%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP571-1 : 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 10:56:21 EDT 2022 % Result : Unsatisfiable 23.36s 23.17s % Output : Proof 23.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GRP571-1 : TPTP v8.1.0. Released v2.6.0. % 0.07/0.13 % Command : moca.sh %s % 0.14/0.35 % Computer : n029.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Mon Jun 13 12:35:25 EDT 2022 % 0.14/0.35 % CPUTime : % 23.36/23.17 % SZS status Unsatisfiable % 23.36/23.17 % SZS output start Proof % 23.36/23.17 The input problem is unsatisfiable because % 23.36/23.17 % 23.36/23.17 [1] the following set of Horn clauses is unsatisfiable: % 23.36/23.17 % 23.36/23.17 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B % 23.36/23.17 multiply(A, B) = double_divide(double_divide(B, A), identity) % 23.36/23.17 inverse(A) = double_divide(A, identity) % 23.36/23.17 identity = double_divide(A, inverse(A)) % 23.36/23.17 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 23.36/23.17 % 23.36/23.17 This holds because % 23.36/23.17 % 23.36/23.17 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 23.36/23.17 % 23.36/23.17 E: % 23.36/23.17 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B % 23.36/23.17 f1(multiply(a3, multiply(b3, c3))) = false__ % 23.36/23.17 f1(multiply(multiply(a3, b3), c3)) = true__ % 23.36/23.17 identity = double_divide(A, inverse(A)) % 23.36/23.17 inverse(A) = double_divide(A, identity) % 23.36/23.17 multiply(A, B) = double_divide(double_divide(B, A), identity) % 23.36/23.17 G: % 23.36/23.17 true__ = false__ % 23.36/23.17 % 23.36/23.17 This holds because % 23.36/23.17 % 23.36/23.17 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 23.36/23.17 % 23.36/23.17 double_divide(Y0, X0) = double_divide(X0, Y0) % 23.36/23.17 double_divide(Y0, double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), inverse(Y0))) % 23.36/23.17 double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 23.36/23.17 double_divide(Y0, double_divide(inverse(Y1), inverse(inverse(Y0)))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity)) % 23.36/23.17 double_divide(Y0, inverse(double_divide(X1, X0))) = inverse(double_divide(double_divide(X0, X1), inverse(Y0))) % 23.36/23.17 double_divide(double_divide(Y0, Y1), X0) = double_divide(X0, double_divide(Y1, Y0)) % 23.36/23.17 double_divide(double_divide(identity, X0), inverse(identity)) = double_divide(Y1, double_divide(inverse(inverse(X0)), inverse(inverse(Y1)))) % 23.36/23.17 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))) % 23.36/23.17 double_divide(false__, double_divide(double_divide(X1, inverse(false__)), inverse(identity))) = double_divide(X0, double_divide(inverse(X1), inverse(inverse(X0)))) % 23.36/23.17 inverse(double_divide(X1, double_divide(X0, X2))) = double_divide(X0, double_divide(X1, inverse(X2))) % 23.36/23.17 inverse(double_divide(X1, inverse(Y1))) = double_divide(Y1, inverse(X1)) % 23.36/23.17 inverse(double_divide(Y0, X0)) = inverse(double_divide(X0, Y0)) % 23.36/23.17 inverse(double_divide(Y0, double_divide(X1, Y2))) = double_divide(double_divide(Y0, inverse(Y2)), X1) % 23.36/23.17 inverse(double_divide(Y0, double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), inverse(Y0)) % 23.36/23.17 inverse(double_divide(Y0, double_divide(X1, inverse(Y2)))) = double_divide(double_divide(Y0, Y2), X1) % 23.36/23.17 inverse(double_divide(Y0, inverse(double_divide(X1, X0)))) = double_divide(double_divide(X0, X1), inverse(Y0)) % 23.36/23.17 inverse(double_divide(double_divide(X0, X2), X1)) = double_divide(X0, double_divide(X1, inverse(X2))) % 23.36/23.17 inverse(double_divide(double_divide(X0, inverse(X2)), X1)) = double_divide(X0, double_divide(X1, X2)) % 23.36/23.17 inverse(double_divide(double_divide(Y0, Y1), X0)) = inverse(double_divide(X0, double_divide(Y1, Y0))) % 23.36/23.17 inverse(double_divide(double_divide(Y1, Y0), Y2)) = double_divide(Y0, double_divide(Y2, inverse(Y1))) % 23.36/23.17 