%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP710-10 : TPTP v8.1.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n018.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 10:58:03 EDT 2022 % Result : Unsatisfiable 13.14s 13.21s % Output : Proof 13.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP710-10 : TPTP v8.1.0. Released v8.1.0. % 0.07/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n018.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Tue Jun 14 12:58:58 EDT 2022 % 0.13/0.33 % CPUTime : % 13.14/13.21 % SZS status Unsatisfiable % 13.14/13.21 % SZS output start Proof % 13.14/13.21 The input problem is unsatisfiable because % 13.14/13.21 % 13.14/13.21 [1] the following set of Horn clauses is unsatisfiable: % 13.14/13.21 % 13.14/13.21 mult(A, unit) = A % 13.14/13.21 mult(unit, A) = A % 13.14/13.21 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C) % 13.14/13.21 mult(A, i(A)) = unit % 13.14/13.21 mult(i(A), A) = unit % 13.14/13.21 mult(x0, X2) = x1 ==> \bottom % 13.14/13.21 % 13.14/13.21 This holds because % 13.14/13.21 % 13.14/13.21 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 13.14/13.21 % 13.14/13.21 E: % 13.14/13.21 f1(mult(x0, X2)) = true__ % 13.14/13.21 f1(x1) = false__ % 13.14/13.21 mult(A, i(A)) = unit % 13.14/13.21 mult(A, mult(B, mult(B, C))) = mult(mult(mult(A, B), B), C) % 13.14/13.21 mult(A, unit) = A % 13.14/13.21 mult(i(A), A) = unit % 13.14/13.21 mult(unit, A) = A % 13.14/13.21 G: % 13.14/13.21 true__ = false__ % 13.14/13.21 % 13.14/13.21 This holds because % 13.14/13.21 % 13.14/13.21 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 13.14/13.21 % 13.14/13.21 % 13.14/13.21 f1(X1) -> true__ % 13.14/13.21 f1(i(mult(x0, x0))) -> true__ % 13.14/13.21 f1(i(x0)) -> true__ % 13.14/13.21 f1(mult(i(x0), X1)) -> true__ % 13.14/13.21 f1(mult(x0, X2)) -> true__ % 13.14/13.21 f1(unit) -> true__ % 13.14/13.21 f1(x0) -> true__ % 13.14/13.21 f1(x1) -> false__ % 13.14/13.21 i(i(X0)) -> X0 % 13.14/13.21 i(mult(X0, mult(X0, mult(X0, X0)))) -> mult(i(X0), mult(i(X0), mult(i(X0), i(X0)))) % 13.14/13.21 i(mult(Y0, Y0)) -> mult(i(Y0), i(Y0)) % 13.14/13.21 i(mult(i(X0), i(X0))) -> mult(X0, X0) % 13.14/13.21 i(mult(i(X0), mult(i(X0), mult(i(X0), i(X0))))) -> mult(X0, mult(X0, mult(X0, X0))) % 13.14/13.21 i(mult(i(mult(X0, X0)), X0)) -> X0 % 13.14/13.21 i(mult(i(mult(X0, mult(X0, mult(X0, X0)))), mult(X0, X0))) -> mult(X0, X0) % 13.14/13.21 i(mult(i(mult(X0, mult(X1, mult(X1, mult(X0, mult(X1, X1)))))), mult(X0, mult(X1, X1)))) -> mult(X0, mult(X1, X1)) % 