%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP590-1 : 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 10:56:29 EDT 2022 % Result : Unsatisfiable 6.02s 6.18s % Output : Proof 6.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP590-1 : TPTP v8.1.0. Released v2.6.0. % 0.11/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n023.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Mon Jun 13 17:37:06 EDT 2022 % 0.19/0.34 % CPUTime : % 6.02/6.18 % SZS status Unsatisfiable % 6.02/6.18 % SZS output start Proof % 6.02/6.18 The input problem is unsatisfiable because % 6.02/6.18 % 6.02/6.18 [1] the following set of Horn clauses is unsatisfiable: % 6.02/6.18 % 6.02/6.18 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) = C % 6.02/6.18 multiply(A, B) = inverse(double_divide(B, A)) % 6.02/6.18 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 6.02/6.18 % 6.02/6.18 This holds because % 6.02/6.18 % 6.02/6.18 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.02/6.18 % 6.02/6.18 E: % 6.02/6.18 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) = C % 6.02/6.18 f1(a2) = false__ % 6.02/6.18 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 6.02/6.18 multiply(A, B) = inverse(double_divide(B, A)) % 6.02/6.18 G: % 6.02/6.18 true__ = false__ % 6.02/6.18 % 6.02/6.18 This holds because % 6.02/6.18 % 6.02/6.18 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.02/6.18 % 6.02/6.18 double_divide(X1, inverse(X1)) = double_divide(Y1, inverse(Y1)) % 6.02/6.18 double_divide(double_divide(X0, double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__)))), X0) = double_divide(Y1, inverse(Y1)) % 6.02/6.18 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(Y1, inverse(Y1)) % 6.02/6.18 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(false__, inverse(false__)) % 6.02/6.18 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(inverse(Y1), inverse(inverse(Y1))) % 6.02/6.18 double_divide(double_divide(Y0, inverse(Y0)), X0) = double_divide(X0, double_divide(false__, inverse(false__))) % 6.02/6.18 double_divide(double_divide(false__, inverse(false__)), X0) = double_divide(X0, double_divide(false__, inverse(false__))) % 6.02/6.18 double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__))) = double_divide(Y1, inverse(Y1)) % 6.02/6.18 double_divide(double_divide(inverse(Y0), inverse(inverse(Y0))), double_divide(X1, inverse(X1))) = double_divide(X0, inverse(X0)) % 6.02/6.18 double_divide(false__, inverse(false__)) = double_divide(Y1, inverse(Y1)) % 6.02/6.18 double_divide(inverse(Y0), inverse(inverse(Y0))) = inverse(double_divide(X0, inverse(X0))) % 6.02/6.18 double_divide(inverse(double_divide(Y0, double_divide(X1, inverse(X1)))), inverse(Y0)) = double_divide(X0, inverse(X0)) % 6.02/6.18 double_divide(inverse(double_divide(double_divide(inverse(Y1), Y2), inverse(Y1))), Y2) = inverse(double_divide(X0, inverse(X0))) % 6.02/6.18 inverse(double_divide(Y1, inverse(Y1))) = double_divide(X0, inverse(X0)) % 6.02/6.18 inverse(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(Y1, inverse(Y1)) % 6.02/6.18 inverse(inverse(double_divide(Y1, inverse(Y1)))) = double_divide(X0, inverse(X0)) % 6.02/6.18 double_divide(double_divide(X0, double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__)))), X0) -> double_divide(false__, inverse(false__)) % 6.02/6.18 double_divide(double_divide(X1, inverse(X1)), inverse(Y1)) -> Y1 % 6.02/6.18 double_divide(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))), inverse(Y1)) -> Y1 % 6.02/6.18 double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__))) -> double_divide(false__, inverse(false__)) % 6.02/6.18 double_divide(inverse(X1), inverse(inverse(double_divide(Y1, inverse(X1))))) -> Y1 % 6.02/6.18 double_divide(inverse(X2), inverse(inverse(double_divide(double_divide(X0, inverse(Y1)), inverse(double_divide(X0, inverse(X2))))))) -> Y1 % 6.02/6.18 double_divide(inverse(Y0), inverse(inverse(inverse(inverse(double_divide(X0, inverse(X0))))))) -> Y0 % 6.02/6.18 double_divide(inverse(Y1), double_divide(X1, inverse(X1))) -> Y1 % 6.02/6.18 double_divide(inverse(Y1), double_divide(false__, inverse(false__))) -> Y1 % 6.02/6.18 double_divide(inverse(Y1), inverse(inverse(double_divide(X0, inverse(X0))))) -> Y1 % 6.02/6.18 double_divide(inverse(Y1), inverse(inverse(inverse(double_divide(X0, inverse(X0)))))) -> Y1 % 6.02/6.18 double_divide(inverse(double_divide(X1, inverse(Y2))), inverse(X1)) -> Y2 % 6.02/6.18 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 % 6.02/6.18 double_divide(inverse(double_divide(Y0, inverse(Y0))), inverse(Y3)) -> Y3 % 6.02/6.18 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(X1, inverse(Y0))), inverse(Y3))))), inverse(X1)) -> Y3 % 6.02/6.18 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(X2, inverse(double_divide(inverse(double_divide(double_divide(X0, Y2), inverse(double_divide(X0, inverse(X2))))), inverse(Y0))))), inverse(Y3))))), Y2) -> Y3 % 6.02/6.18 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(X3, inverse(double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X1, Y2), inverse(double_divide(X1, inverse(X0))))), inverse(X3))))), inverse(Y0))))), inverse(Y3))))), Y2) -> Y3 % 6.02/6.18 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(X0))), Y2), inverse(Y0))), inverse(Y3))))), Y2) -> Y3 % 6.02/6.18 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X1, inverse(Y0)), inverse(double_divide(X1, inverse(X0))))), inverse(X3))))), Y2), inverse(X3))), inverse(Y3))))), Y2) -> Y3 % 6.02/6.18 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y0)), inverse(double_divide(X0, inverse(X2))))), Y2), inverse(X2))), inverse(Y3))))), Y2) -> Y3 % 6.02/6.18 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) -> C % 6.02/6.18 double_divide(inverse(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), inverse(Y1)) -> Y1 % 6.02/6.18 double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(X0))), Y1), inverse(Y2))), Y1) -> Y2 % 6.02/6.18 double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X1, inverse(Y2)), inverse(double_divide(X1, inverse(X0))))), inverse(X3))))), Y1), inverse(X3))), Y1) -> Y2 % 6.02/6.18 double_divide(inverse(double_divide(double_divide(inverse(double_divide(Y1, inverse(Y2))), Y3), inverse(Y2))), Y3) -> Y1 % 6.02/6.18 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 % 6.02/6.18 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y2)), inverse(double_divide(X0, inverse(X2))))), inverse(Y1)), inverse(X2))), Y3), inverse(Y2))), Y3) -> Y1 % 6.02/6.18 double_divide(inverse(double_divide(double_divide(inverse(inverse(double_divide(X0, inverse(X0)))), Y1), inverse(Y2))), Y1) -> Y2 % 6.02/6.18 double_divide(inverse(double_divide(inverse(double_divide(double_divide(Y1, Y2), inverse(double_divide(Y1, inverse(inverse(double_divide(X0, inverse(X0)))))))), inverse(Y3))), Y2) -> Y3 % 6.02/6.18 double_divide(inverse(inverse(double_divide(X0, inverse(X0)))), inverse(Y1)) -> Y1 % 6.02/6.18 double_divide(inverse(inverse(inverse(double_divide(X0, inverse(X0))))), inverse(Y1)) -> Y1 % 6.02/6.18 double_divide(inverse(inverse(inverse(inverse(double_divide(X0, inverse(X0)))))), inverse(Y1)) -> Y1 % 6.02/6.18 f1(a2) -> false__ % 6.02/6.18 f1(inverse(double_divide(a2, inverse(double_divide(b2, inverse(b2)))))) -> true__ % 6.02/6.18 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 6.02/6.18 inverse(double_divide(Y0, double_divide(X1, inverse(X1)))) -> Y0 % 6.02/6.18 inverse(double_divide(Y0, inverse(X1))) -> double_divide(inverse(Y0), inverse(inverse(X1))) % 6.02/6.18 inverse(double_divide(Y1, inverse(double_divide(X0, inverse(X0))))) -> Y1 % 6.02/6.18 multiply(A, B) -> inverse(double_divide(B, A)) % 6.02/6.18 true__ -> false__ % 6.02/6.18 with the LPO induced by % 6.02/6.18 b2 > a2 > f1 > multiply > inverse > double_divide > true__ > false__ % 6.02/6.18 % 6.02/6.18 % SZS output end Proof % 6.02/6.18 %------------------------------------------------------------------------------