%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP575-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n023.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 10:56:23 EDT 2022 % Result : Unsatisfiable 41.28s 41.14s % Output : Proof 41.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP575-1 : TPTP v8.1.0. Released v2.6.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.35 % Computer : n023.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Tue Jun 14 05:32:36 EDT 2022 % 0.13/0.35 % CPUTime : % 41.28/41.14 % SZS status Unsatisfiable % 41.28/41.14 % SZS output start Proof % 41.28/41.14 The input problem is unsatisfiable because % 41.28/41.14 % 41.28/41.14 [1] the following set of Horn clauses is unsatisfiable: % 41.28/41.14 % 41.28/41.14 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) = B % 41.28/41.14 multiply(A, B) = double_divide(double_divide(B, A), identity) % 41.28/41.14 inverse(A) = double_divide(A, identity) % 41.28/41.14 identity = double_divide(A, inverse(A)) % 41.28/41.14 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 41.28/41.14 % 41.28/41.14 This holds because % 41.28/41.14 % 41.28/41.14 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 41.28/41.14 % 41.28/41.14 E: % 41.28/41.14 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) = B % 41.28/41.14 f1(multiply(a3, multiply(b3, c3))) = false__ % 41.28/41.14 f1(multiply(multiply(a3, b3), c3)) = true__ % 41.28/41.14 identity = double_divide(A, inverse(A)) % 41.28/41.14 inverse(A) = double_divide(A, identity) % 41.28/41.14 multiply(A, B) = double_divide(double_divide(B, A), identity) % 41.28/41.14 G: % 41.28/41.14 true__ = false__ % 41.28/41.14 % 41.28/41.14 This holds because % 41.28/41.14 % 41.28/41.14 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 41.28/41.14 % 41.28/41.14 double_divide(X1, double_divide(X0, inverse(Y1))) = double_divide(Y1, double_divide(X0, inverse(X1))) % 41.28/41.14 double_divide(Y0, X0) = double_divide(X0, Y0) % 41.28/41.14 double_divide(Y0, double_divide(Y1, X0)) = inverse(double_divide(Y1, inverse(double_divide(X0, inverse(Y0))))) % 41.28/41.14 double_divide(Y0, inverse(double_divide(X1, X0))) = double_divide(X0, inverse(double_divide(X1, Y0))) % 41.28/41.14 double_divide(Y0, inverse(double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), Y0) % 41.28/41.14 double_divide(double_divide(X1, X0), Y1) = double_divide(Y1, double_divide(X0, X1)) % 41.28/41.14 double_divide(double_divide(Y1, Y2), Y0) = inverse(double_divide(Y2, double_divide(Y0, inverse(Y1)))) % 41.28/41.14 double_divide(double_divide(identity, double_divide(X1, inverse(identity))), inverse(identity)) = double_divide(X0, double_divide(double_divide(X1, double_divide(X2, X0)), inverse(X2))) % 41.28/41.14 double_divide(identity, double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 41.28/41.14 double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1))) = double_divide(inverse(identity), inverse(identity)) % 41.28/41.14 double_divide(inverse(Y2), double_divide(inverse(Y1), inverse(Y2))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 41.28/41.14 inverse(double_divide(X1, double_divide(X2, X0))) = double_divide(X0, double_divide(X1, inverse(X2))) % 41.28/41.14 inverse(double_divide(Y0, X0)) = double_divide(inverse(X0), inverse(Y0)) % 41.28/41.14 inverse(double_divide(Y0, double_divide(X0, inverse(Y2)))) = double_divide(X0, double_divide(Y2, Y0)) % 41.28/41.14 inverse(double_divide(Y0, double_divide(X1, X0))) = double_divide(X0, inverse(double_divide(X1, inverse(Y0)))) % 41.28/41.14 