13.14/13.21 i(unit) -> unit % 13.14/13.21 mult(A, i(A)) -> unit % 13.14/13.21 mult(A, unit) -> A % 13.14/13.21 mult(X0, mult(X0, mult(Y1, mult(Y1, i(mult(X0, mult(X0, mult(Y1, Y1)))))))) -> unit % 13.14/13.21 mult(X0, mult(X0, mult(i(mult(X0, X0)), mult(i(mult(X0, X0)), Y1)))) -> mult(i(mult(X0, X0)), Y1) % 13.14/13.21 mult(X0, mult(X0, mult(i(mult(X0, mult(X0, mult(X0, X0)))), mult(X0, X0)))) -> unit % 13.14/13.21 mult(X0, mult(X1, mult(X1, mult(i(mult(X0, mult(X1, mult(X1, mult(X0, mult(X1, X1)))))), mult(X0, mult(X1, X1)))))) -> unit % 13.14/13.21 mult(X0, mult(i(X0), Y1)) -> Y1 % 13.14/13.21 mult(X0, mult(i(X0), mult(X0, X1))) -> mult(X0, X1) % 13.14/13.21 mult(X0, mult(i(mult(X0, X0)), X0)) -> unit % 13.14/13.21 mult(X0, mult(mult(i(mult(X0, X0)), X0), mult(i(mult(X0, X0)), X0))) -> mult(i(mult(X0, X0)), X0) % 13.14/13.21 mult(X0, mult(mult(i(mult(X0, X0)), X0), mult(mult(i(mult(X0, X0)), X0), Y1))) -> mult(mult(i(mult(X0, X0)), X0), Y1) % 13.14/13.21 mult(X1, mult(X1, i(mult(i(Y0), mult(X1, X1))))) -> Y0 % 13.14/13.21 mult(Y0, i(mult(Y0, Y0))) -> i(Y0) % 13.14/13.21 mult(Y0, i(mult(i(X1), mult(Y0, Y0)))) -> mult(i(Y0), X1) % 13.14/13.21 mult(Y0, mult(X0, mult(X0, mult(X0, mult(X0, i(mult(Y0, mult(X0, mult(X0, mult(X0, X0)))))))))) -> unit % 13.14/13.21 mult(Y0, mult(Y0, i(mult(X0, mult(Y0, Y0))))) -> i(X0) % 13.14/13.21 mult(Y0, mult(Y0, i(mult(Y0, mult(Y0, mult(Y0, Y0)))))) -> i(mult(Y0, Y0)) % 13.14/13.21 mult(Y0, mult(Y0, mult(Y0, mult(Y0, i(mult(Y0, mult(Y0, mult(Y0, Y0)))))))) -> unit % 13.14/13.21 mult(Y0, mult(Y0, mult(i(mult(Y0, Y0)), i(mult(Y0, Y0))))) -> i(mult(Y0, Y0)) % 13.14/13.21 mult(Y0, mult(Y1, mult(Y1, i(mult(Y0, mult(Y1, Y1)))))) -> unit % 13.14/13.21 mult(Y0, mult(Y1, mult(Y1, i(mult(Y0, mult(Y1, mult(Y1, mult(Y0, mult(Y1, Y1))))))))) -> i(mult(Y0, mult(Y1, Y1))) % 13.14/13.21 mult(Y0, mult(Y1, mult(Y1, i(mult(mult(Y0, Y1), Y1))))) -> unit % 13.14/13.21 mult(Y0, mult(Y1, mult(Y1, mult(i(mult(Y0, mult(Y1, Y1))), X1)))) -> X1 % 13.14/13.21 mult(Y0, mult(Y1, mult(Y1, mult(i(mult(Y0, mult(Y1, Y1))), i(mult(Y0, mult(Y1, Y1))))))) -> i(mult(Y0, mult(Y1, Y1))) % 13.14/13.21 mult(Y0, mult(i(Y0), i(Y0))) -> i(Y0) % 13.14/13.21 mult(Y0, mult(i(Y0), mult(i(Y0), Y2))) -> mult(i(Y0), Y2) % 13.14/13.21 mult(Y0, mult(i(mult(Y0, Y0)), i(mult(Y0, Y0)))) -> mult(i(Y0), i(mult(Y0, Y0))) % 13.14/13.21 mult(Y0, mult(i(mult(Y0, Y0)), mult(i(mult(Y0, Y0)), i(mult(i(Y0), i(mult(Y0, Y0))))))) -> unit % 13.14/13.21 