%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP710-11 : TPTP v8.1.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n028.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 10:58:04 EDT 2022 % Result : Unsatisfiable 9.30s 9.41s % Output : Proof 9.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP710-11 : TPTP v8.1.0. Released v8.1.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n028.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 10:32:37 EDT 2022 % 0.13/0.34 % CPUTime : % 9.30/9.41 % SZS status Unsatisfiable % 9.30/9.41 % SZS output start Proof % 9.30/9.41 The input problem is unsatisfiable because % 9.30/9.41 % 9.30/9.41 [1] the following set of Horn clauses is unsatisfiable: % 9.30/9.41 % 9.30/9.41 mult(A, unit) = A % 9.30/9.41 mult(unit, A) = A % 9.30/9.41 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C) % 9.30/9.41 mult(A, i(A)) = unit % 9.30/9.41 mult(i(A), A) = unit % 9.30/9.41 mult(X5, x4) = x3 ==> \bottom % 9.30/9.41 % 9.30/9.41 This holds because % 9.30/9.41 % 9.30/9.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 9.30/9.41 % 9.30/9.41 E: % 9.30/9.41 f1(mult(X5, x4)) = true__ % 9.30/9.41 f1(x3) = false__ % 9.30/9.41 mult(A, i(A)) = unit % 9.30/9.41 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C) % 9.30/9.41 mult(A, unit) = A % 9.30/9.41 mult(i(A), A) = unit % 9.30/9.41 mult(unit, A) = A % 9.30/9.41 G: % 9.30/9.41 true__ = false__ % 9.30/9.41 % 9.30/9.41 This holds because % 9.30/9.41 % 9.30/9.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 9.30/9.41 % 9.30/9.41 % 9.30/9.41 f1(Y0) -> true__ % 9.30/9.41 f1(i(mult(X0, mult(X0, mult(X0, mult(X0, x4)))))) -> true__ % 9.30/9.41 f1(i(mult(Y1, mult(Y1, i(x4))))) -> true__ % 9.30/9.41 f1(i(mult(Y1, mult(Y1, x4)))) -> true__ % 9.30/9.41 f1(i(mult(i(mult(x4, x4)), x4))) -> true__ % 9.30/9.41 f1(i(mult(i(x4), i(x4)))) -> true__ % 9.30/9.41 f1(i(mult(i(x4), mult(i(x4), i(x4))))) -> true__ % 9.30/9.41 f1(i(mult(mult(X0, x4), mult(X0, mult(x4, x4))))) -> true__ % 9.30/9.41 f1(i(mult(x4, mult(x4, mult(x4, x4))))) -> true__ % 9.30/9.41 f1(i(mult(x4, x4))) -> true__ % 9.30/9.41 f1(i(x4)) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, i(x4)))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, i(x4)))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, mult(X0, mult(X0, mult(X0, mult(X0, x4))))))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, mult(Y1, mult(Y1, x4))))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, mult(i(x4), i(x4))))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, mult(x4, x4)))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(X0, mult(X0, x4))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(Y1, mult(Y1, i(x4)))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(Y1, mult(Y1, mult(x4, x4)))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(Y1, mult(Y1, x4))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(i(mult(x4, x4)), x4)))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(i(x4), i(x4))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(x4, mult(x4, mult(x4, x4)))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, mult(x4, x4)))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X0, x4))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X1, mult(X1, i(x4))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X1, mult(X1, mult(X0, mult(X1, mult(X1, x4))))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X1, mult(X1, mult(x4, x4))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(X1, mult(X1, x4)))) -> true__ % 9.30/9.41 f1(mult(X0, mult(i(x4), i(x4)))) -> true__ % 9.30/9.41 f1(mult(X0, mult(i(x4), mult(i(x4), mult(i(x4), i(x4)))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(mult(Y1, mult(Y1, i(x4))), mult(Y1, mult(Y1, i(x4)))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(mult(Y1, mult(Y1, mult(x4, x4))), mult(Y1, mult(Y1, mult(x4, x4)))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(mult(Y1, mult(Y1, x4)), mult(Y1, mult(Y1, x4))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(mult(i(mult(x4, x4)), x4), mult(i(mult(x4, x4)), x4)))) -> true__ % 9.30/9.41 f1(mult(X0, mult(x4, mult(x4, mult(x4, mult(x4, mult(x4, mult(x4, mult(x4, x4))))))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(x4, mult(x4, mult(x4, x4))))) -> true__ % 9.30/9.41 f1(mult(X0, mult(x4, x4))) -> true__ % 9.30/9.41 f1(mult(X5, x4)) -> true__ % 9.30/9.41 f1(mult(Y0, i(mult(x4, x4)))) -> true__ % 9.30/9.41 f1(mult(Y0, i(x4))) -> true__ % 9.30/9.41 f1(mult(Y0, mult(X0, mult(X0, mult(X0, mult(X0, i(x4))))))) -> true__ % 9.30/9.41 f1(mult(Y0, mult(X0, mult(X0, mult(X0, mult(X0, x4)))))) -> true__ % 9.30/9.41 f1(mult(Y0, mult(Y0, mult(X0, mult(X0, mult(X0, mult(X0, x4))))))) -> true__ % 9.30/9.41 f1(mult(Y0, mult(Y0, mult(mult(X0, x4), mult(X0, mult(x4, x4)))))) -> true__ % 9.30/9.41 f1(mult(Y0, mult(i(mult(x4, x4)), x4))) -> true__ % 9.30/9.41 f1(mult(Y0, mult(i(x4), mult(i(x4), i(x4))))) -> true__ % 9.30/9.41 f1(mult(Y0, mult(mult(X0, i(x4)), mult(X0, mult(i(x4), i(x4)))))) -> true__ % 9.30/9.41 f1(mult(Y0, mult(mult(X0, mult(x4, x4)), mult(X0, mult(x4, mult(x4, mult(x4, x4))))))) -> true__ % 9.30/9.41 f1(mult(Y0, mult(mult(X0, x4), mult(X0, mult(x4, x4))))) -> true__ % 9.30/9.41 f1(mult(i(mult(x4, x4)), mult(i(mult(x4, x4)), i(mult(x4, x4))))) -> true__ % 9.30/9.41 f1(mult(i(x4), i(x4))) -> true__ % 9.30/9.41 f1(mult(i(x4), mult(i(x4), i(x4)))) -> true__ % 9.30/9.41 f1(mult(mult(X0, i(x4)), mult(X0, mult(i(x4), i(x4))))) -> true__ % 9.30/9.41 f1(mult(mult(X0, mult(X0, x4)), mult(X0, mult(X0, mult(x4, x4))))) -> true__ % 9.30/9.41 f1(mult(mult(X0, mult(Y1, mult(Y1, x4))), mult(X0, mult(mult(Y1, mult(Y1, x4)), mult(Y1, mult(Y1, x4)))))) -> true__ % 9.30/9.41 f1(mult(mult(X0, mult(i(x4), i(x4))), mult(X0, mult(i(x4), mult(i(x4), mult(i(x4), i(x4))))))) -> true__ % 9.30/9.41 f1(mult(mult(X0, mult(x4, x4)), mult(X0, mult(x4, mult(x4, mult(x4, x4)))))) -> true__ % 9.30/9.41 f1(mult(mult(X0, mult(x4, x4)), mult(mult(X0, x4), mult(x4, x4)))) -> true__ % 9.30/9.41 f1(mult(mult(X0, x4), mult(X0, mult(x4, x4)))) -> true__ % 9.30/9.41 f1(mult(mult(X0, x4), mult(mult(X0, x4), mult(mult(X0, x4), mult(X0, mult(x4, x4)))))) -> true__ % 9.30/9.41 f1(mult(mult(mult(X0, x4), mult(x4, x4)), mult(X0, mult(x4, mult(x4, mult(x4, x4)))))) -> true__ % 9.30/9.41 f1(mult(x4, mult(x4, mult(x4, x4)))) -> true__ % 9.30/9.41 f1(unit) -> true__ % 9.30/9.41 f1(x3) -> false__ % 9.30/9.41 f1(x4) -> true__ % 9.30/9.41 i(i(X0)) -> X0 % 9.30/9.41 i(unit) -> unit % 9.30/9.41 mult(A, i(A)) -> unit % 9.30/9.41 mult(A, unit) -> A % 9.30/9.41 mult(X0, mult(X0, mult(X0, i(mult(X0, mult(X0, X0)))))) -> unit % 9.30/9.41 mult(X0, mult(X0, mult(i(mult(X0, X0)), mult(X0, mult(X0, Y1))))) -> mult(X0, mult(X0, Y1)) % 9.30/9.41 mult(X0, mult(i(X0), mult(X0, X1))) -> mult(X0, X1) % 9.30/9.41 