)), X0))) -> inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))) % 6.74/6.82 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(Y0))))) -> Y1 % 6.74/6.82 inverse(double_divide(Y0, inverse(double_divide(inverse(Y0), Y1)))) -> Y1 % 6.74/6.82 inverse(double_divide(Y0, inverse(inverse(inverse(double_divide(Y1, inverse(inverse(inverse(Y0))))))))) -> Y1 % 6.74/6.82 inverse(double_divide(double_divide(X0, inverse(inverse(inverse(X0)))), inverse(inverse(inverse(inverse(Y1)))))) -> Y1 % 6.74/6.82 inverse(double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0 % 6.74/6.82 inverse(double_divide(identity, inverse(double_divide(identity, Y0)))) -> Y0 % 6.74/6.82 inverse(double_divide(inverse(X0), double_divide(X1, inverse(X0)))) -> inverse(X1) % 6.74/6.82 inverse(double_divide(inverse(X0), double_divide(inverse(X0), inverse(Y1)))) -> Y1 % 6.74/6.82 inverse(double_divide(inverse(X0), inverse(double_divide(Y1, X0)))) -> Y1 % 6.74/6.82 inverse(double_divide(inverse(X1), double_divide(X0, double_divide(X0, X1)))) -> identity % 6.74/6.82 inverse(double_divide(inverse(X1), double_divide(inverse(X0), double_divide(inverse(X0), X1)))) -> identity % 6.74/6.82 inverse(double_divide(inverse(Y0), Y0)) -> identity % 6.74/6.82 inverse(double_divide(inverse(Y0), double_divide(double_divide(identity, Y0), inverse(Y1)))) -> Y1 % 6.74/6.82 inverse(double_divide(inverse(Y0), double_divide(inverse(Y0), X0))) -> inverse(X0) % 6.74/6.82 inverse(double_divide(inverse(Y0), double_divide(inverse(inverse(inverse(Y0))), X0))) -> inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))) % 6.74/6.82 inverse(double_divide(inverse(Y0), double_divide(inverse(inverse(inverse(Y0))), inverse(Y1)))) -> Y1 % 6.74/6.82 inverse(double_divide(inverse(Y0), inverse(double_divide(Y0, Y1)))) -> Y1 % 6.74/6.82 inverse(double_divide(inverse(Y0), inverse(double_divide(identity, Y0)))) -> identity % 6.74/6.82 inverse(double_divide(inverse(Y0), inverse(inverse(inverse(inverse(Y0)))))) -> identity % 6.74/6.82 inverse(double_divide(inverse(inverse(double_divide(identity, Y0))), Y0)) -> identity % 6.74/6.82 inverse(double_divide(inverse(inverse(inverse(inverse(inverse(Y0))))), Y0)) -> identity % 6.74/6.82 inverse(double_divide(inverse(inverse(inverse(inverse(inverse(inverse(X0)))))), double_divide(X0, inverse(Y1)))) -> Y1 % 6.74/6.82 inverse(double_divide(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))), double_divide(inverse(X0), inverse(Y1)))) -> Y1 % 6.74/6.82 inverse(identity) -> identity % 6.74/6.82 inverse(inverse(Y0)) -> Y0 % 6.74/6.82 inverse(inverse(inverse(inverse(Y0)))) -> inverse(inverse(Y0)) % 6.74/6.82 inverse(inverse(inverse(inverse(double_divide(inverse(inverse(inverse(Y0))), double_divide(Y1, inverse(Y0))))))) -> Y1 % 6.74/6.82 inverse(inverse(inverse(inverse(inverse(Y0))))) -> inverse(inverse(inverse(Y0))) % 6.74/6.82 inverse(inverse(inverse(inverse(inverse(inverse(Y1)))))) -> Y1 % 6.74/6.82 inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(Y0)))))))) -> Y0 % 6.74/6.82 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 6.74/6.82 true__ -> false__ % 6.74/6.82 with the LPO induced by % 6.74/6.82 a > b > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 6.74/6.82 % 6.74/6.82 % SZS output end Proof % 6.74/6.82 %------------------------------------------------------------------------------