%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP585-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n012.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 118.09s 118.19s % Output : Proof 118.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP585-1 : TPTP v8.1.0. Released v2.6.0. % 0.07/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n012.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jun 13 14:41:40 EDT 2022 % 0.12/0.34 % CPUTime : % 118.09/118.19 % SZS status Unsatisfiable % 118.09/118.19 % SZS output start Proof % 118.09/118.19 The input problem is unsatisfiable because % 118.09/118.19 % 118.09/118.19 [1] the following set of Horn clauses is unsatisfiable: % 118.09/118.19 % 118.09/118.19 double_divide(A, inverse(double_divide(inverse(double_divide(double_divide(A, B), inverse(C))), B))) = C % 118.09/118.19 multiply(A, B) = inverse(double_divide(B, A)) % 118.09/118.19 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 118.09/118.19 % 118.09/118.19 This holds because % 118.09/118.19 % 118.09/118.19 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 118.09/118.19 % 118.09/118.19 E: % 118.09/118.19 double_divide(A, inverse(double_divide(inverse(double_divide(double_divide(A, B), inverse(C))), B))) = C % 118.09/118.19 f1(multiply(inverse(a1), a1)) = true__ % 118.09/118.19 f1(multiply(inverse(b1), b1)) = false__ % 118.09/118.19 multiply(A, B) = inverse(double_divide(B, A)) % 118.09/118.19 G: % 118.09/118.19 true__ = false__ % 118.09/118.19 % 118.09/118.19 This holds because % 118.09/118.19 % 118.09/118.19 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 118.09/118.19 % 118.09/118.19 double_divide(Y0, inverse(Y0)) = double_divide(X0, inverse(X0)) % 118.09/118.19 double_divide(Y0, inverse(double_divide(inverse(X2), Y1))) = double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), X1), inverse(X2))), X1) % 118.09/118.19 double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(double_divide(inverse(Y1), X2), X3), inverse(X1))), X3))) = double_divide(inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), X2))), Y3), inverse(Y1))), Y3) % 118.09/118.19 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(Y1, inverse(Y1)) % 118.09/118.19 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(false__, inverse(false__)) % 118.09/118.19 double_divide(inverse(Y0), inverse(inverse(Y0))) = inverse(double_divide(X0, inverse(X0))) % 118.09/118.19 double_divide(inverse(double_divide(X2, inverse(Y2))), inverse(double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1))) = double_divide(inverse(double_divide(double_divide(Y0, Y3), inverse(Y2))), Y3) % 118.09/118.19 double_divide(inverse(double_divide(X2, inverse(Y3))), inverse(double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), X1), inverse(X2))), X1))) = double_divide(Y0, inverse(double_divide(inverse(Y3), Y1))) % 118.09/118.19 double_divide(inverse(double_divide(double_divide(X2, Y2), inverse(Y3))), Y2) = double_divide(Y0, inverse(double_divide(inverse(Y3), inverse(double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1))))) % 118.09/118.19 double_divide(inverse(double_divide(double_divide(Y0, Y1), inverse(X2))), Y1) = double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1) % 118.09/118.19 double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y2), X3), inverse(Y1))), X3) = double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y2), Y3), inverse(Y1))), Y3) % 118.09/118.19 inverse(double_divide(Y1, inverse(Y1))) = double_divide(X0, inverse(X0)) % 118.09/118.19 inverse(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(Y1, inverse(Y1)) % 118.09/118.19 double_divide(A, inverse(double_divide(inverse(double_divide(double_divide(A, B), inverse(C))), B))) -> C % 118.09/118.19 double_divide(X1, inverse(double_divide(inverse(Y2), inverse(X1)))) -> Y2 % 118.09/118.19 double_divide(Y0, inverse(double_divide(inverse(double_divide(X2, inverse(Y2))), inverse(double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1))))) -> Y2 % 118.09/118.19 