inverse(double_divide(double_divide(Y1, Y2), Y0)) = double_divide(double_divide(Y0, inverse(Y2)), Y1) % 23.36/23.17 inverse(double_divide(double_divide(Y1, inverse(Y2)), Y0)) = double_divide(double_divide(Y0, Y2), Y1) % 23.36/23.17 double_divide(A, identity) -> inverse(A) % 23.36/23.17 double_divide(A, inverse(A)) -> identity % 23.36/23.17 double_divide(X0, double_divide(X0, inverse(Y1))) -> inverse(Y1) % 23.36/23.17 double_divide(X0, double_divide(X1, X0)) -> X1 % 23.36/23.17 double_divide(X0, double_divide(X2, double_divide(X1, double_divide(X0, inverse(X2))))) -> inverse(X1) % 23.36/23.17 double_divide(X0, double_divide(X2, double_divide(double_divide(X0, inverse(X2)), X1))) -> inverse(X1) % 23.36/23.17 double_divide(X0, double_divide(inverse(X1), X0)) -> inverse(X1) % 23.36/23.17 double_divide(X0, inverse(double_divide(X1, inverse(X0)))) -> inverse(X1) % 23.36/23.17 double_divide(X1, double_divide(X0, double_divide(X2, double_divide(X1, double_divide(X0, inverse(X2)))))) -> identity % 23.36/23.17 double_divide(X1, double_divide(X0, double_divide(inverse(X1), X0))) -> identity % 23.36/23.17 double_divide(X1, double_divide(X1, Y0)) -> Y0 % 23.36/23.17 double_divide(Y0, double_divide(Y1, double_divide(Y2, inverse(double_divide(Y1, inverse(Y0)))))) -> inverse(Y2) % 23.36/23.17 double_divide(Y0, double_divide(Y1, inverse(double_divide(double_divide(Y1, inverse(Y0)), inverse(Y2))))) -> inverse(Y2) % 23.36/23.17 double_divide(Y0, double_divide(double_divide(Y1, X1), inverse(double_divide(X1, Y0)))) -> inverse(Y1) % 23.36/23.17 double_divide(Y0, double_divide(double_divide(identity, inverse(Y0)), inverse(identity))) -> identity % 23.36/23.17 double_divide(Y0, double_divide(identity, Y0)) -> identity % 23.36/23.17 double_divide(Y0, double_divide(identity, inverse(inverse(Y0)))) -> identity % 23.36/23.17 double_divide(Y0, double_divide(inverse(identity), inverse(inverse(Y0)))) -> identity % 23.36/23.17 double_divide(Y0, inverse(double_divide(X0, inverse(double_divide(Y2, double_divide(Y0, X0)))))) -> inverse(Y2) % 23.36/23.17 double_divide(Y0, inverse(double_divide(X0, inverse(double_divide(double_divide(Y0, X0), Y2))))) -> inverse(Y2) % 23.36/23.17 double_divide(Y0, inverse(double_divide(Y2, inverse(double_divide(double_divide(Y2, Y0), Y1))))) -> inverse(Y1) % 23.36/23.17 double_divide(Y0, inverse(double_divide(double_divide(Y0, inverse(X0)), inverse(X0)))) -> identity % 23.36/23.17 double_divide(Y0, inverse(double_divide(identity, inverse(Y0)))) -> identity % 23.36/23.17 double_divide(Y1, double_divide(double_divide(Y0, double_divide(Y1, Y2)), inverse(Y2))) -> inverse(Y0) % 23.36/23.17 double_divide(Y1, double_divide(double_divide(identity, double_divide(Y1, Y2)), inverse(Y2))) -> double_divide(inverse(identity), inverse(identity)) % 23.36/23.17 double_divide(Y1, double_divide(inverse(inverse(identity)), inverse(inverse(Y1)))) -> identity % 23.36/23.17 double_divide(Y1, double_divide(inverse(inverse(inverse(identity))), inverse(inverse(Y1)))) -> identity % 23.36/23.17 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) -> B % 23.36/23.17 double_divide(double_divide(X0, double_divide(X1, X0)), inverse(X1)) -> identity % 23.36/23.17 double_divide(double_divide(X0, double_divide(X1, X2)), double_divide(double_divide(X0, inverse(X2)), X1)) -> identity % 23.36/23.17 double_divide(double_divide(X0, double_divide(X1, X2)), inverse(double_divide(double_divide(X2, X1), X0))) -> identity % 23.36/23.17 double_divide(double_divide(X0, double_divide(X1, inverse(X2))), double_divide(double_divide(X0, X2), X1)) -> identity % 23.36/23.17 double_divide(double_divide(X0, double_divide(inverse(X1), X0)), X1) -> identity % 23.36/23.17 double_divide(double_divide(X0, inverse(double_divide(X1, X2))), double_divide(double_divide(X2, X1), inverse(X0))) -> identity % 23.36/23.17 double_divide(double_divide(X1, X2), double_divide(double_divide(X2, X1), Y1)) -> Y1 % 23.36/23.17 double_divide(double_divide(X1, Y1), X1) -> Y1 % 23.36/23.17 