%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP492-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n029.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 10:55:48 EDT 2022 % Result : Unsatisfiable 25.57s 25.37s % Output : Proof 25.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP492-1 : TPTP v8.1.0. Released v2.6.0. % 0.11/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n029.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 % 0.13/0.34 % DateTime : Tue Jun 14 04:37:40 EDT 2022 % 0.13/0.34 % CPUTime : % 25.57/25.37 % SZS status Unsatisfiable % 25.57/25.37 % SZS output start Proof % 25.57/25.37 The input problem is unsatisfiable because % 25.57/25.37 % 25.57/25.37 [1] the following set of Horn clauses is unsatisfiable: % 25.57/25.37 % 25.57/25.37 double_divide(double_divide(identity, A), double_divide(identity, double_divide(double_divide(double_divide(A, B), identity), double_divide(C, B)))) = C % 25.57/25.37 multiply(A, B) = double_divide(double_divide(B, A), identity) % 25.57/25.37 inverse(A) = double_divide(A, identity) % 25.57/25.37 identity = double_divide(A, inverse(A)) % 25.57/25.37 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 25.57/25.37 % 25.57/25.37 This holds because % 25.57/25.37 % 25.57/25.37 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 25.57/25.37 % 25.57/25.37 E: % 25.57/25.37 double_divide(double_divide(identity, A), double_divide(identity, double_divide(double_divide(double_divide(A, B), identity), double_divide(C, B)))) = C % 25.57/25.37 f1(multiply(a3, multiply(b3, c3))) = false__ % 25.57/25.37 f1(multiply(multiply(a3, b3), c3)) = true__ % 25.57/25.37 identity = double_divide(A, inverse(A)) % 25.57/25.37 inverse(A) = double_divide(A, identity) % 25.57/25.37 multiply(A, B) = double_divide(double_divide(B, A), identity) % 25.57/25.37 G: % 25.57/25.37 true__ = false__ % 25.57/25.37 % 25.57/25.37 This holds because % 25.57/25.37 % 25.57/25.37 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 25.57/25.37 % 25.57/25.37 double_divide(X0, double_divide(Y1, double_divide(inverse(X0), Y2))) = double_divide(Y2, inverse(Y1)) % 25.57/25.37 double_divide(X0, double_divide(inverse(Y1), Y2)) = double_divide(double_divide(Y2, inverse(X0)), Y1) % 25.57/25.37 double_divide(X0, double_divide(inverse(Y1), double_divide(inverse(X0), Y2))) = double_divide(Y2, Y1) % 25.57/25.37 double_divide(X0, inverse(identity)) = inverse(inverse(double_divide(identity, double_divide(inverse(inverse(inverse(identity))), inverse(X0))))) % 25.57/25.37 double_divide(X2, inverse(X0)) = double_divide(inverse(X1), double_divide(X0, double_divide(X1, X2))) % 25.57/25.37 double_divide(Y0, X0) = inverse(double_divide(inverse(X0), inverse(Y0))) % 25.57/25.37 double_divide(Y0, double_divide(X1, X0)) = inverse(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y0))) % 25.57/25.37 double_divide(Y0, double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), inverse(Y0))) % 25.57/25.37 double_divide(Y0, double_divide(Y1, X1)) = double_divide(double_divide(X1, inverse(Y0)), inverse(Y1)) % 25.57/25.37 double_divide(Y0, double_divide(inverse(X1), X0)) = inverse(double_divide(double_divide(inverse(X0), X1), inverse(Y0))) % 25.57/25.37 double_divide(Y0, double_divide(inverse(X1), inverse(X0))) = inverse(double_divide(double_divide(X0, X1), inverse(Y0))) % 