mult(Y0, mult(mult(X1, mult(X1, i(mult(Y0, mult(X1, X1))))), mult(X1, mult(X1, i(mult(Y0, mult(X1, X1))))))) -> mult(X1, mult(X1, i(mult(Y0, mult(X1, X1))))) % 13.14/13.21 mult(Y0, mult(mult(Y0, i(mult(Y0, Y0))), mult(Y0, i(mult(Y0, Y0))))) -> mult(Y0, i(mult(Y0, Y0))) % 13.14/13.21 mult(Y0, mult(mult(i(Y0), X1), mult(i(Y0), X1))) -> mult(X1, mult(i(Y0), X1)) % 13.14/13.21 mult(Y0, mult(mult(i(Y0), X1), mult(mult(i(Y0), X1), i(mult(X1, mult(i(Y0), X1)))))) -> unit % 13.14/13.21 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))) % 13.14/13.21 mult(Y0, mult(mult(i(Y0), mult(i(Y0), X1)), mult(i(Y0), mult(i(Y0), X1)))) -> mult(mult(i(Y0), X1), mult(i(Y0), mult(i(Y0), X1))) % 13.14/13.21 mult(Y1, mult(Y1, i(mult(Y1, Y1)))) -> unit % 13.14/13.21 mult(Y1, mult(Y1, mult(i(mult(Y1, Y1)), i(Y1)))) -> i(Y1) % 13.14/13.21 mult(i(A), A) -> unit % 13.14/13.21 mult(i(X0), mult(X0, mult(i(X0), Y1))) -> mult(i(X0), Y1) % 13.14/13.21 mult(i(X0), mult(i(X0), mult(i(mult(i(X0), i(X0))), X0))) -> X0 % 13.14/13.21 mult(i(X0), mult(i(mult(i(X0), i(X0))), i(mult(i(X0), i(X0))))) -> mult(X0, i(mult(i(X0), i(X0)))) % 13.14/13.21 mult(i(X0), mult(i(mult(i(X0), i(X0))), mult(i(mult(i(X0), i(X0))), i(mult(X0, i(mult(i(X0), i(X0)))))))) -> unit % 13.14/13.21 mult(i(X0), mult(mult(X0, X1), mult(X0, X1))) -> mult(X1, mult(X0, X1)) % 13.14/13.21 mult(i(X0), mult(mult(X0, X1), mult(mult(X0, X1), i(mult(X1, mult(X0, X1)))))) -> unit % 13.14/13.21 mult(i(X0), mult(mult(X0, mult(X0, X1)), mult(X0, mult(X0, X1)))) -> mult(mult(X0, X1), mult(X0, mult(X0, X1))) % 13.14/13.21 mult(i(Y0), i(mult(i(X1), mult(i(Y0), i(Y0))))) -> mult(Y0, X1) % 13.14/13.21 mult(i(Y0), i(mult(i(Y0), i(Y0)))) -> Y0 % 13.14/13.21 mult(i(Y0), mult(Y0, Y1)) -> Y1 % 13.14/13.21 mult(i(Y1), mult(Y1, Y1)) -> Y1 % 13.14/13.21 mult(i(Y1), mult(Y1, mult(Y1, Y2))) -> mult(Y1, Y2) % 13.14/13.21 mult(i(mult(X0, X0)), X0) -> i(X0) % 13.14/13.21 mult(i(mult(X0, X0)), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, X0) % 13.14/13.21 mult(i(mult(X0, X0)), mult(X0, mult(X0, mult(X0, mult(X0, Y1))))) -> mult(X0, mult(X0, Y1)) % 13.14/13.21 mult(i(mult(X0, X0)), mult(mult(X0, mult(X0, X1)), mult(X0, mult(X0, X1)))) -> mult(X1, mult(X0, mult(X0, X1))) % 13.14/13.21 mult(i(mult(X0, Y1)), mult(X0, mult(Y1, Y1))) -> Y1 % 13.14/13.21 mult(i(mult(X0, Y1)), mult(mult(X0, Y1), mult(X0, mult(Y1, Y1)))) -> mult(X0, mult(Y1, Y1)) % 13.14/13.21 mult(i(mult(X0, mult(X0, mult(X0, X0)))), mult(X0, X0)) -> i(mult(X0, X0)) % 13.14/13.21 mult(i(mult(X0, mult(X0, mult(X0, X0)))), mult(X0, mult(X0, mult(X0, mult(X0, Y1))))) -> Y1 % 13.14/13.21 mult(i(mult(X0, mult(X0, mult(X0, mult(X0, mult(X0, X0)))))), mult(X0, mult(X0, X0))) -> i(mult(X0, mult(X0, X0))) % 13.14/13.21 mult(i(mult(X0, mult(X1, X1))), mult(X0, mult(X1, mult(X1, mult(X0, mult(X1, X1)))))) -> mult(X0, mult(X1, X1)) % 13.14/13.21 mult(i(mult(X0, mult(X1, mult(X1, mult(X0, mult(X1, X1)))))), mult(X0, mult(X1, X1))) -> i(mult(X0, mult(X1, X1))) % 13.14/13.21 mult(i(mult(Y1, Y1)), mult(Y1, mult(Y1, Y2))) -> Y2 % 13.14/13.21 mult(i(mult(i(Y1), mult(i(Y1), i(Y1)))), mult(i(Y1), i(Y1))) -> Y1 % 13.14/13.21 mult(i(mult(i(mult(Y1, Y1)), i(mult(Y1, Y1)))), mult(i(mult(Y1, Y1)), i(Y1))) -> Y1 % 13.14/13.21 mult(i(mult(mult(X0, Y1), mult(X0, Y1))), mult(mult(X0, Y1), mult(X0, mult(Y1, Y1)))) -> Y1 % 13.14/13.21 mult(mult(X0, Y1), mult(i(mult(X0, Y1)), mult(X0, mult(Y1, Y1)))) -> mult(X0, mult(Y1, Y1)) % 13.14/13.21 mult(mult(X0, mult(X0, X0)), Y2) -> mult(X0, mult(X0, mult(X0, Y2))) % 13.14/13.21 mult(mult(X0, mult(X0, Y1)), Y1) -> mult(X0, mult(X0, mult(Y1, Y1))) % 13.14/13.21 mult(mult(X0, mult(X0, mult(X0, X0))), Y1) -> mult(X0, mult(X0, mult(X0, mult(X0, Y1)))) % 13.14/13.21 mult(mult(X0, mult(Y1, Y1)), Y1) -> mult(mult(X0, Y1), mult(Y1, Y1)) % 13.14/13.21 mult(mult(X0, mult(Y1, Y1)), mult(Y1, mult(Y1, i(mult(X0, mult(Y1, mult(Y1, mult(Y1, Y1)))))))) -> unit % 13.14/13.21 mult(mult(X1, mult(i(Y0), X1)), Y2) -> mult(Y0, mult(mult(i(Y0), X1), mult(mult(i(Y0), X1), Y2))) % 13.14/13.21 mult(mult(Y0, Y1), Y1) -> mult(Y0, mult(Y1, Y1)) % 13.14/13.21 mult(mult(Y1, Y1), Y2) -> mult(Y1, mult(Y1, Y2)) % 13.14/13.21 mult(mult(i(Y0), i(mult(Y0, Y0))), Y2) -> mult(Y0, mult(i(mult(Y0, Y0)), mult(i(mult(Y0, Y0)), Y2))) % 13.14/13.21 mult(mult(i(mult(X0, X0)), X0), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, mult(X0, X0)) % 13.14/13.21 mult(mult(i(mult(X0, X0)), X0), mult(X0, mult(mult(i(mult(X0, X0)), X0), Y1))) -> mult(mult(i(mult(X0, X0)), X0), Y1) % 13.14/13.21 mult(mult(i(mult(X0, mult(X0, mult(X0, X0)))), mult(X0, X0)), mult(X0, mult(X0, mult(X0, X0)))) -> mult(X0, X0) % 13.14/13.21 mult(mult(i(mult(Y1, Y1)), Y1), mult(Y1, Y1)) -> Y1 % 13.14/13.21 mult(mult(mult(A, B), B), C) -> mult(A, mult(B, mult(B, C))) % 13.14/13.21 mult(unit, A) -> A % 13.14/13.21 true__ -> false__ % 13.14/13.21 with the LPO induced by % 13.14/13.21 x0 > x1 > f1 > i > unit > mult > true__ > false__ % 13.14/13.21 % 13.14/13.21 % SZS output end Proof % 13.14/13.21 %------------------------------------------------------------------------------