%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP589-1 : 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 10:56:29 EDT 2022 % Result : Unsatisfiable 6.13s 6.28s % Output : Proof 6.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GRP589-1 : TPTP v8.1.0. Released v2.6.0. % 0.06/0.12 % Command : moca.sh %s % 0.11/0.33 % Computer : n029.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Mon Jun 13 13:47:10 EDT 2022 % 0.11/0.33 % CPUTime : % 6.13/6.28 % SZS status Unsatisfiable % 6.13/6.28 % SZS output start Proof % 6.13/6.28 The input problem is unsatisfiable because % 6.13/6.28 % 6.13/6.28 [1] the following set of Horn clauses is unsatisfiable: % 6.13/6.28 % 6.13/6.28 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) = C % 6.13/6.28 multiply(A, B) = inverse(double_divide(B, A)) % 6.13/6.28 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 6.13/6.28 % 6.13/6.28 This holds because % 6.13/6.28 % 6.13/6.28 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.13/6.28 % 6.13/6.28 E: % 6.13/6.28 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) = C % 6.13/6.28 f1(multiply(inverse(a1), a1)) = true__ % 6.13/6.28 f1(multiply(inverse(b1), b1)) = false__ % 6.13/6.28 multiply(A, B) = inverse(double_divide(B, A)) % 6.13/6.28 G: % 6.13/6.28 true__ = false__ % 6.13/6.28 % 6.13/6.28 This holds because % 6.13/6.28 % 6.13/6.28 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.13/6.28 % 6.13/6.28 % 6.13/6.28 double_divide(X0, inverse(X0)) -> g1 % 6.13/6.28 double_divide(X0, inverse(X0)) -> inverse(g1) % 6.13/6.28 double_divide(g1, g1) -> g1 % 6.13/6.28 double_divide(inverse(X1), inverse(inverse(double_divide(Y1, inverse(X1))))) -> Y1 % 6.13/6.28 double_divide(inverse(X2), inverse(inverse(double_divide(double_divide(X0, inverse(Y1)), inverse(double_divide(X0, inverse(X2))))))) -> Y1 % 6.13/6.28 double_divide(inverse(Y0), inverse(inverse(X1))) -> inverse(double_divide(Y0, inverse(X1))) % 6.13/6.28 double_divide(inverse(Y0), inverse(inverse(inverse(inverse(double_divide(X0, inverse(X0))))))) -> Y0 % 6.13/6.28 double_divide(inverse(Y1), inverse(inverse(inverse(double_divide(X0, inverse(X0)))))) -> Y1 % 6.13/6.28 double_divide(inverse(double_divide(X1, inverse(Y2))), inverse(X1)) -> Y2 % 6.13/6.28 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 % 6.13/6.28 double_divide(inverse(double_divide(Y0, inverse(Y0))), inverse(Y3)) -> Y3 % 6.13/6.28 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(X1, inverse(Y0))), inverse(Y3))))), inverse(X1)) -> Y3 % 6.13/6.28 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) -> C % 6.13/6.28 double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(X0))), Y1), inverse(Y2))), Y1) -> Y2 % 6.13/6.28 double_divide(inverse(double_divide(double_divide(inverse(double_divide(Y1, inverse(Y2))), Y3), inverse(Y2))), Y3) -> Y1 % 6.13/6.28 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 % 6.13/6.28 double_divide(inverse(double_divide(double_divide(inverse(inverse(double_divide(X0, inverse(X0)))), Y1), inverse(Y2))), Y1) -> Y2 % 6.13/6.28 double_divide(inverse(g1), g1) -> g1 % 6.13/6.28 double_divide(inverse(g1), g1) -> inverse(g1) % 6.13/6.28 double_divide(inverse(inverse(double_divide(X0, inverse(X0)))), inverse(Y1)) -> Y1 % 6.13/6.28 double_divide(inverse(inverse(inverse(double_divide(X0, inverse(X0))))), inverse(Y1)) -> Y1 % 6.13/6.28 double_divide(inverse(inverse(inverse(inverse(double_divide(X0, inverse(X0)))))), inverse(Y1)) -> Y1 % 6.13/6.28 f1(inverse(double_divide(a1, inverse(a1)))) -> true__ % 6.13/6.28 f1(inverse(double_divide(b1, inverse(b1)))) -> false__ % 6.13/6.28 f1(multiply(inverse(X1), X1)) -> false__ % 6.13/6.28 f1(multiply(inverse(X1), X1)) -> true__ % 6.13/6.28 f1(multiply(inverse(a1), a1)) -> true__ % 6.13/6.28 inverse(double_divide(Y1, inverse(Y1))) -> g1 % 6.13/6.28 inverse(double_divide(Y1, inverse(double_divide(X0, inverse(X0))))) -> Y1 % 6.13/6.28 inverse(double_divide(inverse(g1), g1)) -> g1 % 6.13/6.28 inverse(g1) -> g1 % 6.13/6.28 inverse(inverse(g1)) -> g1 % 6.13/6.28 inverse(multiply(inverse(false__), false__)) -> g1 % 6.13/6.28 multiply(A, B) -> inverse(double_divide(B, A)) % 6.13/6.28 true__ -> false__ % 6.13/6.28 with the LPO induced by % 6.13/6.28 multiply > double_divide > inverse > g1 > a1 > b1 > f1 > true__ > false__ % 6.13/6.28 % 6.13/6.28 % SZS output end Proof % 6.13/6.28 %------------------------------------------------------------------------------