double_divide(double_divide(X1, inverse(Y1)), X1) -> inverse(Y1) % 23.36/23.17 double_divide(double_divide(Y0, Y2), Y1) -> inverse(double_divide(Y0, inverse(double_divide(Y2, inverse(Y1))))) % 23.36/23.17 double_divide(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, Y2)), inverse(Y2))), inverse(identity)) -> Y1 % 23.36/23.17 double_divide(double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))), inverse(identity)) -> Y1 % 23.36/23.17 double_divide(double_divide(Y0, double_divide(inverse(Y1), inverse(inverse(Y0)))), inverse(identity)) -> Y1 % 23.36/23.17 double_divide(double_divide(Y0, inverse(Y2)), Y1) -> inverse(double_divide(Y0, double_divide(Y2, Y1))) % 23.36/23.17 double_divide(double_divide(Y0, inverse(false__)), double_divide(false__, inverse(Y0))) -> identity % 23.36/23.17 double_divide(double_divide(Y1, X0), X0) -> Y1 % 23.36/23.17 double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2)) -> Y1 % 23.36/23.17 double_divide(double_divide(Y2, inverse(X1)), inverse(double_divide(double_divide(Y1, X1), Y2))) -> Y1 % 23.36/23.17 double_divide(double_divide(double_divide(X0, X1), X2), inverse(double_divide(X2, double_divide(X1, X0)))) -> identity % 23.36/23.17 double_divide(double_divide(double_divide(X0, X2), X1), double_divide(X0, double_divide(X1, inverse(X2)))) -> identity % 23.36/23.17 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 % 23.36/23.17 double_divide(double_divide(double_divide(X0, inverse(X2)), X1), double_divide(X0, double_divide(X1, X2))) -> identity % 23.36/23.17 double_divide(double_divide(double_divide(X2, X1), inverse(X0)), double_divide(X0, inverse(double_divide(X1, X2)))) -> identity % 23.36/23.17 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 % 23.36/23.17 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 % 23.36/23.17 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 % 23.36/23.17 double_divide(double_divide(false__, inverse(X0)), double_divide(X0, inverse(false__))) -> identity % 23.36/23.17 double_divide(double_divide(identity, X0), X0) -> identity % 23.36/23.17 double_divide(double_divide(inverse(X0), double_divide(double_divide(Y1, X0), inverse(inverse(identity)))), inverse(identity)) -> Y1 % 23.36/23.17 double_divide(double_divide(inverse(X0), inverse(double_divide(X1, X0))), X1) -> identity % 23.36/23.17 double_divide(double_divide(inverse(X1), Y1), inverse(X1)) -> Y1 % 23.36/23.17 double_divide(double_divide(inverse(identity), double_divide(inverse(Y1), inverse(inverse(identity)))), inverse(identity)) -> Y1 % 23.36/23.17 double_divide(double_divide(inverse(inverse(Y1)), double_divide(identity, inverse(inverse(identity)))), inverse(identity)) -> Y1 % 23.36/23.17 double_divide(false__, double_divide(double_divide(X0, inverse(false__)), inverse(identity))) -> inverse(X0) % 23.36/23.17 double_divide(false__, inverse(double_divide(Y0, inverse(false__)))) -> inverse(Y0) % 23.36/23.17 double_divide(identity, X0) -> inverse(X0) % 23.36/23.17 double_divide(identity, inverse(Y1)) -> Y1 % 23.36/23.17 double_divide(inverse(X0), X0) -> identity % 23.36/23.17 double_divide(inverse(X0), double_divide(double_divide(identity, X0), inverse(inverse(identity)))) -> identity % 23.36/23.17 double_divide(inverse(X0), double_divide(identity, inverse(X0))) -> identity % 23.36/23.17 double_divide(inverse(X0), false__) -> inverse(double_divide(X0, inverse(false__))) % 23.36/23.17 double_divide(inverse(X0), inverse(double_divide(X1, X0))) -> inverse(X1) % 23.36/23.17 double_divide(inverse(X1), double_divide(X0, double_divide(X1, X0))) -> identity % 23.36/23.17 double_divide(inverse(Y0), X1) -> inverse(double_divide(Y0, inverse(X1))) % 23.36/23.17 double_divide(inverse(Y0), double_divide(false__, double_divide(inverse(inverse(Y0)), inverse(inverse(false__))))) -> identity % 23.36/23.17 double_divide(inverse(Y0), inverse(double_divide(identity, Y0))) -> identity % 23.36/23.17 double_divide(inverse(Y0), inverse(identity)) -> Y0 % 23.36/23.17 double_divide(inverse(double_divide(X0, inverse(false__))), inverse(X0)) -> false__ % 23.36/23.17 double_divide(inverse(double_divide(X1, inverse(Y1))), inverse(X1)) -> Y1 % 23.36/23.17 double_divide(inverse(inverse(identity)), double_divide(identity, inverse(inverse(identity)))) -> identity % 23.36/23.17 f1(double_divide(double_divide(a3, b3), inverse(c3))) -> true__ % 23.36/23.17 f1(inverse(double_divide(a3, inverse(double_divide(b3, c3))))) -> false__ % 23.36/23.17 f1(inverse(double_divide(c3, inverse(double_divide(b3, a3))))) -> true__ % 23.36/23.17 f1(inverse(double_divide(inverse(double_divide(c3, b3)), a3))) -> false__ % 23.36/23.17 f1(multiply(a3, multiply(b3, c3))) -> false__ % 23.36/23.17 f1(multiply(multiply(a3, b3), c3)) -> true__ % 23.36/23.17 inverse(double_divide(X0, double_divide(X0, Y1))) -> inverse(Y1) % 23.36/23.17 inverse(double_divide(X1, double_divide(X1, inverse(Y0)))) -> Y0 % 23.36/23.17 inverse(double_divide(Y0, double_divide(X0, Y0))) -> inverse(X0) % 23.36/23.17 inverse(double_divide(Y0, double_divide(X0, double_divide(double_divide(Y0, inverse(X0)), Y1)))) -> Y1 % 23.36/23.17 inverse(double_divide(Y0, double_divide(Y2, inverse(double_divide(double_divide(Y2, inverse(Y0)), inverse(Y1)))))) -> Y1 % 23.36/23.17 inverse(double_divide(Y0, double_divide(double_divide(Y1, X1), inverse(double_divide(X1, Y0))))) -> Y1 % 23.36/23.17 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, Y2)), inverse(Y2)))) -> Y1 % 23.36/23.17 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, inverse(X0))), X0))) -> Y1 % 23.36/23.17 inverse(double_divide(Y0, double_divide(identity, Y0))) -> identity % 23.36/23.17 inverse(double_divide(Y0, double_divide(identity, inverse(inverse(Y0))))) -> identity % 23.36/23.17 inverse(double_divide(Y0, double_divide(inverse(Y1), Y0))) -> Y1 % 23.36/23.17 inverse(double_divide(Y0, inverse(double_divide(X0, inverse(double_divide(double_divide(Y0, X0), Y2)))))) -> Y2 % 23.36/23.17 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(Y0))))) -> Y1 % 23.36/23.17 inverse(double_divide(Y0, inverse(double_divide(Y2, inverse(double_divide(Y1, double_divide(Y0, Y2))))))) -> Y1 % 23.36/23.17 inverse(double_divide(Y0, inverse(double_divide(Y2, inverse(double_divide(double_divide(Y2, Y0), Y1)))))) -> Y1 % 23.36/23.17 inverse(double_divide(Y0, inverse(double_divide(double_divide(Y0, Y2), Y2)))) -> identity % 23.36/23.17 inverse(double_divide(double_divide(X1, Y1), X1)) -> inverse(Y1) % 23.36/23.17 inverse(double_divide(double_divide(X1, inverse(Y1)), X1)) -> Y1 % 23.36/23.17 inverse(double_divide(double_divide(X2, double_divide(X1, X0)), inverse(double_divide(double_divide(X0, X1), X2)))) -> identity % 23.36/23.17 inverse(double_divide(double_divide(Y2, X1), double_divide(double_divide(Y1, X1), inverse(Y2)))) -> Y1 % 23.36/23.17 inverse(double_divide(double_divide(double_divide(X2, X1), X0), inverse(double_divide(X0, double_divide(X1, X2))))) -> identity % 23.36/23.17 inverse(double_divide(double_divide(identity, X0), X0)) -> identity % 23.36/23.17 inverse(double_divide(identity, Y1)) -> Y1 % 23.36/23.17 inverse(double_divide(inverse(X0), double_divide(identity, inverse(X0)))) -> identity % 23.36/23.17 inverse(double_divide(inverse(X0), inverse(double_divide(Y1, X0)))) -> Y1 % 23.36/23.17 inverse(double_divide(inverse(Y0), inverse(X1))) -> double_divide(Y0, X1) % 23.36/23.17 inverse(double_divide(inverse(double_divide(X1, Y1)), inverse(X1))) -> Y1 % 23.36/23.17 inverse(double_divide(inverse(false__), X1)) -> double_divide(false__, inverse(X1)) % 23.36/23.17 inverse(identity) -> identity % 23.36/23.17 inverse(inverse(Y0)) -> Y0 % 23.36/23.17 inverse(inverse(identity)) -> identity % 23.36/23.17 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 23.36/23.17 true__ -> false__ % 23.36/23.17 with the LPO induced by % 23.36/23.17 c3 > b3 > a3 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 23.36/23.17 % 23.36/23.17 % SZS output end Proof % 23.36/23.17 %------------------------------------------------------------------------------