inverse(double_divide(Y0, double_divide(X1, X0))) = inverse(double_divide(double_divide(X0, X1), Y0)) % 41.28/41.14 inverse(double_divide(Y0, double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), inverse(Y0)) % 41.28/41.14 inverse(double_divide(Y0, double_divide(Y1, X0))) = double_divide(Y1, inverse(double_divide(X0, inverse(Y0)))) % 41.28/41.14 inverse(double_divide(Y0, double_divide(Y2, Y1))) = double_divide(Y2, double_divide(Y0, inverse(Y1))) % 41.28/41.14 inverse(double_divide(Y0, inverse(X0))) = double_divide(X0, inverse(Y0)) % 41.28/41.14 inverse(double_divide(Y0, inverse(double_divide(X1, X0)))) = double_divide(double_divide(X0, X1), inverse(Y0)) % 41.28/41.14 inverse(double_divide(Y0, inverse(double_divide(X1, X0)))) = inverse(double_divide(X0, inverse(double_divide(X1, Y0)))) % 41.28/41.14 inverse(double_divide(Y0, inverse(double_divide(Y2, inverse(Y1))))) = double_divide(Y1, double_divide(Y2, Y0)) % 41.28/41.14 inverse(double_divide(double_divide(X1, X0), inverse(Y1))) = double_divide(Y1, inverse(double_divide(X0, X1))) % 41.28/41.14 inverse(double_divide(double_divide(X1, inverse(X0)), Y1)) = double_divide(double_divide(X0, inverse(X1)), inverse(Y1)) % 41.28/41.14 inverse(double_divide(double_divide(X1, inverse(X0)), inverse(Y1))) = double_divide(Y1, double_divide(X0, inverse(X1))) % 41.28/41.14 inverse(double_divide(double_divide(Y1, Y2), Y0)) = double_divide(Y2, double_divide(Y0, inverse(Y1))) % 41.28/41.14 inverse(double_divide(inverse(Y0), inverse(X0))) = double_divide(X0, Y0) % 41.28/41.14 double_divide(A, identity) -> inverse(A) % 41.28/41.14 double_divide(A, inverse(A)) -> identity % 41.28/41.14 double_divide(X0, double_divide(X1, X0)) -> X1 % 41.28/41.14 double_divide(X0, double_divide(X1, double_divide(X2, inverse(double_divide(X1, inverse(X0)))))) -> inverse(X2) % 41.28/41.14 double_divide(X0, double_divide(X1, inverse(double_divide(Y0, double_divide(X1, inverse(X0)))))) -> Y0 % 41.28/41.14 double_divide(X0, double_divide(Y0, inverse(double_divide(Y1, inverse(double_divide(X0, inverse(Y0))))))) -> Y1 % 41.28/41.14 double_divide(X0, double_divide(identity, X0)) -> identity % 41.28/41.14 double_divide(X0, double_divide(inverse(X1), X0)) -> inverse(inverse(inverse(X1))) % 41.28/41.14 double_divide(X0, inverse(double_divide(X1, double_divide(Y0, inverse(double_divide(X0, X1)))))) -> Y0 % 41.28/41.14 double_divide(X0, inverse(double_divide(X1, inverse(X0)))) -> inverse(X1) % 41.28/41.14 double_divide(X0, inverse(double_divide(X2, inverse(double_divide(X1, double_divide(X2, X0)))))) -> inverse(X1) % 41.28/41.14 double_divide(X0, inverse(double_divide(X2, inverse(double_divide(double_divide(X2, X0), X1))))) -> inverse(X1) % 41.28/41.14 double_divide(X0, inverse(double_divide(Y1, double_divide(Y2, inverse(double_divide(Y1, X0)))))) -> Y2 % 41.28/41.14 double_divide(X1, double_divide(X0, double_divide(double_divide(X1, inverse(X0)), inverse(Y0)))) -> Y0 % 41.28/41.14 double_divide(X1, double_divide(X0, inverse(double_divide(X2, inverse(double_divide(double_divide(X2, X0), X1)))))) -> identity % 41.28/41.14 double_divide(X1, double_divide(X1, Y0)) -> Y0 % 41.28/41.14 double_divide(X1, double_divide(inverse(X0), inverse(double_divide(X1, X0)))) -> identity % 41.28/41.14 double_divide(X1, inverse(double_divide(X0, inverse(double_divide(double_divide(X1, X0), inverse(Y0)))))) -> Y0 % 41.28/41.14 double_divide(X2, double_divide(X0, double_divide(X1, inverse(double_divide(double_divide(X1, inverse(X0)), inverse(X2)))))) -> identity % 41.28/41.14 