mult(Y0, i(mult(Y0, Y0))) -> i(Y0) % 9.30/9.41 mult(Y0, mult(Y0, i(mult(Y0, mult(Y0, mult(Y0, Y0)))))) -> i(mult(Y0, Y0)) % 9.30/9.41 mult(Y0, mult(Y0, mult(Y0, mult(Y0, i(mult(Y0, mult(Y0, mult(Y0, Y0)))))))) -> unit % 9.30/9.41 mult(Y0, mult(Y0, mult(i(mult(Y0, Y0)), i(mult(Y0, Y0))))) -> i(mult(Y0, Y0)) % 9.30/9.41 mult(Y0, mult(Y1, mult(Y1, i(mult(Y0, mult(Y1, mult(Y1, mult(Y0, mult(Y1, Y1))))))))) -> i(mult(Y0, mult(Y1, Y1))) % 9.30/9.41 mult(Y0, mult(Y1, mult(Y1, i(mult(mult(Y0, Y1), Y1))))) -> unit % 9.30/9.41 mult(Y0, mult(i(Y0), i(Y0))) -> i(Y0) % 9.30/9.41 mult(Y0, mult(i(Y0), mult(i(Y0), Y2))) -> mult(i(Y0), Y2) % 9.30/9.41 mult(Y0, mult(i(mult(Y0, Y0)), i(mult(Y0, Y0)))) -> mult(i(Y0), i(mult(Y0, Y0))) % 9.30/9.41 mult(Y0, mult(i(mult(Y0, Y0)), mult(i(mult(Y0, Y0)), i(mult(i(Y0), i(mult(Y0, Y0))))))) -> unit % 9.30/9.41 mult(Y0, mult(mult(Y0, i(mult(Y0, Y0))), mult(Y0, i(mult(Y0, Y0))))) -> mult(Y0, i(mult(Y0, Y0))) % 9.30/9.41 mult(Y0, mult(mult(i(Y0), mult(Y0, X1)), mult(i(Y0), mult(Y0, X1)))) -> mult(mult(Y0, X1), mult(i(Y0), mult(Y0, X1))) % 9.30/9.41 mult(Y1, mult(Y1, i(mult(Y1, Y1)))) -> unit % 9.30/9.41 mult(i(A), A) -> unit % 9.30/9.41 mult(i(X0), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, mult(X0, X0)) % 9.30/9.41 mult(i(X0), mult(X0, mult(X0, mult(X0, mult(X0, i(mult(X0, mult(X0, X0)))))))) -> unit % 9.30/9.41 mult(i(X0), mult(X0, mult(i(X0), Y1))) -> mult(i(X0), Y1) % 9.30/9.41 mult(i(X0), mult(mult(X0, mult(X0, X1)), mult(X0, mult(X0, X1)))) -> mult(mult(X0, X1), mult(X0, mult(X0, X1))) % 9.30/9.41 mult(i(Y1), mult(Y1, Y1)) -> Y1 % 9.30/9.41 mult(i(Y1), mult(Y1, mult(Y1, Y2))) -> mult(Y1, Y2) % 9.30/9.41 mult(i(mult(X0, X0)), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, X0) % 9.30/9.41 mult(i(mult(X0, X0)), mult(X0, mult(X0, mult(X0, mult(X0, Y1))))) -> mult(X0, mult(X0, Y1)) % 9.30/9.41 mult(i(mult(X0, Y1)), mult(mult(X0, Y1), mult(X0, mult(Y1, Y1)))) -> mult(X0, mult(Y1, Y1)) % 9.30/9.41 mult(i(mult(X0, mult(X1, X1))), mult(X0, mult(X1, mult(X1, mult(X0, mult(X1, X1)))))) -> mult(X0, mult(X1, X1)) % 9.30/9.41 mult(mult(X0, Y1), mult(i(mult(X0, Y1)), mult(X0, mult(Y1, Y1)))) -> mult(X0, mult(Y1, Y1)) % 9.30/9.41 mult(mult(X0, mult(X0, X0)), Y2) -> mult(X0, mult(X0, mult(X0, Y2))) % 9.30/9.41 mult(mult(X0, mult(X0, Y1)), Y1) -> mult(X0, mult(X0, mult(Y1, Y1))) % 9.30/9.41 mult(mult(X0, mult(X0, mult(X0, X0))), Y1) -> mult(X0, mult(X0, mult(X0, mult(X0, Y1)))) % 9.30/9.41 mult(mult(X0, mult(Y1, Y1)), Y1) -> mult(mult(X0, Y1), mult(Y1, Y1)) % 9.30/9.41 mult(mult(Y0, Y1), Y1) -> mult(Y0, mult(Y1, Y1)) % 9.30/9.41 mult(mult(Y1, Y1), Y2) -> mult(Y1, mult(Y1, Y2)) % 9.30/9.41 mult(mult(i(Y0), i(mult(Y0, Y0))), Y2) -> mult(Y0, mult(i(mult(Y0, Y0)), mult(i(mult(Y0, Y0)), Y2))) % 9.30/9.41 mult(mult(i(mult(X0, X0)), X0), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, mult(X0, X0)) % 9.30/9.41 mult(mult(i(mult(X0, mult(X0, mult(X0, X0)))), mult(X0, X0)), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, X0) % 9.30/9.41 mult(mult(i(mult(Y1, Y1)), Y1), mult(Y1, Y1)) -> Y1 % 9.30/9.41 mult(mult(mult(A, B), B), C) -> mult(A, mult(B, mult(B, C))) % 9.30/9.41 mult(unit, A) -> A % 9.30/9.41 true__ -> false__ % 9.30/9.41 with the LPO induced by % 9.30/9.41 x4 > x3 > f1 > i > unit > mult > true__ > false__ % 9.30/9.41 % 9.30/9.41 % SZS output end Proof % 9.30/9.41 %------------------------------------------------------------------------------