%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP657-10 : TPTP v8.1.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 5.23s 5.36s % Output : Proof 5.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP657-10 : TPTP v8.1.0. Released v8.1.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n020.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 % 0.12/0.34 % DateTime : Tue Jun 14 12:16:04 EDT 2022 % 0.12/0.34 % CPUTime : % 5.23/5.36 % SZS status Unsatisfiable % 5.23/5.36 % SZS output start Proof % 5.23/5.36 The input problem is unsatisfiable because % 5.23/5.36 % 5.23/5.36 [1] the following set of Horn clauses is unsatisfiable: % 5.23/5.36 % 5.23/5.36 mult(A, ld(A, B)) = B % 5.23/5.36 ld(A, mult(A, B)) = B % 5.23/5.36 mult(rd(A, B), B) = A % 5.23/5.36 rd(mult(A, B), B) = A % 5.23/5.36 mult(mult(A, B), mult(C, A)) = mult(A, mult(mult(B, C), A)) % 5.23/5.36 tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)) = tuple(x1(X0), x1_2(X0)) ==> \bottom % 5.23/5.36 % 5.23/5.36 This holds because % 5.23/5.36 % 5.23/5.36 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.23/5.36 % 5.23/5.36 E: % 5.23/5.36 f1(tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)), X0) = true__ % 5.23/5.36 f1(tuple(x1(X0), x1_2(X0)), X0) = false__ % 5.23/5.36 ld(A, mult(A, B)) = B % 5.23/5.36 mult(A, ld(A, B)) = B % 5.23/5.36 mult(mult(A, B), mult(C, A)) = mult(A, mult(mult(B, C), A)) % 5.23/5.36 mult(rd(A, B), B) = A % 5.23/5.36 rd(mult(A, B), B) = A % 5.23/5.36 G: % 5.23/5.36 true__ = false__ % 5.23/5.36 % 5.23/5.36 This holds because % 5.23/5.36 % 5.23/5.36 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.23/5.36 % 5.23/5.36 mult(mult(A, B), mult(C, A)) = mult(A, mult(mult(B, C), A)) % 5.23/5.36 mult(mult(ld(X0, rd(X0, Y1)), rd(mult(Y2, rd(X0, Y1)), X0)), X0) = mult(ld(Y1, Y2), rd(X0, Y1)) % 5.23/5.36 mult(mult(ld(Y1, g1), rd(Y2, Y1)), Y1) = ld(Y1, Y2) % 5.23/5.36 mult(mult(ld(Y2, X1), Y1), X1) = mult(ld(Y2, X1), mult(mult(Y1, Y2), ld(Y2, X1))) % 5.23/5.36 f1(tuple(mult(X0, x1(X0)), mult(x1_2(X0), X0)), X0) -> true__ % 5.23/5.36 f1(tuple(x1(X0), x1_2(X0)), X0) -> false__ % 5.23/5.36 f1(tuple(x1(ld(X0, X0)), mult(x1_2(ld(X0, X0)), ld(X0, X0))), ld(X0, X0)) -> true__ % 5.23/5.36 ld(X0, X0) -> g1 % 5.23/5.36 ld(Y0, mult(Y1, X0)) -> mult(mult(ld(Y0, Y1), rd(X0, Y0)), Y0) % 5.23/5.36 ld(g1, Y1) -> Y1 % 5.23/5.36 ld(ld(Y0, Y0), X1) -> X1 % 5.23/5.36 ld(mult(Y0, Y1), X1) -> mult(ld(Y1, rd(ld(Y0, X1), Y0)), Y0) % 5.23/5.36 ld(mult(Y0, Y1), mult(Y0, X0)) -> mult(ld(Y1, rd(X0, Y0)), Y0) % 5.23/5.36 ld(mult(ld(Y1, Y1), X1), mult(X1, Y1)) -> Y1 % 5.23/5.36 ld(rd(X0, Y1), X0) -> Y1 % 5.23/5.36 mult(A, ld(A, B)) -> B % 5.23/5.36 mult(X1, mult(ld(ld(Y0, X1), Y2), Y0)) -> mult(Y0, mult(Y2, Y0)) % 5.23/5.36 mult(Y1, g1) -> Y1 % 5.23/5.36 mult(Y1, mult(ld(Y1, Y0), Y1)) -> mult(Y0, Y1) % 5.23/5.36 mult(g1, Y1) -> Y1 % 5.23/5.36 mult(ld(Y1, Y1), X1) -> X1 % 5.23/5.36 mult(ld(Y2, rd(Y2, Y0)), Y0) -> g1 % 5.23/5.36 mult(ld(ld(Y0, X1), Y2), Y0) -> mult(mult(ld(X1, Y0), rd(mult(Y2, Y0), X1)), X1) % 5.23/5.36 mult(mult(Y0, Y1), Y0) -> mult(Y0, mult(Y1, Y0)) % 5.23/5.36 mult(mult(Y0, Y1), mult(ld(Y1, X1), Y0)) -> mult(Y0, mult(X1, Y0)) % 5.23/5.36 mult(mult(Y0, rd(X0, Y2)), mult(Y2, Y0)) -> mult(Y0, mult(X0, Y0)) % 5.23/5.36 mult(mult(Y0, rd(g1, Y1)), Y1) -> Y0 % 5.23/5.36 mult(mult(Y1, Y2), ld(X0, X0)) -> mult(Y1, mult(Y2, ld(X0, X0))) % 5.23/5.36 mult(mult(ld(Y0, rd(X0, mult(Y2, Y0))), Y2), Y0) -> ld(Y0, X0) % 5.23/5.36 mult(mult(mult(ld(Y0, rd(Y0, X1)), rd(mult(X1, rd(Y0, X1)), Y0)), Y0), X1) -> Y0 % 5.23/5.36 mult(rd(A, B), B) -> A % 5.23/5.36 mult(rd(X0, Y1), mult(mult(Y1, Y2), rd(X0, Y1))) -> mult(X0, mult(Y2, rd(X0, Y1))) % 5.23/5.36 rd(X1, X1) -> g1 % 5.23/5.36 rd(X1, ld(Y0, X1)) -> Y0 % 5.23/5.36 rd(Y0, g1) -> Y0 % 5.23/5.36 rd(mult(A, B), B) -> A % 5.23/5.36 rd(mult(Y0, X0), mult(ld(Y2, rd(X0, Y0)), Y0)) -> mult(Y0, Y2) % 5.23/5.36 rd(mult(Y0, mult(X0, Y0)), mult(Y2, Y0)) -> mult(Y0, rd(X0, Y2)) % 5.23/5.36 rd(mult(ld(Y1, X1), X1), mult(ld(Y2, Y1), ld(Y1, X1))) -> mult(ld(Y1, X1), Y2) % 5.23/5.36 rd(mult(ld(Y2, X1), mult(mult(Y1, Y2), ld(Y2, X1))), X1) -> mult(ld(Y2, X1), Y1) % 5.23/5.36 rd(mult(mult(Y0, X1), mult(X2, Y0)), mult(mult(X1, X2), Y0)) -> Y0 % 5.23/5.36 rd(mult(mult(Y0, Y1), Y0), mult(Y1, Y0)) -> Y0 % 5.23/5.36 true__ -> false__ % 5.23/5.36 with the LPO induced by % 5.23/5.36 x1_2 > x1 > tuple > f1 > ld > rd > mult > g1 > true__ > false__ % 5.23/5.36 % 5.23/5.36 % SZS output end Proof % 5.23/5.36 %------------------------------------------------------------------------------