25.57/25.37 double_divide(Y0, inverse(X1)) = inverse(double_divide(X1, inverse(Y0))) % 25.57/25.37 double_divide(double_divide(X1, inverse(X0)), Y1) = inverse(double_divide(inverse(Y1), double_divide(X0, inverse(X1)))) % 25.57/25.37 double_divide(double_divide(inverse(X1), X0), Y1) = inverse(double_divide(inverse(Y1), double_divide(inverse(X0), X1))) % 25.57/25.37 double_divide(double_divide(inverse(X1), inverse(X0)), Y1) = inverse(double_divide(inverse(Y1), double_divide(X0, X1))) % 25.57/25.37 double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)) = inverse(double_divide(Y1, double_divide(X0, X1))) % 25.57/25.37 double_divide(inverse(X1), Y0) = inverse(double_divide(inverse(Y0), X1)) % 25.57/25.37 double_divide(inverse(Y0), double_divide(X0, Y2)) = double_divide(double_divide(Y2, Y0), inverse(X0)) % 25.57/25.37 double_divide(inverse(Y0), double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), Y0)) % 25.57/25.37 double_divide(inverse(Y0), double_divide(inverse(X1), X0)) = inverse(double_divide(double_divide(inverse(X0), X1), Y0)) % 25.57/25.37 double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0))) = inverse(double_divide(double_divide(X0, X1), Y0)) % 25.57/25.37 double_divide(inverse(Y0), double_divide(inverse(Y1), X1)) = double_divide(double_divide(X1, Y0), Y1) % 25.57/25.37 double_divide(inverse(Y0), double_divide(inverse(Y1), double_divide(Y0, X1))) = double_divide(X1, Y1) % 25.57/25.37 inverse(double_divide(Y0, X0)) = double_divide(inverse(X0), inverse(Y0)) % 25.57/25.37 inverse(double_divide(Y0, double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), inverse(Y0)) % 25.57/25.37 inverse(double_divide(Y0, double_divide(inverse(X1), X0))) = double_divide(double_divide(inverse(X0), X1), inverse(Y0)) % 25.57/25.37 inverse(double_divide(Y0, double_divide(inverse(X1), inverse(X0)))) = double_divide(double_divide(X0, X1), inverse(Y0)) % 25.57/25.37 inverse(double_divide(double_divide(inverse(X1), inverse(X0)), Y1)) = double_divide(inverse(Y1), double_divide(X0, X1)) % 25.57/25.37 inverse(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0)))) = double_divide(double_divide(X0, X1), Y0) % 25.57/25.37 double_divide(A, identity) -> inverse(A) % 25.57/25.37 double_divide(A, inverse(A)) -> identity % 25.57/25.37 double_divide(X0, double_divide(Y1, X0)) -> Y1 % 25.57/25.37 double_divide(X0, double_divide(identity, X0)) -> identity % 25.57/25.37 double_divide(X0, double_divide(identity, double_divide(inverse(X0), inverse(Y1)))) -> Y1 % 25.57/25.37 double_divide(X0, double_divide(inverse(Y1), double_divide(inverse(X0), double_divide(Y1, Y2)))) -> Y2 % 25.57/25.37 double_divide(X0, inverse(double_divide(inverse(Y1), double_divide(Y2, double_divide(Y1, inverse(X0)))))) -> Y2 % 25.57/25.37 double_divide(X0, inverse(double_divide(inverse(double_divide(inverse(X0), Y1)), double_divide(Y2, Y1)))) -> Y2 % 25.57/25.37 double_divide(Y0, double_divide(X0, double_divide(inverse(Y0), double_divide(inverse(X0), Y2)))) -> Y2 % 25.57/25.37 double_divide(Y0, inverse(double_divide(inverse(Y0), X0))) -> inverse(X0) % 25.57/25.37 double_divide(Y0, inverse(double_divide(inverse(Y0), inverse(Y1)))) -> Y1 % 25.57/25.37 double_divide(Y2, inverse(double_divide(double_divide(inverse(Y0), Y2), X1))) -> double_divide(Y0, X1) % 25.57/25.37 