%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP572-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n026.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 10:56:21 EDT 2022 % Result : Unsatisfiable 7.09s 7.07s % Output : Proof 7.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : GRP572-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.04/0.14 % Command : moca.sh %s % 0.15/0.36 % Computer : n026.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Mon Jun 13 10:06:06 EDT 2022 % 0.15/0.36 % CPUTime : % 7.09/7.07 % SZS status Unsatisfiable % 7.09/7.07 % SZS output start Proof % 7.09/7.07 The input problem is unsatisfiable because % 7.09/7.07 % 7.09/7.07 [1] the following set of Horn clauses is unsatisfiable: % 7.09/7.07 % 7.09/7.07 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B % 7.09/7.07 multiply(A, B) = double_divide(double_divide(B, A), identity) % 7.09/7.07 inverse(A) = double_divide(A, identity) % 7.09/7.07 identity = double_divide(A, inverse(A)) % 7.09/7.07 multiply(a, b) = multiply(b, a) ==> \bottom % 7.09/7.07 % 7.09/7.07 This holds because % 7.09/7.07 % 7.09/7.07 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 7.09/7.07 % 7.09/7.07 E: % 7.09/7.07 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B % 7.09/7.07 f1(multiply(a, b)) = true__ % 7.09/7.07 f1(multiply(b, a)) = false__ % 7.09/7.07 identity = double_divide(A, inverse(A)) % 7.09/7.07 inverse(A) = double_divide(A, identity) % 7.09/7.07 multiply(A, B) = double_divide(double_divide(B, A), identity) % 7.09/7.07 G: % 7.09/7.07 true__ = false__ % 7.09/7.07 % 7.09/7.07 This holds because % 7.09/7.07 % 7.09/7.07 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 7.09/7.07 % 7.09/7.07 double_divide(Y0, X0) = double_divide(X0, Y0) % 7.09/7.07 double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 7.09/7.07 double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))) = double_divide(false__, double_divide(double_divide(Y1, inverse(false__)), inverse(identity))) % 7.09/7.07 double_divide(Y0, double_divide(inverse(Y1), inverse(inverse(Y0)))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 7.09/7.07 double_divide(Y0, inverse(double_divide(X1, X0))) = inverse(double_divide(double_divide(X0, X1), inverse(Y0))) % 7.09/7.07 double_divide(double_divide(identity, double_divide(X1, inverse(identity))), inverse(identity)) = double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), inverse(X2))) % 7.09/7.07 double_divide(false__, double_divide(double_divide(X1, inverse(false__)), inverse(identity))) = double_divide(X0, double_divide(inverse(X1), inverse(inverse(X0)))) % 7.09/7.07 double_divide(false__, inverse(X0)) = inverse(double_divide(X0, inverse(false__))) % 7.09/7.07 inverse(double_divide(X1, inverse(X0))) = double_divide(X0, inverse(X1)) % 7.09/7.07 inverse(double_divide(Y0, X0)) = inverse(double_divide(X0, Y0)) % 7.09/7.07 inverse(double_divide(Y0, inverse(double_divide(X1, X0)))) = double_divide(double_divide(X0, X1), inverse(Y0)) % 7.09/7.07 inverse(double_divide(false__, inverse(X0))) = double_divide(X0, inverse(false__)) % 7.09/7.07 double_divide(A, identity) -> inverse(A) % 7.09/7.07 double_divide(A, inverse(A)) -> identity % 7.09/7.07 double_divide(X0, double_divide(X0, inverse(X1))) -> inverse(X1) % 7.09/7.07 double_divide(X0, double_divide(X0, inverse(false__))) -> inverse(false__) % 7.09/7.07 double_divide(X0, double_divide(X1, X0)) -> X1 % 7.09/7.07 double_divide(X0, double_divide(X2, double_divide(X1, double_divide(X0, inverse(X2))))) -> inverse(X1) % 7.09/7.07 double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), inverse(X2))) -> inverse(X1) % 7.09/7.07 double_divide(X0, double_divide(inverse(X1), X0)) -> inverse(X1) % 7.09/7.07 double_divide(X0, inverse(double_divide(X1, inverse(X0)))) -> inverse(X1) % 7.09/7.07 double_divide(X1, double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), inverse(X2)))) -> identity % 7.09/7.07 double_divide(X1, double_divide(X0, double_divide(inverse(X1), X0))) -> identity % 7.09/7.07 double_divide(X1, double_divide(X1, Y0)) -> Y0 % 7.09/7.07 double_divide(Y0, double_divide(double_divide(identity, inverse(Y0)), inverse(identity))) -> identity % 7.09/7.07 double_divide(Y0, double_divide(identity, Y0)) -> identity % 7.09/7.07 double_divide(Y0, double_divide(identity, inverse(inverse(Y0)))) -> identity % 7.09/7.07 double_divide(Y0, double_divide(inverse(false__), Y0)) -> inverse(false__) % 7.09/7.07 double_divide(Y0, double_divide(inverse(identity), inverse(inverse(Y0)))) -> identity % 7.09/7.07 double_divide(Y0, inverse(double_divide(double_divide(Y0, X0), X0))) -> identity % 7.09/7.07 double_divide(Y0, inverse(double_divide(double_divide(Y0, inverse(X0)), inverse(X0)))) -> identity % 7.09/7.07 double_divide(Y0, inverse(double_divide(identity, inverse(Y0)))) -> identity % 7.09/7.07 double_divide(Y1, double_divide(double_divide(identity, double_divide(Y1, Y2)), inverse(Y2))) -> double_divide(inverse(identity), inverse(identity)) % 7.09/7.07 double_divide(Y1, double_divide(inverse(false__), inverse(inverse(Y1)))) -> inverse(false__) % 7.09/7.07 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) -> B % 7.09/7.07 double_divide(double_divide(X0, double_divide(X1, X0)), inverse(X1)) -> identity % 7.09/7.07 double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), inverse(X2))), X1) -> identity % 7.09/7.07 double_divide(double_divide(X0, double_divide(inverse(X1), X0)), X1) -> identity % 7.09/7.07 double_divide(double_divide(X0, inverse(false__)), double_divide(false__, inverse(X0))) -> identity % 7.09/7.07 double_divide(double_divide(X0, inverse(false__)), inverse(double_divide(double_divide(false__, inverse(X0)), inverse(Y1)))) -> Y1 % 7.09/7.07 double_divide(double_divide(X1, Y1), X1) -> Y1 % 7.09/7.07 double_divide(double_divide(X1, inverse(Y1)), X1) -> inverse(Y1) % 7.09/7.07 double_divide(double_divide(X1, inverse(false__)), X1) -> inverse(false__) % 7.09/7.07 double_divide(double_divide(Y0, X0), X0) -> Y0 % 7.09/7.07 double_divide(double_divide(Y0, double_divide(X0, inverse(false__))), inverse(double_divide(false__, inverse(X0)))) -> Y0 % 7.09/7.07 double_divide(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, Y2)), inverse(Y2))), inverse(identity)) -> Y1 % 7.09/7.07 double_divide(double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))), inverse(identity)) -> Y1 % 7.09/7.07 double_divide(double_divide(Y0, double_divide(inverse(Y1), inverse(inverse(Y0)))), inverse(identity)) -> Y1 % 7.09/7.07 double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2)) -> Y1 % 7.09/7.07 double_divide(double_divide(Y1, inverse(false__)), inverse(false__)) -> Y1 % 7.09/7.07 double_divide(double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), inverse(X2))), double_divide(double_divide(Y1, X1), inverse(inverse(identity)))), inverse(identity)) -> Y1 % 7.09/7.07 double_divide(double_divide(double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))), double_divide(double_divide(Y3, Y1), inverse(inverse(identity)))), inverse(identity)) -> Y3 % 7.09/7.07 double_divide(double_divide(double_divide(Y0, double_divide(double_divide(identity, double_divide(Y0, Y2)), inverse(Y2))), double_divide(inverse(Y3), inverse(inverse(identity)))), inverse(identity)) -> Y3 % 7.09/7.07 double_divide(double_divide(double_divide(Y0, double_divide(inverse(Y1), inverse(inverse(Y0)))), double_divide(double_divide(Y3, Y1), inverse(inverse(identity)))), inverse(identity)) -> Y3 % 7.09/7.07 double_divide(double_divide(false__, inverse(X0)), double_divide(X0, inverse(false__))) -> identity % 7.09/7.07 double_divide(double_divide(identity, X0), X0) -> identity % 7.09/7.07 double_divide(double_divide(identity, X0), double_divide(identity, inverse(X0))) -> identity % 7.09/7.07 double_divide(double_divide(inverse(X0), double_divide(double_divide(Y1, X0), inverse(inverse(identity)))), inverse(identity)) -> Y1 % 7.09/7.07 double_divide(double_divide(inverse(X1), Y1), inverse(X1)) -> Y1 % 7.09/7.07 double_divide(double_divide(inverse(false__), Y1), inverse(false__)) -> Y1 % 7.09/7.07 double_divide(double_divide(inverse(identity), double_divide(inverse(Y1), inverse(inverse(identity)))), inverse(identity)) -> Y1 % 7.09/7.07 double_divide(double_divide(inverse(inverse(Y1)), double_divide(identity, inverse(inverse(identity)))), inverse(identity)) -> Y1 % 7.09/7.07 double_divide(false__, double_divide(double_divide(X0, inverse(false__)), inverse(identity))) -> inverse(X0) % 7.09/7.07 double_divide(false__, double_divide(false__, Y1)) -> Y1 % 7.09/7.07 double_divide(false__, inverse(double_divide(Y0, inverse(false__)))) -> inverse(Y0) % 7.09/7.07 double_divide(identity, X0) -> inverse(X0) % 7.09/7.07 double_divide(identity, false__) -> inverse(false__) % 7.09/7.07 double_divide(identity, inverse(inverse(false__))) -> inverse(false__) % 7.09/7.07 double_divide(inverse(X0), X0) -> identity % 7.09/7.07 double_divide(inverse(X0), double_divide(double_divide(identity, X0), inverse(inverse(identity)))) -> identity % 7.09/7.07 double_divide(inverse(X0), double_divide(identity, inverse(X0))) -> identity % 7.09/7.07 double_divide(inverse(X0), double_divide(inverse(false__), inverse(X0))) -> inverse(false__) % 7.09/7.07 double_divide(inverse(X0), false__) -> inverse(double_divide(X0, inverse(false__))) % 7.09/7.07 double_divide(inverse(X0), inverse(double_divide(X1, X0))) -> inverse(X1) % 7.09/7.07 double_divide(inverse(X1), double_divide(X0, double_divide(X1, X0))) -> identity % 7.09/7.07 double_divide(inverse(Y0), X1) -> inverse(double_divide(Y0, inverse(X1))) % 7.09/7.07 double_divide(inverse(Y0), inverse(double_divide(identity, Y0))) -> identity % 7.09/7.07 double_divide(inverse(Y0), inverse(identity)) -> Y0 % 7.09/7.07 double_divide(inverse(double_divide(X0, inverse(false__))), inverse(X0)) -> false__ % 7.09/7.07 double_divide(inverse(identity), double_divide(identity, inverse(inverse(identity)))) -> identity % 7.09/7.07 double_divide(inverse(inverse(identity)), double_divide(identity, inverse(inverse(identity)))) -> identity % 7.09/7.07 f1(inverse(double_divide(a, b))) -> false__ % 7.09/7.07 f1(inverse(double_divide(b, a))) -> true__ % 7.09/7.07 f1(multiply(a, b)) -> true__ % 7.09/7.07 f1(multiply(b, a)) -> false__ % 7.09/7.07 inverse(double_divide(X0, double_divide(X0, Y1))) -> inverse(Y1) % 7.09/7.07 inverse(double_divide(Y0, double_divide(X0, Y0))) -> inverse(X0) % 7.09/7.07 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, Y2)), inverse(Y2)))) -> Y1 % 7.09/7.07 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, inverse(X0))), X0))) -> Y1 % 7.09/7.07 inverse(double_divide(Y0, double_divide(inverse(Y1), Y0))) -> Y1 % 7.09/7.07 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(Y0))))) -> Y1 % 7.09/7.07 inverse(double_divide(double_divide(X1, Y1), X1)) -> inverse(Y1) % 7.09/7.07 inverse(double_divide(double_divide(X1, inverse(Y1)), X1)) -> Y1 % 7.09/7.07 inverse(double_divide(double_divide(false__, inverse(X0)), inverse(double_divide(double_divide(X0, inverse(false__)), Y1)))) -> Y1 % 7.09/7.07 inverse(double_divide(identity, Y1)) -> Y1 % 7.09/7.07 inverse(double_divide(inverse(X0), inverse(double_divide(Y1, X0)))) -> Y1 % 7.09/7.07 inverse(double_divide(inverse(Y0), inverse(X1))) -> double_divide(Y0, X1) % 7.09/7.07 inverse(double_divide(inverse(double_divide(X1, Y1)), inverse(X1))) -> Y1 % 7.09/7.07 inverse(double_divide(inverse(false__), X1)) -> double_divide(false__, inverse(X1)) % 7.09/7.07 inverse(identity) -> identity % 7.09/7.07 inverse(inverse(Y0)) -> Y0 % 7.09/7.07 inverse(inverse(identity)) -> identity % 7.09/7.07 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 7.09/7.07 true__ -> false__ % 7.09/7.07 with the LPO induced by % 7.09/7.07 a > b > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 7.09/7.07 % 7.09/7.07 % SZS output end Proof % 7.09/7.07 %------------------------------------------------------------------------------