double_divide(X2, inverse(double_divide(X0, inverse(double_divide(X1, double_divide(X2, X0)))))) -> inverse(X1) % 41.28/41.14 double_divide(Y1, double_divide(double_divide(identity, double_divide(Y2, Y1)), inverse(Y2))) -> double_divide(inverse(identity), inverse(identity)) % 41.28/41.14 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) -> B % 41.28/41.14 double_divide(double_divide(X0, X1), double_divide(inverse(X1), inverse(X0))) -> identity % 41.28/41.14 double_divide(double_divide(X0, double_divide(X1, X2)), inverse(double_divide(double_divide(X2, X1), X0))) -> identity % 41.28/41.14 double_divide(double_divide(X0, double_divide(X1, inverse(X2))), double_divide(X1, double_divide(X2, X0))) -> identity % 41.28/41.14 double_divide(double_divide(X0, double_divide(inverse(X1), X0)), X1) -> identity % 41.28/41.14 double_divide(double_divide(X0, inverse(X1)), inverse(double_divide(Y1, double_divide(X1, inverse(X0))))) -> inverse(Y1) % 41.28/41.14 double_divide(double_divide(X0, inverse(double_divide(X1, X2))), double_divide(double_divide(X2, X1), inverse(X0))) -> identity % 41.28/41.14 double_divide(double_divide(X0, inverse(double_divide(X1, inverse(X0)))), X1) -> identity % 41.28/41.14 double_divide(double_divide(Y0, X0), X0) -> Y0 % 41.28/41.14 double_divide(double_divide(Y0, double_divide(X0, Y0)), inverse(X0)) -> identity % 41.28/41.14 double_divide(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y2, Y0)), inverse(Y2))), inverse(identity)) -> Y1 % 41.28/41.14 double_divide(double_divide(Y0, inverse(Y1)), inverse(Y1)) -> Y0 % 41.28/41.14 double_divide(double_divide(Y2, Y1), double_divide(X0, double_divide(Y1, Y2))) -> X0 % 41.28/41.14 double_divide(double_divide(double_divide(X0, X1), X2), inverse(double_divide(X2, double_divide(X1, X0)))) -> identity % 41.28/41.14 double_divide(double_divide(double_divide(X0, X1), inverse(X2)), double_divide(X2, inverse(double_divide(X1, X0)))) -> identity % 41.28/41.14 double_divide(double_divide(identity, X0), inverse(inverse(X0))) -> identity % 41.28/41.14 double_divide(double_divide(identity, double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2))), inverse(identity)) -> Y1 % 41.28/41.14 double_divide(double_divide(identity, double_divide(identity, inverse(X0))), X0) -> identity % 41.28/41.14 double_divide(double_divide(identity, double_divide(identity, inverse(Y1))), inverse(identity)) -> Y1 % 41.28/41.14 double_divide(double_divide(inverse(X0), double_divide(inverse(X1), inverse(X0))), X1) -> identity % 41.28/41.14 double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(X1, X0)) -> identity % 41.28/41.14 double_divide(double_divide(inverse(X0), inverse(double_divide(X1, X0))), X1) -> identity % 41.28/41.14 double_divide(double_divide(inverse(Y2), double_divide(inverse(Y1), inverse(Y2))), inverse(identity)) -> Y1 % 41.28/41.14 double_divide(double_divide(inverse(identity), X0), inverse(identity)) -> inverse(inverse(X0)) % 41.28/41.14 double_divide(double_divide(inverse(identity), double_divide(double_divide(Y0, Y1), inverse(double_divide(identity, double_divide(double_divide(Y1, inverse(Y3)), inverse(Y3)))))), inverse(identity)) -> Y0 % 41.28/41.14 double_divide(double_divide(inverse(identity), double_divide(double_divide(Y1, X0), inverse(inverse(inverse(inverse(X0)))))), inverse(identity)) -> Y1 % 41.28/41.14 double_divide(double_divide(inverse(identity), double_divide(double_divide(Y1, X1), inverse(double_divide(X0, double_divide(double_divide(X1, double_divide(X2, X0)), inverse(X2)))))), inverse(identity)) -> Y1 % 41.28/41.14 