double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(double_divide(inverse(Y2), X1))))) -> Y2 % 118.09/118.19 double_divide(double_divide(X1, inverse(X1)), inverse(Y1)) -> Y1 % 118.09/118.19 double_divide(double_divide(false__, inverse(false__)), inverse(Y1)) -> Y1 % 118.09/118.19 double_divide(double_divide(inverse(X1), inverse(inverse(Y1))), inverse(X1)) -> Y1 % 118.09/118.19 double_divide(inverse(X1), inverse(inverse(double_divide(Y1, inverse(X1))))) -> Y1 % 118.09/118.19 double_divide(inverse(Y0), inverse(inverse(inverse(double_divide(X0, inverse(X0)))))) -> Y0 % 118.09/118.19 double_divide(inverse(Y1), inverse(inverse(double_divide(X0, inverse(X0))))) -> Y1 % 118.09/118.19 double_divide(inverse(double_divide(X0, inverse(X1))), inverse(double_divide(inverse(double_divide(X1, inverse(Y2))), inverse(X0)))) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(X2, inverse(X2))), inverse(Y2)) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(X2, inverse(double_divide(Y0, inverse(Y2))))), inverse(double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1))) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(X2, inverse(double_divide(double_divide(Y0, Y1), inverse(Y3))))), inverse(double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), X1), inverse(X2))), X1))) -> Y3 % 118.09/118.19 double_divide(inverse(double_divide(X2, inverse(double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(double_divide(X0, inverse(X2))))), inverse(Y2))))), Y1) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(X3, inverse(double_divide(inverse(double_divide(double_divide(double_divide(X0, X1), Y1), inverse(double_divide(double_divide(X0, X1), inverse(X3))))), inverse(Y2))))), Y1) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(Y1, inverse(Y2))), inverse(Y1)) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(X2))), inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, X3), inverse(X2))), X3), inverse(Y2))), Y1))) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(double_divide(X0, inverse(X2))))), inverse(double_divide(inverse(double_divide(X2, inverse(Y2))), Y1))) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(X2, Y2), inverse(double_divide(X2, inverse(Y3))))), Y2) -> Y3 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1) -> double_divide(inverse(X2), inverse(Y0)) % 118.09/118.19 double_divide(inverse(double_divide(double_divide(Y0, Y3), inverse(double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), X1), inverse(X2))), X1)))), Y3) -> double_divide(inverse(X2), Y1) % 118.09/118.19 double_divide(inverse(double_divide(double_divide(double_divide(X0, X1), Y1), inverse(X3))), inverse(double_divide(inverse(double_divide(double_divide(X0, inverse(double_divide(inverse(X3), X1))), inverse(Y2))), Y1))) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(double_divide(X0, X1), Y1), inverse(double_divide(double_divide(X0, X1), inverse(X3))))), inverse(double_divide(inverse(double_divide(X3, inverse(Y2))), Y1))) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), Y2), inverse(double_divide(inverse(double_divide(double_divide(double_divide(double_divide(Y0, Y1), X2), X3), inverse(X1))), X3)))), Y2) -> double_divide(inverse(X1), X2) % 118.09/118.19 double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y2), Y3), inverse(double_divide(double_divide(X0, Y2), inverse(double_divide(X0, inverse(X2))))))), Y3) -> double_divide(Y0, inverse(X2)) % 118.09/118.19 double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y2), Y3), inverse(double_divide(double_divide(Y0, Y2), inverse(X2))))), Y3) -> X2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y2), Y3), inverse(double_divide(double_divide(double_divide(X0, X1), Y2), inverse(double_divide(double_divide(X0, X1), inverse(X3))))))), Y3) -> double_divide(Y0, inverse(X3)) % 118.09/118.19 double_divide(inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), X2))), Y2), inverse(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(Y0, X2), X3), inverse(X1))), X3), inverse(Y3))))), Y2) -> Y3 