%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP613-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 10:56:37 EDT 2022 % Result : Unsatisfiable 8.74s 8.88s % Output : Proof 8.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : GRP613-1 : TPTP v8.1.0. Released v2.6.0. % 0.10/0.12 % Command : moca.sh %s % 0.14/0.33 % Computer : n020.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 600 % 0.14/0.33 % DateTime : Mon Jun 13 09:02:50 EDT 2022 % 0.14/0.34 % CPUTime : % 8.74/8.88 % SZS status Unsatisfiable % 8.74/8.88 % SZS output start Proof % 8.74/8.88 The input problem is unsatisfiable because % 8.74/8.88 % 8.74/8.88 [1] the following set of Horn clauses is unsatisfiable: % 8.74/8.88 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(A, inverse(B))), C)), double_divide(A, C)) = B % 8.74/8.88 multiply(A, B) = inverse(double_divide(B, A)) % 8.74/8.88 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 8.74/8.88 % 8.74/8.88 This holds because % 8.74/8.88 % 8.74/8.88 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 8.74/8.88 % 8.74/8.88 E: % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(A, inverse(B))), C)), double_divide(A, C)) = B % 8.74/8.88 f1(multiply(inverse(a1), a1)) = true__ % 8.74/8.88 f1(multiply(inverse(b1), b1)) = false__ % 8.74/8.88 multiply(A, B) = inverse(double_divide(B, A)) % 8.74/8.88 G: % 8.74/8.88 true__ = false__ % 8.74/8.88 % 8.74/8.88 This holds because % 8.74/8.88 % 8.74/8.88 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 8.74/8.88 % 8.74/8.88 double_divide(X0, double_divide(inverse(Y1), Y1)) = inverse(X0) % 8.74/8.88 double_divide(X0, inverse(X0)) = double_divide(Y1, inverse(Y1)) % 8.74/8.88 double_divide(X0, inverse(X0)) = double_divide(inverse(Y1), Y1) % 8.74/8.88 double_divide(Y0, double_divide(X0, inverse(X0))) = inverse(Y0) % 8.74/8.88 double_divide(inverse(Y0), X1) = double_divide(inverse(inverse(X1)), inverse(Y0)) % 8.74/8.88 double_divide(inverse(Y0), Y0) = double_divide(inverse(X1), X1) % 8.74/8.88 double_divide(inverse(double_divide(X0, inverse(X0))), Y1) = inverse(Y1) % 8.74/8.88 double_divide(inverse(double_divide(inverse(X0), X0)), X1) = inverse(X1) % 8.74/8.88 double_divide(X0, double_divide(X0, Y1)) -> Y1 % 8.74/8.88 double_divide(double_divide(Y0, double_divide(X1, inverse(X1))), double_divide(false__, inverse(false__))) -> Y0 % 8.74/8.88 double_divide(double_divide(Y0, double_divide(inverse(X1), X1)), double_divide(false__, inverse(false__))) -> Y0 % 8.74/8.88 double_divide(inverse(X1), double_divide(Y0, double_divide(inverse(inverse(X1)), inverse(double_divide(Y0, inverse(Y1)))))) -> Y1 % 8.74/8.88 double_divide(inverse(X1), double_divide(inverse(double_divide(X0, inverse(X1))), double_divide(X0, inverse(Y1)))) -> Y1 % 8.74/8.88 double_divide(inverse(X1), double_divide(inverse(double_divide(inverse(inverse(Y2)), inverse(double_divide(inverse(Y1), inverse(X1))))), Y1)) -> Y2 % 8.74/8.88 double_divide(inverse(X1), double_divide(inverse(inverse(Y1)), inverse(X1))) -> Y1 % 8.74/8.88 double_divide(inverse(X2), double_divide(Y0, double_divide(inverse(double_divide(X1, inverse(double_divide(Y0, inverse(Y1))))), double_divide(X1, inverse(X2))))) -> Y1 % 8.74/8.88 double_divide(inverse(X3), double_divide(Y0, double_divide(X1, double_divide(inverse(double_divide(X2, inverse(double_divide(X1, inverse(X3))))), double_divide(X2, inverse(double_divide(Y0, inverse(Y1)))))))) -> Y1 % 8.74/8.88 double_divide(inverse(X4), double_divide(Y0, double_divide(X1, double_divide(X2, double_divide(inverse(double_divide(X3, inverse(double_divide(X2, inverse(double_divide(Y0, inverse(Y1))))))), double_divide(X3, inverse(double_divide(X1, inverse(X4))))))))) -> Y1 % 8.74/8.88 double_divide(inverse(Y0), double_divide(X0, inverse(X0))) -> Y0 % 8.74/8.88 