%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP656-10 : TPTP v8.1.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n019.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 10:57:28 EDT 2022 % Result : Unsatisfiable 5.85s 5.99s % Output : Proof 5.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : GRP656-10 : TPTP v8.1.0. Released v8.1.0. % 0.04/0.14 % Command : moca.sh %s % 0.14/0.35 % Computer : n019.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Mon Jun 13 08:32:10 EDT 2022 % 0.14/0.35 % CPUTime : % 5.85/5.99 % SZS status Unsatisfiable % 5.85/5.99 % SZS output start Proof % 5.85/5.99 The input problem is unsatisfiable because % 5.85/5.99 % 5.85/5.99 [1] the following set of Horn clauses is unsatisfiable: % 5.85/5.99 % 5.85/5.99 mult(A, ld(A, B)) = B % 5.85/5.99 ld(A, mult(A, B)) = B % 5.85/5.99 mult(rd(A, B), B) = A % 5.85/5.99 rd(mult(A, B), B) = A % 5.85/5.99 mult(mult(A, B), mult(C, A)) = mult(mult(A, mult(B, C)), A) % 5.85/5.99 tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)) = tuple(x1(X0), x1_2(X0)) ==> \bottom % 5.85/5.99 % 5.85/5.99 This holds because % 5.85/5.99 % 5.85/5.99 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.85/5.99 % 5.85/5.99 E: % 5.85/5.99 f1(tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)), X0) = true__ % 5.85/5.99 f1(tuple(x1(X0), x1_2(X0)), X0) = false__ % 5.85/5.99 ld(A, mult(A, B)) = B % 5.85/5.99 mult(A, ld(A, B)) = B % 5.85/5.99 mult(mult(A, B), mult(C, A)) = mult(mult(A, mult(B, C)), A) % 5.85/5.99 mult(rd(A, B), B) = A % 5.85/5.99 rd(mult(A, B), B) = A % 5.85/5.99 G: % 5.85/5.99 true__ = false__ % 5.85/5.99 % 5.85/5.99 This holds because % 5.85/5.99 % 5.85/5.99 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.85/5.99 % 5.85/5.99 mult(X0, mult(ld(Y1, Y2), rd(X0, Y1))) = mult(mult(rd(X0, Y1), Y2), rd(X0, Y1)) % 5.85/5.99 mult(mult(Y0, X1), Y0) = mult(mult(Y0, Y1), mult(ld(Y1, X1), Y0)) % 5.85/5.99 f1(tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)), X0) -> true__ % 5.85/5.99 f1(tuple(x1(X0), x1_2(X0)), X0) -> false__ % 5.85/5.99 f1(tuple(x1(ld(X0, X0)), mult(x1_2(ld(X0, X0)), ld(X0, X0))), ld(X0, X0)) -> true__ % 5.85/5.99 ld(A, mult(A, B)) -> B % 5.85/5.99 ld(X0, mult(rd(X0, Y1), mult(Y1, rd(X0, Y1)))) -> rd(X0, Y1) % 5.85/5.99 ld(X1, X1) -> g1 % 5.85/5.99 ld(X1, mult(Y0, mult(ld(Y0, X1), Y0))) -> Y0 % 5.85/5.99 ld(g1, Y1) -> Y1 % 5.85/5.99 ld(mult(Y0, Y1), mult(X1, Y0)) -> mult(ld(Y1, ld(Y0, X1)), Y0) % 