double_divide(double_divide(inverse(identity), double_divide(inverse(Y0), inverse(double_divide(Y2, double_divide(double_divide(identity, double_divide(Y3, Y2)), inverse(Y3)))))), inverse(identity)) -> Y0 % 41.28/41.14 double_divide(identity, X0) -> inverse(X0) % 41.28/41.14 double_divide(identity, double_divide(double_divide(X0, inverse(false__)), inverse(false__))) -> inverse(inverse(inverse(X0))) % 41.28/41.14 double_divide(identity, double_divide(double_divide(Y1, inverse(false__)), inverse(false__))) -> double_divide(identity, double_divide(identity, inverse(Y1))) % 41.28/41.14 double_divide(identity, double_divide(double_divide(identity, inverse(Y1)), inverse(Y1))) -> double_divide(inverse(identity), inverse(identity)) % 41.28/41.14 double_divide(identity, double_divide(identity, X0)) -> inverse(inverse(X0)) % 41.28/41.14 double_divide(identity, double_divide(identity, inverse(X0))) -> inverse(inverse(inverse(X0))) % 41.28/41.14 double_divide(identity, double_divide(identity, inverse(false__))) -> inverse(inverse(inverse(false__))) % 41.28/41.14 double_divide(identity, double_divide(identity, inverse(inverse(Y1)))) -> Y1 % 41.28/41.14 double_divide(inverse(X0), X0) -> identity % 41.28/41.14 double_divide(inverse(X0), double_divide(inverse(X1), inverse(X0))) -> inverse(inverse(inverse(X1))) % 41.28/41.14 double_divide(inverse(X0), inverse(double_divide(X1, X0))) -> inverse(X1) % 41.28/41.14 double_divide(inverse(X1), inverse(double_divide(X1, inverse(Y1)))) -> Y1 % 41.28/41.14 double_divide(inverse(Y0), double_divide(identity, inverse(Y0))) -> identity % 41.28/41.14 double_divide(inverse(Y0), double_divide(inverse(identity), inverse(Y0))) -> identity % 41.28/41.14 double_divide(inverse(Y1), Y0) -> inverse(double_divide(Y1, inverse(Y0))) % 41.28/41.14 double_divide(inverse(Y1), inverse(Y0)) -> inverse(double_divide(Y1, Y0)) % 41.28/41.14 double_divide(inverse(identity), inverse(identity)) -> identity % 41.28/41.14 double_divide(inverse(inverse(X1)), double_divide(X0, double_divide(inverse(X1), X0))) -> identity % 41.28/41.14 double_divide(inverse(inverse(identity)), inverse(identity)) -> inverse(inverse(identity)) % 41.28/41.15 double_divide(inverse(inverse(inverse(X0))), X0) -> identity % 41.28/41.15 double_divide(inverse(inverse(inverse(Y1))), inverse(identity)) -> Y1 % 41.28/41.15 f1(double_divide(double_divide(a3, b3), inverse(c3))) -> true__ % 41.28/41.15 f1(double_divide(inverse(a3), inverse(double_divide(inverse(b3), inverse(c3))))) -> false__ % 41.28/41.15 f1(double_divide(inverse(double_divide(inverse(a3), inverse(b3))), inverse(c3))) -> true__ % 41.28/41.15 f1(inverse(double_divide(a3, double_divide(inverse(b3), inverse(c3))))) -> false__ % 41.28/41.15 f1(inverse(double_divide(a3, inverse(double_divide(b3, c3))))) -> false__ % 41.28/41.15 f1(inverse(double_divide(c3, inverse(double_divide(b3, a3))))) -> true__ % 41.28/41.15 f1(inverse(double_divide(inverse(double_divide(c3, b3)), a3))) -> false__ % 41.28/41.15 f1(multiply(a3, multiply(b3, c3))) -> false__ % 41.28/41.15 f1(multiply(multiply(a3, b3), c3)) -> true__ % 41.28/41.15 inverse(double_divide(X0, double_divide(inverse(Y1), X0))) -> Y1 % 41.28/41.15 inverse(double_divide(X1, double_divide(X0, inverse(double_divide(X2, inverse(double_divide(double_divide(X2, X0), X1))))))) -> identity % 41.28/41.15 inverse(double_divide(X1, double_divide(inverse(X0), inverse(double_divide(X1, X0))))) -> identity % 41.28/41.15 inverse(double_divide(X2, inverse(double_divide(double_divide(X0, inverse(X1)), inverse(double_divide(X0, double_divide(X1, X2))))))) -> identity % 41.28/41.15 