%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP529-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n015.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 10:56:03 EDT 2022 % Result : Unsatisfiable 2.05s 2.13s % Output : Proof 2.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP529-1 : TPTP v8.1.0. Released v2.6.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n015.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jun 13 13:23:23 EDT 2022 % 0.13/0.34 % CPUTime : % 2.05/2.13 % SZS status Unsatisfiable % 2.05/2.13 % SZS output start Proof % 2.05/2.13 The input problem is unsatisfiable because % 2.05/2.13 % 2.05/2.13 [1] the following set of Horn clauses is unsatisfiable: % 2.05/2.13 % 2.05/2.13 divide(divide(A, divide(B, C)), divide(A, B)) = C % 2.05/2.13 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 2.05/2.13 inverse(A) = divide(divide(B, B), A) % 2.05/2.13 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 2.05/2.13 % 2.05/2.13 This holds because % 2.05/2.13 % 2.05/2.13 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.05/2.13 % 2.05/2.13 E: % 2.05/2.13 divide(divide(A, divide(B, C)), divide(A, B)) = C % 2.05/2.13 f1(multiply(inverse(a1), a1)) = true__ % 2.05/2.13 f1(multiply(inverse(b1), b1)) = false__ % 2.05/2.13 inverse(A) = divide(divide(B, B), A) % 2.05/2.13 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 2.05/2.13 G: % 2.05/2.13 true__ = false__ % 2.05/2.13 % 2.05/2.13 This holds because % 2.05/2.13 % 2.05/2.13 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.05/2.13 % 2.05/2.13 divide(X0, divide(Y1, divide(g1, X0))) = divide(g1, Y1) % 2.05/2.13 divide(X1, inverse(divide(Y1, X1))) -> Y1 % 2.05/2.13 divide(X2, divide(divide(Y1, divide(Y2, X2)), Y1)) -> Y2 % 2.05/2.13 divide(Y0, Y0) -> g1 % 2.05/2.13 divide(Y0, divide(Y0, Y1)) -> Y1 % 2.05/2.13 divide(Y0, divide(g1, divide(Y1, Y0))) -> Y1 % 2.05/2.13 divide(Y0, g1) -> Y0 % 2.05/2.13 divide(divide(A, divide(B, C)), divide(A, B)) -> C % 2.05/2.13 divide(divide(X0, X1), X0) -> divide(g1, X1) % 2.05/2.13 divide(divide(Y0, g1), divide(Y0, Y2)) -> Y2 % 2.05/2.13 divide(divide(Y0, inverse(Y2)), divide(Y0, divide(X0, X0))) -> Y2 % 2.05/2.13 divide(divide(divide(g1, divide(g1, Y0)), divide(g1, Y1)), Y0) -> Y1 % 2.05/2.13 divide(divide(g1, X1), divide(Y1, X1)) -> divide(g1, Y1) % 2.05/2.13 divide(divide(g1, divide(divide(g1, Y0), Y1)), Y0) -> Y1 % 2.05/2.13 divide(g1, divide(g1, Y0)) -> Y0 % 2.05/2.13 divide(g1, inverse(Y2)) -> Y2 % 2.05/2.13 divide(inverse(divide(divide(divide(X0, X1), X0), Y1)), X1) -> Y1 % 2.05/2.13 divide(inverse(divide(inverse(X0), Y1)), X0) -> Y1 % 2.05/2.13 f1(divide(inverse(a1), inverse(a1))) -> true__ % 2.05/2.13 f1(g1) -> false__ % 2.05/2.13 f1(g1) -> true__ % 2.05/2.13 f1(multiply(inverse(a1), a1)) -> true__ % 2.05/2.13 f1(multiply(inverse(b1), b1)) -> false__ % 2.05/2.13 inverse(Y1) -> divide(g1, Y1) % 2.05/2.13 inverse(divide(X1, Y0)) -> divide(divide(g1, X1), divide(g1, Y0)) % 2.05/2.13 inverse(divide(X1, inverse(Y0))) -> divide(divide(g1, X1), Y0) % 2.05/2.13 inverse(divide(divide(Y1, Y2), Y1)) -> Y2 % 2.05/2.13 multiply(A, B) -> divide(A, divide(g1, B)) % 2.05/2.13 true__ -> false__ % 2.05/2.13 with the LPO induced by % 2.05/2.13 a1 > b1 > multiply > inverse > divide > g1 > f1 > true__ > false__ % 2.05/2.13 % 2.05/2.13 % SZS output end Proof % 2.05/2.13 %------------------------------------------------------------------------------