%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP449-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 10:55:31 EDT 2022 % Result : Unsatisfiable 6.00s 6.16s % Output : Proof 6.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP449-1 : TPTP v8.1.0. Released v2.6.0. % 0.14/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n007.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 07:46:24 EDT 2022 % 0.14/0.34 % CPUTime : % 6.00/6.16 % SZS status Unsatisfiable % 6.00/6.16 % SZS output start Proof % 6.00/6.16 The input problem is unsatisfiable because % 6.00/6.16 % 6.00/6.16 [1] the following set of Horn clauses is unsatisfiable: % 6.00/6.16 % 6.00/6.16 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) = B % 6.00/6.16 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 6.00/6.16 inverse(A) = divide(divide(B, B), A) % 6.00/6.16 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 6.00/6.16 % 6.00/6.16 This holds because % 6.00/6.16 % 6.00/6.16 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.00/6.16 % 6.00/6.16 E: % 6.00/6.16 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) = B % 6.00/6.16 f1(a2) = false__ % 6.00/6.16 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 6.00/6.16 inverse(A) = divide(divide(B, B), A) % 6.00/6.16 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 6.00/6.16 G: % 6.00/6.16 true__ = false__ % 6.00/6.16 % 6.00/6.16 This holds because % 6.00/6.16 % 6.00/6.16 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.00/6.16 % 6.00/6.16 % 6.00/6.16 divide(A, divide(divide(C, C), B)) -> multiply(A, B) % 6.00/6.16 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) -> B % 6.00/6.16 divide(X0, X0) -> g1 % 6.00/6.16 divide(Y0, divide(X1, divide(inverse(Y0), divide(divide(inverse(X1), X2), divide(inverse(inverse(Y1)), X2))))) -> Y1 % 6.00/6.16 divide(Y0, divide(Y1, divide(inverse(Y0), inverse(divide(inverse(inverse(Y3)), inverse(Y1)))))) -> Y3 % 6.00/6.16 divide(Y0, divide(divide(X0, Y2), divide(divide(g2, Y0), Y2))) -> divide(g2, divide(g2, divide(g2, X0))) % 6.00/6.16 divide(Y0, divide(divide(inverse(Y1), Y2), divide(inverse(Y0), Y2))) -> Y1 % 6.00/6.16 divide(Y0, divide(g1, divide(divide(g1, Y0), divide(g1, Y1)))) -> Y1 % 6.00/6.16 divide(Y0, divide(g1, divide(g1, Y0))) -> g1 % 6.00/6.16 divide(Y0, divide(g2, divide(divide(g2, Y0), X0))) -> divide(g2, divide(g2, divide(g2, X0))) % 6.00/6.16 divide(Y0, inverse(divide(inverse(Y0), divide(inverse(Y2), divide(inverse(inverse(Y3)), Y2))))) -> Y3 % 6.00/6.16 divide(Y0, inverse(divide(inverse(Y0), inverse(Y1)))) -> Y1 % 6.00/6.16 divide(Y1, g1) -> Y1 % 6.00/6.16 divide(divide(X0, X1), divide(g2, X1)) -> divide(g2, divide(g2, X0)) % 6.00/6.16 divide(divide(Y0, divide(g2, divide(g2, divide(g2, X0)))), X0) -> divide(g2, divide(g2, Y0)) % 6.00/6.16 divide(divide(divide(g1, divide(g1, Y0)), g1), g1) -> Y0 % 6.00/6.16 divide(divide(divide(g2, X0), X1), divide(g2, X1)) -> divide(g2, divide(g2, divide(g2, X0))) % 6.00/6.16 