inverse(double_divide(Y0, double_divide(X0, Y0))) -> inverse(inverse(inverse(X0))) % 41.28/41.15 inverse(double_divide(Y0, double_divide(X0, double_divide(Y1, inverse(double_divide(X0, inverse(Y0))))))) -> Y1 % 41.28/41.15 inverse(double_divide(Y0, double_divide(X0, inverse(double_divide(double_divide(X0, inverse(Y0)), inverse(Y1)))))) -> Y1 % 41.28/41.15 inverse(double_divide(Y0, double_divide(double_divide(X0, inverse(X1)), inverse(double_divide(double_divide(X1, inverse(X0)), Y0))))) -> identity % 41.28/41.15 inverse(double_divide(Y0, double_divide(double_divide(Y1, X0), inverse(double_divide(X0, Y0))))) -> Y1 % 41.28/41.15 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y2, Y0)), inverse(Y2)))) -> Y1 % 41.28/41.15 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(Y0))))) -> Y1 % 41.28/41.15 inverse(double_divide(Y0, inverse(double_divide(Y2, inverse(double_divide(double_divide(Y0, Y2), Y1)))))) -> Y1 % 41.28/41.15 inverse(double_divide(Y0, inverse(inverse(inverse(Y0))))) -> identity % 41.28/41.15 inverse(double_divide(double_divide(X0, X1), double_divide(Y1, double_divide(X1, X0)))) -> inverse(Y1) % 41.28/41.15 inverse(double_divide(double_divide(X0, inverse(X1)), inverse(double_divide(Y1, double_divide(X1, inverse(X0)))))) -> Y1 % 41.28/41.15 inverse(double_divide(double_divide(X1, Y2), double_divide(double_divide(Y1, X1), inverse(Y2)))) -> Y1 % 41.28/41.15 inverse(double_divide(double_divide(X1, inverse(X0)), inverse(double_divide(double_divide(X0, inverse(X1)), Y1)))) -> Y1 % 41.28/41.15 inverse(double_divide(double_divide(Y1, inverse(Y2)), Y0)) -> double_divide(Y1, double_divide(Y2, Y0)) % 41.28/41.15 inverse(double_divide(double_divide(Y2, X1), double_divide(double_divide(Y1, X1), inverse(Y2)))) -> Y1 % 41.28/41.15 inverse(double_divide(double_divide(double_divide(X2, X1), X0), inverse(double_divide(X0, double_divide(X1, X2))))) -> identity % 41.28/41.15 inverse(double_divide(identity, Y0)) -> inverse(inverse(Y0)) % 41.28/41.15 inverse(double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0 % 41.28/41.15 inverse(double_divide(inverse(X0), X0)) -> identity % 41.28/41.15 inverse(double_divide(inverse(X0), inverse(double_divide(Y1, X0)))) -> Y1 % 41.28/41.15 inverse(double_divide(inverse(X1), inverse(double_divide(X1, Y1)))) -> Y1 % 41.28/41.15 inverse(double_divide(inverse(Y0), double_divide(X0, inverse(Y0)))) -> inverse(inverse(inverse(X0))) % 41.28/41.15 inverse(double_divide(inverse(Y0), double_divide(identity, inverse(Y0)))) -> identity % 41.28/41.15 inverse(double_divide(inverse(Y0), double_divide(inverse(Y1), inverse(Y0)))) -> Y1 % 41.28/41.15 inverse(double_divide(inverse(Y1), Y0)) -> double_divide(Y1, inverse(Y0)) % 41.28/41.15 inverse(double_divide(inverse(Y1), inverse(Y0))) -> double_divide(Y1, Y0) % 41.28/41.15 inverse(identity) -> identity % 41.28/41.15 inverse(inverse(Y0)) -> Y0 % 41.28/41.15 inverse(inverse(double_divide(double_divide(Y0, inverse(Y1)), inverse(Y1)))) -> Y0 % 41.28/41.15 inverse(inverse(identity)) -> identity % 41.28/41.15 inverse(inverse(inverse(identity))) -> identity % 41.28/41.15 inverse(inverse(inverse(inverse(Y0)))) -> Y0 % 41.28/41.15 inverse(inverse(inverse(inverse(identity)))) -> identity % 41.28/41.15 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 41.28/41.15 true__ -> false__ % 41.28/41.15 with the LPO induced by % 41.28/41.15 c3 > b3 > a3 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 41.28/41.15 % 41.28/41.15 % SZS output end Proof % 41.28/41.15 %------------------------------------------------------------------------------