double_divide(double_divide(X0, X1), double_divide(inverse(X1), inverse(X0))) -> identity % 25.57/25.37 double_divide(double_divide(X0, X1), inverse(double_divide(double_divide(inverse(X1), inverse(X0)), Y1))) -> inverse(Y1) % 25.57/25.37 double_divide(double_divide(X0, X1), inverse(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)))) -> Y1 % 25.57/25.37 double_divide(double_divide(X1, X0), double_divide(Y1, inverse(double_divide(inverse(X0), inverse(X1))))) -> Y1 % 25.57/25.37 double_divide(double_divide(X1, Y1), X1) -> Y1 % 25.57/25.37 double_divide(double_divide(X1, inverse(X0)), X1) -> inverse(X0) % 25.57/25.37 double_divide(double_divide(Y0, double_divide(X0, X1)), double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y0))) -> identity % 25.57/25.37 double_divide(double_divide(double_divide(X0, X1), Y1), double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0)))) -> identity % 25.57/25.37 double_divide(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)), double_divide(Y1, double_divide(X0, X1))) -> identity % 25.57/25.37 double_divide(double_divide(identity, A), double_divide(identity, double_divide(double_divide(double_divide(A, B), identity), double_divide(C, B)))) -> C % 25.57/25.37 double_divide(double_divide(identity, X0), X0) -> identity % 25.57/25.37 double_divide(double_divide(identity, X0), inverse(inverse(X0))) -> identity % 25.57/25.37 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, X0))) -> inverse(X0) % 25.57/25.37 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, inverse(Y1)))) -> Y1 % 25.57/25.37 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(identity, double_divide(Y1, inverse(Y0))))) -> Y1 % 25.57/25.37 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(inverse(double_divide(Y0, Y1)), double_divide(Y2, Y1)))) -> Y2 % 25.57/25.37 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(inverse(identity), double_divide(Y2, inverse(Y0))))) -> Y2 % 25.57/25.37 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(inverse(inverse(Y0)), inverse(Y2)))) -> Y2 % 25.57/25.37 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(inverse(double_divide(Y0, inverse(Y2)))))) -> Y2 % 25.57/25.37 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(inverse(inverse(Y0))))) -> inverse(inverse(identity)) % 25.57/25.37 double_divide(double_divide(identity, Y0), inverse(double_divide(Y0, X0))) -> inverse(X0) % 25.57/25.37 double_divide(double_divide(identity, Y0), inverse(identity)) -> inverse(inverse(Y0)) % 25.57/25.37 double_divide(double_divide(identity, Y1), double_divide(identity, inverse(inverse(identity)))) -> Y1 % 25.57/25.37 double_divide(double_divide(identity, inverse(inverse(identity))), double_divide(identity, double_divide(inverse(identity), inverse(Y1)))) -> Y1 % 25.57/25.37 double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(X1, X0)) -> identity % 25.57/25.37 double_divide(double_divide(inverse(X1), inverse(X0)), double_divide(Y1, inverse(double_divide(X0, X1)))) -> Y1 % 25.57/25.37 double_divide(double_divide(inverse(X1), inverse(X0)), inverse(double_divide(double_divide(X0, X1), Y1))) -> inverse(Y1) % 25.57/25.37 double_divide(double_divide(inverse(X1), inverse(X0)), inverse(double_divide(double_divide(X0, X1), inverse(Y1)))) -> Y1 % 25.57/25.37 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0))), double_divide(double_divide(X0, X1), Y0)) -> identity % 25.57/25.37 double_divide(identity, X0) -> inverse(X0) % 25.57/25.37 double_divide(identity, double_divide(identity, X0)) -> inverse(inverse(X0)) % 25.57/25.37 double_divide(identity, double_divide(identity, double_divide(identity, X0))) -> double_divide(identity, X0) % 25.57/25.37 double_divide(identity, double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0 % 25.57/25.37 double_divide(identity, double_divide(identity, double_divide(inverse(double_divide(identity, Y0)), double_divide(Y1, Y0)))) -> Y1 % 25.57/25.37 double_divide(identity, double_divide(identity, double_divide(inverse(double_divide(inverse(identity), Y1)), double_divide(Y2, Y1)))) -> Y2 % 25.57/25.37 double_divide(identity, double_divide(identity, double_divide(inverse(identity), double_divide(Y1, inverse(inverse(identity)))))) -> Y1 % 25.57/25.37 double_divide(identity, double_divide(identity, double_divide(inverse(inverse(inverse(identity))), inverse(Y1)))) -> Y1 % 25.57/25.37 double_divide(identity, double_divide(identity, inverse(X0))) -> inverse(X0) % 25.57/25.37 double_divide(identity, double_divide(identity, inverse(inverse(double_divide(identity, inverse(Y0)))))) -> Y0 % 25.57/25.37 double_divide(identity, double_divide(identity, inverse(inverse(double_divide(inverse(identity), inverse(Y1)))))) -> Y1 % 25.57/25.37 double_divide(identity, double_divide(identity, inverse(inverse(identity)))) -> inverse(identity) % 25.57/25.37 double_divide(identity, inverse(X0)) -> inverse(inverse(X0)) % 25.57/25.37 double_divide(identity, inverse(inverse(identity))) -> identity % 25.57/25.37 double_divide(inverse(X0), X0) -> identity % 25.57/25.37 double_divide(inverse(X0), inverse(double_divide(X0, inverse(Y1)))) -> Y1 % 25.57/25.37 double_divide(inverse(Y0), double_divide(X0, double_divide(Y0, double_divide(inverse(X0), Y2)))) -> Y2 % 25.57/25.37 double_divide(inverse(Y0), double_divide(Y1, inverse(Y0))) -> Y1 % 25.57/25.37 double_divide(inverse(Y0), double_divide(inverse(X1), double_divide(Y0, double_divide(X1, Y2)))) -> Y2 % 25.57/25.37 double_divide(inverse(Y0), double_divide(inverse(double_divide(Y2, X1)), double_divide(Y0, X1))) -> Y2 % 25.57/25.37 double_divide(inverse(Y0), inverse(double_divide(Y0, Y1))) -> inverse(Y1) % 25.57/25.37 double_divide(inverse(Y0), inverse(double_divide(inverse(X1), double_divide(Y2, double_divide(X1, Y0))))) -> Y2 % 25.57/25.37 double_divide(inverse(Y0), inverse(double_divide(inverse(double_divide(Y0, Y1)), double_divide(Y2, Y1)))) -> Y2 % 25.57/25.37 double_divide(inverse(double_divide(X0, X1)), double_divide(Y1, double_divide(inverse(X1), inverse(X0)))) -> Y1 % 25.57/25.37 double_divide(inverse(double_divide(X0, X1)), inverse(double_divide(inverse(X1), inverse(X0)))) -> identity % 25.57/25.37 double_divide(inverse(double_divide(X0, inverse(X1))), X1) -> inverse(X0) % 25.57/25.37 double_divide(inverse(double_divide(Y2, X1)), double_divide(inverse(Y1), X1)) -> double_divide(Y2, Y1) % 25.57/25.37 double_divide(inverse(double_divide(inverse(X0), inverse(X1))), double_divide(Y1, double_divide(X1, X0))) -> Y1 % 25.57/25.37 double_divide(inverse(double_divide(inverse(X0), inverse(X1))), inverse(double_divide(X1, X0))) -> identity % 25.57/25.37 double_divide(inverse(double_divide(inverse(Y1), X1)), inverse(X1)) -> Y1 % 25.57/25.37 double_divide(inverse(double_divide(inverse(Y1), inverse(X1))), X1) -> Y1 % 25.57/25.37 double_divide(inverse(identity), double_divide(identity, double_divide(inverse(double_divide(identity, Y1)), double_divide(Y2, Y1)))) -> Y2 % 25.57/25.37 double_divide(inverse(identity), double_divide(identity, double_divide(inverse(identity), double_divide(Y1, inverse(identity))))) -> Y1 % 25.57/25.37 double_divide(inverse(identity), double_divide(identity, double_divide(inverse(inverse(identity)), inverse(Y1)))) -> Y1 % 25.57/25.37 double_divide(inverse(identity), double_divide(identity, inverse(inverse(double_divide(identity, inverse(Y1)))))) -> Y1 % 25.57/25.37 double_divide(inverse(identity), double_divide(identity, inverse(inverse(identity)))) -> identity % 25.57/25.37 double_divide(inverse(identity), inverse(identity)) -> inverse(inverse(identity)) % 25.57/25.37 f1(double_divide(double_divide(b3, a3), inverse(c3))) -> true__ % 25.57/25.37 f1(double_divide(inverse(a3), double_divide(false__, double_divide(inverse(b3), double_divide(inverse(false__), c3))))) -> false__ % 25.57/25.37 f1(double_divide(inverse(a3), double_divide(inverse(false__), double_divide(inverse(b3), double_divide(false__, c3))))) -> false__ % 25.57/25.37 f1(double_divide(inverse(a3), inverse(double_divide(inverse(b3), inverse(c3))))) -> false__ % 25.57/25.37 f1(double_divide(inverse(double_divide(inverse(a3), inverse(b3))), inverse(c3))) -> true__ % 25.57/25.37 f1(inverse(double_divide(c3, inverse(double_divide(b3, a3))))) -> true__ % 25.57/25.37 f1(inverse(double_divide(inverse(double_divide(c3, b3)), a3))) -> false__ % 25.57/25.37 f1(multiply(a3, multiply(b3, c3))) -> false__ % 25.57/25.37 f1(multiply(multiply(a3, b3), c3)) -> true__ % 25.57/25.37 inverse(double_divide(X0, double_divide(X1, X0))) -> inverse(X1) % 25.57/25.37 inverse(double_divide(double_divide(X1, Y1), X1)) -> inverse(Y1) % 25.57/25.37 inverse(double_divide(double_divide(X1, inverse(X2)), inverse(double_divide(X1, double_divide(inverse(Y1), X2))))) -> Y1 % 25.57/25.37 inverse(double_divide(double_divide(inverse(X1), inverse(X2)), inverse(double_divide(inverse(X1), double_divide(X0, X2))))) -> inverse(X0) % 25.57/25.37 inverse(double_divide(identity, Y0)) -> Y0 % 25.57/25.37 inverse(double_divide(identity, Y0)) -> inverse(inverse(Y0)) % 25.57/25.37 inverse(double_divide(inverse(double_divide(inverse(Y1), X1)), double_divide(double_divide(Y1, Y2), X1))) -> Y2 % 25.57/25.37 inverse(identity) -> identity % 25.57/25.37 inverse(inverse(Y0)) -> Y0 % 25.57/25.37 inverse(inverse(double_divide(identity, double_divide(identity, inverse(X0))))) -> inverse(X0) % 25.57/25.37 inverse(inverse(double_divide(identity, inverse(inverse(identity))))) -> inverse(inverse(identity)) % 25.57/25.37 inverse(inverse(identity)) -> inverse(identity) % 25.57/25.37 inverse(inverse(inverse(identity))) -> identity % 25.57/25.37 inverse(inverse(inverse(inverse(X0)))) -> inverse(inverse(X0)) % 25.57/25.37 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 25.57/25.37 true__ -> false__ % 25.57/25.37 with the LPO induced by % 25.57/25.37 c3 > b3 > a3 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 25.57/25.37 % 25.57/25.37 % SZS output end Proof % 25.57/25.37 %------------------------------------------------------------------------------