divide(divide(divide(g2, X0), divide(g2, divide(g2, divide(g2, X1)))), X1) -> divide(g2, divide(g2, divide(g2, X0))) % 6.00/6.16 divide(divide(g2, divide(g2, divide(g2, X0))), divide(divide(Y1, Y2), divide(X0, Y2))) -> divide(g2, divide(g2, divide(g2, Y1))) % 6.00/6.16 divide(divide(g2, divide(g2, divide(g2, Y0))), divide(g2, divide(Y0, X0))) -> divide(g2, divide(g2, divide(g2, X0))) % 6.00/6.16 divide(g1, divide(divide(divide(g1, Y0), g1), g1)) -> Y0 % 6.00/6.16 divide(g1, divide(g1, Y0)) -> Y0 % 6.00/6.16 divide(g1, divide(g1, divide(divide(Y0, g1), g1))) -> Y0 % 6.00/6.16 divide(g1, divide(g1, divide(g1, divide(g1, Y1)))) -> Y1 % 6.00/6.16 divide(g2, A) -> divide(g1, A) % 6.00/6.16 divide(g2, divide(divide(X0, Y1), divide(g2, Y1))) -> divide(g2, divide(g2, divide(g2, X0))) % 6.00/6.16 divide(g2, divide(divide(Y0, divide(g2, divide(g2, divide(g2, X0)))), X0)) -> divide(g2, divide(g2, divide(g2, Y0))) % 6.00/6.16 divide(g2, inverse(divide(g2, divide(inverse(Y1), divide(inverse(inverse(Y2)), Y1))))) -> Y2 % 6.00/6.16 divide(inverse(inverse(inverse(X0))), divide(divide(inverse(Y1), Y2), divide(X0, Y2))) -> Y1 % 6.00/6.16 divide(inverse(inverse(inverse(X0))), inverse(divide(X0, inverse(Y1)))) -> Y1 % 6.00/6.16 f1(a2) -> false__ % 6.00/6.16 f1(divide(divide(a2, false__), divide(g1, false__))) -> true__ % 6.00/6.16 f1(divide(divide(a2, g1), g1)) -> true__ % 6.00/6.16 f1(divide(g1, divide(g1, a2))) -> true__ % 6.00/6.16 f1(inverse(inverse(a2))) -> true__ % 6.00/6.16 f1(multiply(multiply(divide(g1, b2), b2), a2)) -> true__ % 6.00/6.16 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 6.00/6.16 g2 -> g1 % 6.00/6.16 inverse(Y1) -> divide(g2, Y1) % 6.00/6.16 inverse(divide(Y0, Y0)) -> g1 % 6.00/6.16 inverse(divide(Y0, inverse(divide(divide(inverse(Y0), Y1), divide(g2, Y1))))) -> g2 % 6.00/6.16 inverse(divide(Y1, inverse(divide(divide(inverse(Y1), Y2), divide(inverse(inverse(Y3)), Y2))))) -> Y3 % 6.00/6.16 inverse(divide(divide(inverse(Y0), inverse(inverse(inverse(X0)))), X0)) -> Y0 % 6.00/6.16 inverse(divide(divide(inverse(Y1), Y2), divide(inverse(divide(X0, X0)), Y2))) -> Y1 % 6.00/6.16 inverse(divide(divide(inverse(Y1), Y2), inverse(Y2))) -> Y1 % 6.00/6.16 inverse(divide(g2, inverse(divide(divide(g2, Y1), divide(inverse(inverse(Y2)), Y1))))) -> Y2 % 6.00/6.16 inverse(divide(inverse(inverse(inverse(X0))), inverse(divide(divide(X0, Y1), divide(inverse(inverse(Y2)), Y1))))) -> Y2 % 6.00/6.16 inverse(inverse(Y0)) -> divide(divide(Y0, g2), g2) % 6.00/6.16 inverse(inverse(divide(X0, X0))) -> g2 % 6.00/6.16 inverse(inverse(divide(Y0, Y0))) -> g1 % 6.00/6.16 inverse(inverse(divide(inverse(inverse(divide(X0, X0))), inverse(Y1)))) -> Y1 % 6.00/6.16 inverse(inverse(inverse(inverse(Y1)))) -> Y1 % 6.00/6.16 multiply(g1, g1) -> g1 % 6.00/6.16 true__ -> false__ % 6.00/6.16 with the LPO induced by % 6.00/6.16 f1 > b2 > inverse > divide > g2 > g1 > multiply > a2 > true__ > false__ % 6.00/6.16 % 6.00/6.16 % SZS output end Proof % 6.00/6.16 %------------------------------------------------------------------------------