5.85/5.99 ld(mult(Y0, mult(Y1, rd(X0, Y0))), mult(mult(Y0, Y1), X0)) -> Y0 % 5.85/5.99 ld(mult(Y0, mult(Y1, rd(ld(mult(Y0, Y1), X1), Y0))), X1) -> Y0 % 5.85/5.99 ld(mult(Y0, mult(ld(Y0, X1), Y2)), mult(X1, mult(Y2, Y0))) -> Y0 % 5.85/5.99 ld(mult(Y0, mult(ld(Y0, rd(X0, mult(Y2, Y0))), Y2)), X0) -> Y0 % 5.85/5.99 ld(mult(Y0, rd(X0, Y0)), mult(Y0, X0)) -> Y0 % 5.85/5.99 ld(mult(Y1, X1), mult(mult(Y1, X2), mult(ld(X2, X1), Y1))) -> Y1 % 5.85/5.99 ld(mult(Y1, Y2), mult(Y1, mult(Y2, Y1))) -> Y1 % 5.85/5.99 ld(mult(Y1, mult(X1, X2)), mult(mult(Y1, X1), mult(X2, Y1))) -> Y1 % 5.85/5.99 ld(mult(ld(Y1, X1), Y1), mult(ld(Y1, X1), X1)) -> ld(Y1, X1) % 5.85/5.99 ld(mult(ld(Y2, X1), mult(Y1, Y2)), mult(mult(ld(Y2, X1), Y1), X1)) -> ld(Y2, X1) % 5.85/5.99 ld(mult(ld(Y2, X1), mult(ld(ld(Y2, X1), Y1), Y2)), mult(Y1, X1)) -> ld(Y2, X1) % 5.85/5.99 ld(mult(rd(X0, Y1), mult(Y1, Y2)), mult(X0, mult(Y2, rd(X0, Y1)))) -> rd(X0, Y1) % 5.85/5.99 ld(mult(rd(X0, Y2), Y1), mult(X0, mult(ld(Y2, Y1), rd(X0, Y2)))) -> rd(X0, Y2) % 5.85/5.99 ld(rd(X0, Y1), X0) -> Y1 % 5.85/5.99 mult(A, ld(A, B)) -> B % 5.85/5.99 mult(X1, mult(ld(X1, Y0), X1)) -> mult(Y0, X1) % 5.85/5.99 mult(Y1, g1) -> Y1 % 5.85/5.99 mult(Y1, mult(ld(Y1, g1), Y1)) -> Y1 % 5.85/5.99 mult(g1, Y1) -> Y1 % 5.85/5.99 mult(ld(ld(X1, Y0), X2), X1) -> ld(Y0, mult(mult(X1, X2), X1)) % 5.85/5.99 mult(mult(A, mult(B, C)), A) -> mult(mult(A, B), mult(C, A)) % 5.85/5.99 mult(mult(X0, X1), X0) -> mult(X0, mult(X1, X0)) % 5.85/5.99 mult(mult(Y0, Y2), mult(ld(Y2, g1), Y0)) -> mult(Y0, Y0) % 5.85/5.99 mult(mult(Y0, rd(X0, Y2)), mult(Y2, Y0)) -> mult(mult(Y0, X0), Y0) % 5.85/5.99 mult(mult(rd(X0, Y1), Y2), mult(ld(Y2, Y1), rd(X0, Y1))) -> mult(X0, rd(X0, Y1)) % 5.85/5.99 mult(rd(A, B), B) -> A % 5.85/5.99 rd(X1, ld(Y0, X1)) -> Y0 % 5.85/5.99 rd(Y0, g1) -> Y0 % 5.85/5.99 rd(Y1, Y1) -> g1 % 5.85/5.99 rd(mult(A, B), B) -> A % 5.85/5.99 rd(mult(X1, mult(Y2, Y0)), Y0) -> mult(Y0, mult(ld(Y0, X1), Y2)) % 5.85/5.99 rd(mult(Y0, X1), ld(Y1, X1)) -> mult(ld(Y1, X1), ld(X1, mult(mult(Y1, Y0), Y1))) % 5.85/5.99 rd(mult(mult(X0, X2), X0), mult(ld(X1, X2), X0)) -> mult(X0, X1) % 5.85/5.99 true__ -> false__ % 5.85/5.99 with the LPO induced by % 5.85/5.99 x1_2 > x1 > tuple > f1 > rd > ld > mult > g1 > true__ > false__ % 5.85/5.99 % 5.85/5.99 % SZS output end Proof % 5.85/5.99 %------------------------------------------------------------------------------