%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP700-10 : TPTP v8.1.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 10:57:56 EDT 2022 % Result : Unsatisfiable 6.43s 6.56s % Output : Proof 6.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP700-10 : TPTP v8.1.0. Released v8.1.0. % 0.07/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n025.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 14 02:26:54 EDT 2022 % 0.12/0.34 % CPUTime : % 6.43/6.56 % SZS status Unsatisfiable % 6.43/6.56 % SZS output start Proof % 6.43/6.56 The input problem is unsatisfiable because % 6.43/6.56 % 6.43/6.56 [1] the following set of Horn clauses is unsatisfiable: % 6.43/6.56 % 6.43/6.56 mult(A, ld(A, B)) = B % 6.43/6.56 ld(A, mult(A, B)) = B % 6.43/6.56 mult(rd(A, B), B) = A % 6.43/6.56 rd(mult(A, B), B) = A % 6.43/6.56 mult(A, unit) = A % 6.43/6.56 mult(unit, A) = A % 6.43/6.56 mult(mult(mult(A, B), A), mult(A, C)) = mult(A, mult(mult(mult(B, A), A), C)) % 6.43/6.56 mult(mult(A, B), mult(B, mult(C, B))) = mult(mult(A, mult(B, mult(B, C))), B) % 6.43/6.56 tuple(mult(X1, x0), mult(x0, X1)) = tuple(unit, unit) ==> \bottom % 6.43/6.56 % 6.43/6.56 This holds because % 6.43/6.56 % 6.43/6.56 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.43/6.56 % 6.43/6.56 E: % 6.43/6.56 f1(tuple(mult(X1, x0), mult(x0, X1))) = true__ % 6.43/6.56 f1(tuple(unit, unit)) = false__ % 6.43/6.56 ld(A, mult(A, B)) = B % 6.43/6.56 mult(A, ld(A, B)) = B % 6.43/6.56 mult(A, unit) = A % 6.43/6.56 mult(mult(A, B), mult(B, mult(C, B))) = mult(mult(A, mult(B, mult(B, C))), B) % 6.43/6.56 mult(mult(mult(A, B), A), mult(A, C)) = mult(A, mult(mult(mult(B, A), A), C)) % 6.43/6.56 mult(rd(A, B), B) = A % 6.43/6.56 mult(unit, A) = A % 6.43/6.56 rd(mult(A, B), B) = A % 6.43/6.56 G: % 6.43/6.56 true__ = false__ % 6.43/6.56 % 6.43/6.56 This holds because % 6.43/6.56 % 6.43/6.56 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.43/6.56 % 6.43/6.56 % 6.43/6.56 f1(tuple(X0, mult(x0, rd(X0, x0)))) -> true__ % 6.43/6.56 f1(tuple(mult(X1, x0), mult(x0, X1))) -> true__ % 6.43/6.56 f1(tuple(mult(ld(x0, X1), x0), X1)) -> true__ % 6.43/6.56 f1(tuple(mult(x0, mult(x0, x0)), mult(x0, mult(x0, x0)))) -> true__ % 6.43/6.56 f1(tuple(unit, unit)) -> false__ % 6.43/6.56 f1(tuple(x0, x0)) -> true__ % 6.43/6.56 ld(A, mult(A, B)) -> B % 6.43/6.56 ld(Y0, Y0) -> unit % 6.43/6.56 ld(ld(Y1, unit), unit) -> Y1 % 6.43/6.56 ld(mult(X0, X0), mult(X0, mult(mult(X0, X0), X1))) -> mult(X0, X1) % 6.43/6.56 ld(mult(X0, mult(Y1, Y1)), mult(mult(X0, Y1), mult(Y1, Y1))) -> Y1 % 6.43/6.56 ld(mult(Y0, mult(Y0, mult(ld(Y0, rd(X0, Y0)), Y0))), mult(Y0, mult(X0, Y0))) -> Y0 % 6.43/6.56 ld(mult(Y0, mult(Y0, mult(ld(Y0, rd(unit, Y0)), Y0))), mult(Y0, Y0)) -> Y0 % 6.43/6.56 ld(mult(Y1, X1), mult(Y1, mult(Y1, mult(ld(Y1, X1), Y1)))) -> Y1 % 6.43/6.56 ld(mult(Y1, Y1), mult(Y1, mult(Y1, Y1))) -> Y1 % 6.43/6.56 ld(mult(mult(Y1, X1), Y1), mult(Y1, mult(mult(X1, Y1), Y1))) -> Y1 % 6.43/6.56 ld(mult(rd(X0, Y1), mult(Y1, Y1)), mult(X0, mult(Y1, Y1))) -> Y1 % 6.43/6.56 ld(mult(rd(unit, Y1), mult(Y1, Y1)), mult(Y1, Y1)) -> Y1 % 6.43/6.56 ld(rd(X0, Y1), X0) -> Y1 % 6.43/6.56 ld(unit, Y1) -> Y1 % 6.43/6.56 mult(A, ld(A, B)) -> B % 6.43/6.56 mult(A, mult(mult(mult(B, A), A), C)) -> mult(mult(A, mult(A, mult(ld(A, B), A))), mult(A, C)) % 6.43/6.56 mult(A, unit) -> A % 6.43/6.56 mult(X1, rd(unit, X1)) -> unit % 6.43/6.56 mult(Y0, ld(mult(Y0, Y0), X1)) -> ld(mult(Y0, Y0), mult(Y0, X1)) % 6.43/6.56 mult(Y0, mult(Y0, mult(ld(Y0, ld(Y0, X1)), Y0))) -> mult(X1, Y0) % 6.43/6.56 mult(Y0, mult(mult(Y0, Y0), ld(Y0, X1))) -> mult(mult(Y0, Y0), X1) % 6.43/6.56 mult(Y0, mult(mult(ld(Y0, X1), Y0), Y0)) -> mult(mult(X1, Y0), Y0) % 6.43/6.56 mult(ld(Y0, unit), Y0) -> unit % 6.43/6.56 mult(mult(A, mult(B, mult(B, C))), B) -> mult(mult(A, B), mult(B, mult(C, B))) % 6.43/6.56 mult(mult(Y0, X1), Y0) -> mult(Y0, mult(Y0, mult(ld(Y0, X1), Y0))) % 6.43/6.56 mult(mult(Y0, Y0), mult(Y0, Y2)) -> mult(Y0, mult(mult(Y0, Y0), Y2)) % 6.43/6.56 mult(mult(Y0, mult(Y1, Y1)), Y1) -> mult(mult(Y0, Y1), mult(Y1, Y1)) % 6.43/6.56 mult(mult(ld(mult(Y1, Y1), unit), Y1), mult(Y1, Y1)) -> Y1 % 6.43/6.56 mult(mult(rd(X0, mult(Y1, Y1)), Y1), mult(Y1, Y1)) -> mult(X0, Y1) % 6.43/6.56 mult(rd(A, B), B) -> A % 6.43/6.56 mult(rd(unit, X1), mult(X1, rd(unit, X1))) -> rd(unit, X1) % 6.43/6.56 mult(unit, A) -> A % 6.43/6.56 rd(X1, ld(Y0, X1)) -> Y0 % 6.43/6.56 rd(Y0, unit) -> Y0 % 6.43/6.56 rd(Y1, Y1) -> unit % 6.43/6.56 rd(mult(A, B), B) -> A % 6.43/6.56 rd(mult(X0, mult(mult(X0, X0), X1)), mult(X0, X1)) -> mult(X0, X0) % 6.43/6.56 rd(mult(Y1, mult(Y1, Y1)), Y1) -> mult(Y1, Y1) % 6.43/6.56 rd(mult(mult(X0, Y1), mult(Y1, Y1)), Y1) -> mult(X0, mult(Y1, Y1)) % 6.43/6.56 rd(rd(unit, X0), mult(X0, rd(unit, X0))) -> rd(unit, X0) % 6.43/6.56 rd(unit, Y1) -> ld(Y1, unit) % 6.43/6.56 true__ -> false__ % 6.43/6.56 with the LPO induced by % 6.43/6.56 x0 > tuple > f1 > rd > mult > ld > unit > true__ > false__ % 6.43/6.56 % 6.43/6.56 % SZS output end Proof % 6.43/6.56 %------------------------------------------------------------------------------