double_divide(inverse(Y0), double_divide(Y1, double_divide(inverse(X1), double_divide(inverse(double_divide(inverse(inverse(double_divide(Y1, inverse(Y3)))), inverse(X1))), inverse(Y0))))) -> Y3 % 8.74/8.88 double_divide(inverse(Y0), double_divide(Y1, double_divide(inverse(X3), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(double_divide(Y1, inverse(Y3)))))), X2)), inverse(X3))), double_divide(X0, X2))), inverse(Y0))))) -> Y3 % 8.74/8.88 double_divide(inverse(Y0), double_divide(Y1, double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y0)))), X2)), inverse(X3))), double_divide(X0, X2))), inverse(double_divide(Y1, inverse(Y3))))), X3))) -> Y3 % 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(X1), double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(X1))), double_divide(inverse(double_divide(X2, inverse(X0))), double_divide(X2, inverse(inverse(Y0)))))), inverse(Y2)))) -> Y2 % 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(X1), double_divide(inverse(double_divide(inverse(inverse(Y0)), inverse(X1))), inverse(Y2)))) -> Y2 % 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(X3), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y0)))), X2)), inverse(X3))), double_divide(X0, X2))), inverse(Y2)))) -> Y2 % 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(Y0), Y2)) -> Y2 % 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(X0), X0)), double_divide(inverse(inverse(Y0)), inverse(Y2)))) -> Y2 % 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(X1))), double_divide(inverse(double_divide(X2, inverse(X0))), double_divide(X2, inverse(inverse(Y2)))))), inverse(Y0))), X1)) -> Y2 % 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y3)))), X2)), inverse(X3))), double_divide(X0, X2))), double_divide(inverse(double_divide(Y2, inverse(X3))), double_divide(Y2, inverse(Y0))))) -> Y3 % 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y2)))), X2)), inverse(X3))), double_divide(X0, X2))), inverse(Y0))), X3)) -> Y2 % 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(double_divide(inverse(inverse(Y2)), inverse(X1))), inverse(Y0))), X1)) -> Y2 % 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(inverse(Y2)), inverse(X1))), double_divide(inverse(inverse(Y0)), inverse(X1)))) -> Y2 % 8.74/8.88 double_divide(inverse(Y0), inverse(double_divide(inverse(X1), X1))) -> Y0 % 8.74/8.88 double_divide(inverse(Y1), double_divide(Y0, double_divide(Y0, double_divide(inverse(X2), X2)))) -> Y1 % 8.74/8.88 double_divide(inverse(Y1), double_divide(inverse(Y2), Y2)) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(X0, inverse(Y1))), inverse(X0)) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(Y0, inverse(Y1))), double_divide(Y0, double_divide(inverse(X1), X1))) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(X1), X1)), inverse(Y1)) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(X1), Y2)), double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(X1))), double_divide(inverse(double_divide(X2, inverse(X0))), double_divide(X2, inverse(inverse(Y1)))))), Y2)) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(X1), Y2)), double_divide(inverse(double_divide(inverse(inverse(Y1)), inverse(X1))), Y2)) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(X3), Y2)), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y1)))), X2)), inverse(X3))), double_divide(X0, X2))), Y2)) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(Y1), Y2)), double_divide(inverse(double_divide(inverse(X0), X0)), Y2)) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(Y1), inverse(X1))), X1) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(Y1), inverse(Y3))), Y1) -> Y3 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(A, inverse(B))), C)), double_divide(A, C)) -> B % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(Y1))), double_divide(inverse(double_divide(X1, inverse(X0))), double_divide(X1, inverse(X2))))), X2) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(Y1))), double_divide(inverse(inverse(X1)), inverse(X0)))), X1) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(X2), inverse(Y3))), double_divide(Y0, double_divide(inverse(double_divide(X1, inverse(double_divide(Y0, inverse(Y1))))), double_divide(X1, inverse(X2)))))), Y1) -> Y3 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(X3), inverse(Y3))), double_divide(Y0, double_divide(X1, double_divide(inverse(double_divide(X2, inverse(double_divide(X1, inverse(X3))))), double_divide(X2, inverse(double_divide(Y0, inverse(Y1))))))))), Y1) -> Y3 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(Y0), inverse(double_divide(inverse(X1), X1)))), inverse(Y2))), Y0) -> Y2 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X1), X1)), inverse(Y1))), inverse(Y2))), Y1) -> Y2 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X3), Y2)), inverse(Y3))), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y1)))), X2)), inverse(X3))), double_divide(X0, X2))), Y2))), Y1) -> Y3 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(Y2), inverse(X1))), inverse(Y1))), Y2)), X1) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(X1))), X2)), inverse(Y1))), double_divide(X0, X2))), X1) -> Y1 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(Y1))), double_divide(X1, double_divide(inverse(double_divide(X2, inverse(double_divide(X1, inverse(X3))))), double_divide(X2, inverse(X0)))))), inverse(Y3))), X3)), Y1) -> Y3 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(Y1))), double_divide(inverse(double_divide(X1, inverse(X0))), double_divide(X1, inverse(X2))))), inverse(Y3))), X2)), Y1) -> Y3 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(X1))), X2)), inverse(Y1))), double_divide(X0, X2))), inverse(Y3))), X1)), Y1) -> Y3 % 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(Y2))), X2)), inverse(X3))), double_divide(X0, X2))), inverse(Y1))), Y2)), inverse(Y3))), X3)), Y1) -> Y3 % 8.74/8.88 double_divide(inverse(double_divide(inverse(false__), false__)), double_divide(inverse(double_divide(inverse(X1), X1)), Y0)) -> Y0 % 8.74/8.88 double_divide(inverse(inverse(X0)), double_divide(inverse(X1), X0)) -> inverse(X1) % 8.74/8.88 double_divide(inverse(inverse(Y1)), inverse(double_divide(inverse(Y1), inverse(X1)))) -> X1 % 8.74/8.88 double_divide(inverse(inverse(double_divide(inverse(X1), X1))), inverse(Y0)) -> Y0 % 8.74/8.88 f1(double_divide(X1, inverse(X1))) -> false__ % 8.74/8.88 f1(double_divide(X1, inverse(X1))) -> true__ % 8.74/8.88 f1(double_divide(double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__))), double_divide(X1, inverse(X1)))) -> false__ % 8.74/8.88 f1(double_divide(double_divide(inverse(X1), X1), double_divide(false__, inverse(false__)))) -> false__ % 8.74/8.88 f1(double_divide(double_divide(inverse(X1), X1), double_divide(false__, inverse(false__)))) -> true__ % 8.74/8.88 f1(double_divide(false__, inverse(false__))) -> false__ % 8.74/8.88 f1(double_divide(false__, inverse(false__))) -> true__ % 8.74/8.88 f1(double_divide(inverse(X1), X1)) -> false__ % 8.74/8.88 f1(double_divide(inverse(X1), X1)) -> true__ % 8.74/8.88 f1(inverse(double_divide(a1, inverse(a1)))) -> true__ % 8.74/8.88 f1(inverse(double_divide(b1, inverse(b1)))) -> false__ % 8.74/8.88 f1(multiply(inverse(a1), a1)) -> true__ % 8.74/8.88 f1(multiply(inverse(b1), b1)) -> false__ % 8.74/8.88 inverse(inverse(Y1)) -> Y1 % 8.74/8.88 multiply(A, B) -> inverse(double_divide(B, A)) % 8.74/8.88 true__ -> false__ % 8.74/8.88 with the LPO induced by % 8.74/8.88 a1 > b1 > f1 > multiply > inverse > double_divide > true__ > false__ % 8.74/8.88 % 8.74/8.88 % SZS output end Proof % 8.74/8.88 %------------------------------------------------------------------------------