%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL045-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n029.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 : Fri Jul 15 00:37:09 EDT 2022 % Result : Unsatisfiable 16.95s 17.12s % Output : Proof 16.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : COL045-1 : TPTP v8.1.0. Released v1.0.0. % 0.06/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n029.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 May 31 14:41:00 EDT 2022 % 0.12/0.33 % CPUTime : % 16.95/17.12 % SZS status Unsatisfiable % 16.95/17.12 % SZS output start Proof % 16.95/17.12 The input problem is unsatisfiable because % 16.95/17.12 % 16.95/17.12 [1] the following set of Horn clauses is unsatisfiable: % 16.95/17.12 % 16.95/17.12 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)) % 16.95/17.12 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 16.95/17.12 apply(m, X) = apply(X, X) % 16.95/17.12 Y = apply(combinator, Y) ==> \bottom % 16.95/17.12 % 16.95/17.12 This holds because % 16.95/17.12 % 16.95/17.12 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 16.95/17.12 % 16.95/17.12 E: % 16.95/17.12 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 16.95/17.12 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)) % 16.95/17.12 apply(m, X) = apply(X, X) % 16.95/17.12 f1(Y, Y) = true__ % 16.95/17.12 f1(apply(combinator, Y), Y) = false__ % 16.95/17.12 G: % 16.95/17.12 true__ = false__ % 16.95/17.12 % 16.95/17.12 This holds because % 16.95/17.12 % 16.95/17.12 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 16.95/17.12 % 16.95/17.12 apply(X0, apply(Y1, apply(Y1, Y1))) = apply(apply(apply(s, apply(b, X0)), m), Y1) % 16.95/17.12 apply(X0, apply(Y1, apply(Y2, Y1))) = apply(apply(apply(s, apply(b, X0)), Y2), Y1) % 16.95/17.12 apply(Y0, apply(Y1, apply(m, Y1))) = apply(apply(apply(s, apply(b, Y0)), m), Y1) % 16.95/17.12 apply(Y0, apply(apply(m, Y0), Y2)) = apply(Y0, apply(apply(Y0, Y0), Y2)) % 16.95/17.12 apply(apply(Y0, Y1), apply(Y1, Y1)) = apply(apply(apply(s, Y0), m), Y1) % 16.95/17.12 apply(apply(Y1, Y1), apply(Y2, Y1)) = apply(apply(apply(s, m), Y2), Y1) % 16.95/17.12 apply(apply(apply(apply(m, s), X2), Y0), Y2) = apply(apply(Y0, Y2), apply(apply(X2, Y0), Y2)) % 16.95/17.12 apply(apply(apply(apply(m, s), m), Y0), Y2) = apply(apply(Y0, Y2), apply(apply(Y0, Y0), Y2)) % 16.95/17.12 apply(apply(apply(m, s), Y1), Y2) = apply(apply(s, Y2), apply(Y1, Y2)) % 16.95/17.12 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)) % 16.95/17.12 apply(apply(m, Y1), apply(apply(Y1, Y1), Y1)) = apply(apply(apply(apply(m, s), m), Y1), Y1) % 16.95/17.12 apply(apply(m, apply(s, Y0)), Y2) = apply(apply(Y0, Y2), apply(apply(s, Y0), Y2)) % 16.95/17.12 apply(apply(m, apply(s, m)), Y1) = apply(apply(Y1, Y1), apply(apply(s, m), Y1)) % 16.95/17.12 apply(apply(s, Y0), apply(Y0, Y0)) = apply(apply(apply(m, s), m), Y0) % 16.95/17.12 apply(b, apply(Y1, apply(Y1, Y1))) = apply(apply(apply(s, apply(m, b)), m), Y1) % 16.95/17.12 apply(b, apply(Y1, apply(Y2, Y1))) = apply(apply(apply(s, apply(m, b)), Y2), Y1) % 16.95/17.12 apply(m, X) = apply(X, X) % 16.95/17.12 apply(m, apply(apply(b, Y0), Y1)) = apply(Y0, apply(Y1, apply(apply(b, Y0), Y1))) % 16.95/17.12 apply(X0, apply(apply(b, X0), apply(m, apply(b, X0)))) -> apply(m, apply(m, apply(b, X0))) % 