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), X2))), false__), inverse(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(Y0, X2), X3), inverse(X1))), X3), inverse(Y2))))), false__) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(Y0, X2), X3), inverse(X1))), X3), Y2), inverse(double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), X2))), inverse(Y3))))), Y2) -> Y3 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(X0))), Y1), inverse(Y2))), Y1) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, X3), inverse(X2))), X3), inverse(double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(X2))), inverse(Y2))))), Y1) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(double_divide(X0, inverse(X2))))), Y3), inverse(Y2))), Y3) -> double_divide(inverse(double_divide(X2, inverse(Y2))), Y1) % 118.09/118.19 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y2)), inverse(X2))), Y1), inverse(double_divide(inverse(double_divide(double_divide(X0, X3), inverse(X2))), X3)))), Y1) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y2)), inverse(double_divide(X0, inverse(X2))))), Y1), inverse(X2))), Y1) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(X0, X1), inverse(Y2)), inverse(double_divide(double_divide(X0, X1), inverse(X3))))), Y1), inverse(X3))), Y1) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(Y0, X2), X3), inverse(X1))), X3), inverse(double_divide(Y0, inverse(Y2))))), inverse(double_divide(inverse(X1), X2))) -> Y2 % 118.09/118.19 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(double_divide(Y0, Y1), X2), X3), inverse(X1))), X3), inverse(double_divide(double_divide(Y0, Y1), inverse(Y3))))), inverse(double_divide(inverse(X1), X2))) -> Y3 % 118.09/118.19 double_divide(inverse(double_divide(inverse(double_divide(double_divide(double_divide(double_divide(double_divide(Y0, Y1), false__), X3), false__), inverse(double_divide(double_divide(double_divide(double_divide(Y0, Y1), X2), X3), inverse(X1))))), false__)), false__) -> double_divide(inverse(X1), X2) % 118.09/118.19 double_divide(inverse(double_divide(inverse(double_divide(double_divide(double_divide(false__, X3), false__), inverse(double_divide(double_divide(double_divide(double_divide(Y0, Y1), X2), X3), inverse(X1))))), false__)), inverse(double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), false__), inverse(false__))), false__))) -> double_divide(inverse(X1), X2) % 118.09/118.19 double_divide(inverse(inverse(double_divide(X0, inverse(X0)))), inverse(Y1)) -> Y1 % 118.09/118.19 double_divide(inverse(inverse(inverse(double_divide(X0, inverse(X0))))), inverse(Y1)) -> Y1 % 118.09/118.19 f1(double_divide(X1, inverse(X1))) -> false__ % 118.09/118.19 f1(double_divide(X1, inverse(X1))) -> true__ % 118.09/118.19 f1(double_divide(double_divide(X0, double_divide(false__, inverse(false__))), X0)) -> false__ % 118.09/118.19 f1(double_divide(double_divide(X0, double_divide(false__, inverse(false__))), X0)) -> true__ % 118.09/118.19 f1(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) -> false__ % 118.09/118.19 f1(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) -> true__ % 118.09/118.19 f1(double_divide(false__, inverse(false__))) -> false__ % 118.09/118.19 f1(double_divide(false__, inverse(false__))) -> true__ % 118.09/118.19 f1(inverse(double_divide(a1, inverse(a1)))) -> true__ % 118.09/118.19 f1(inverse(double_divide(b1, inverse(b1)))) -> false__ % 118.09/118.19 f1(multiply(inverse(a1), a1)) -> true__ % 118.09/118.19 f1(multiply(inverse(b1), b1)) -> false__ % 118.09/118.19 inverse(double_divide(Y1, inverse(double_divide(X0, inverse(X0))))) -> Y1 % 118.09/118.19 multiply(A, B) -> inverse(double_divide(B, A)) % 118.09/118.19 true__ -> false__ % 118.09/118.19 with the LPO induced by % 118.09/118.19 a1 > b1 > f1 > multiply > inverse > double_divide > true__ > false__ % 118.09/118.19 % 118.09/118.19 % SZS output end Proof % 118.09/118.19 %------------------------------------------------------------------------------