16.95/17.12 apply(apply(Y0, Y0), apply(Y0, Y0)) -> apply(m, apply(m, Y0)) % 16.95/17.12 apply(apply(Y0, Y0), apply(m, Y0)) -> apply(m, apply(Y0, Y0)) % 16.95/17.12 apply(apply(Y0, Y0), apply(m, Y0)) -> apply(m, apply(m, Y0)) % 16.95/17.12 apply(apply(apply(apply(m, s), Y2), Y1), Y1) -> apply(apply(m, Y1), apply(apply(Y2, Y1), Y1)) % 16.95/17.12 apply(apply(apply(apply(s, b), X2), Y0), Y2) -> apply(Y0, apply(apply(X2, Y0), Y2)) % 16.95/17.12 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z)) % 16.95/17.12 apply(apply(apply(m, apply(s, b)), Y0), Y2) -> apply(Y0, apply(apply(apply(s, b), Y0), Y2)) % 16.95/17.12 apply(apply(apply(m, b), Y1), Y2) -> apply(b, apply(Y1, Y2)) % 16.95/17.12 apply(apply(apply(m, s), s), Y1) -> apply(m, apply(s, Y1)) % 16.95/17.12 apply(apply(apply(s, Y2), Y2), Y1) -> apply(m, apply(Y2, Y1)) % 16.95/17.12 apply(apply(apply(s, m), apply(m, X0)), apply(X0, X0)) -> apply(m, apply(m, apply(m, X0))) % 16.95/17.12 apply(apply(m, Y1), apply(Y1, Y1)) -> apply(m, apply(Y1, Y1)) % 16.95/17.12 apply(apply(m, apply(X0, X0)), apply(m, apply(m, X0))) -> apply(m, apply(m, apply(m, X0))) % 16.95/17.12 apply(apply(m, apply(b, Y0)), Y2) -> apply(Y0, apply(apply(b, Y0), Y2)) % 16.95/17.12 apply(apply(m, apply(m, X0)), apply(m, apply(X0, X0))) -> apply(m, apply(m, apply(X0, X0))) % 16.95/17.12 apply(apply(m, apply(m, X0)), apply(m, apply(X0, X0))) -> apply(m, apply(m, apply(m, X0))) % 16.95/17.12 apply(apply(m, apply(m, b)), Y1) -> apply(b, apply(apply(m, b), Y1)) % 16.95/17.12 apply(apply(m, apply(m, s)), s) -> apply(apply(m, s), apply(apply(m, s), s)) % 16.95/17.12 apply(apply(m, apply(s, Y1)), Y1) -> apply(apply(m, Y1), apply(apply(s, Y1), Y1)) % 16.95/17.12 apply(apply(m, apply(s, m)), apply(s, m)) -> apply(m, apply(m, apply(s, m))) % 16.95/17.12 apply(apply(s, Y1), apply(apply(m, s), Y1)) -> apply(apply(m, apply(m, s)), Y1) % 16.95/17.12 apply(b, apply(Y0, apply(apply(m, b), Y0))) -> apply(m, apply(apply(m, b), Y0)) % 16.95/17.12 apply(b, apply(apply(m, b), apply(m, apply(m, b)))) -> apply(m, apply(m, apply(m, b))) % 16.95/17.12 apply(m, apply(Y0, apply(apply(s, Y0), Y0))) -> apply(m, apply(apply(s, Y0), Y0)) % 16.95/17.12 apply(m, apply(s, apply(apply(m, s), s))) -> apply(m, apply(apply(m, s), s)) % 16.95/17.12 f1(Y, Y) -> true__ % 16.95/17.12 f1(apply(apply(apply(s, apply(b, combinator)), X2), X1), apply(X1, apply(X2, X1))) -> false__ % 16.95/17.12 f1(apply(apply(apply(s, apply(b, combinator)), m), X1), apply(X1, apply(X1, X1))) -> false__ % 16.95/17.12 f1(apply(combinator, Y), Y) -> false__ % 16.95/17.12 f1(apply(combinator, apply(Y1, apply(Y1, Y1))), apply(Y1, apply(m, Y1))) -> false__ % 16.95/17.12 f1(apply(m, apply(apply(b, combinator), X1)), apply(X1, apply(apply(b, combinator), X1))) -> false__ % 16.95/17.12 f1(apply(m, apply(m, apply(b, combinator))), apply(apply(b, combinator), apply(m, apply(b, combinator)))) -> false__ % 16.95/17.12 f1(apply(m, combinator), combinator) -> false__ % 16.95/17.12 false__ -> true__ % 16.95/17.12 with the LPO induced by % 16.95/17.12 apply > s > b > m > combinator > f1 > false__ > true__ % 16.95/17.12 % 16.95/17.12 % SZS output end Proof % 16.95/17.12 %------------------------------------------------------------------------------