%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL030-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n026.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 00:36:57 EDT 2022 % Result : Unsatisfiable 28.14s 28.30s % Output : Proof 28.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COL030-1 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n026.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Tue May 31 09:18:26 EDT 2022 % 0.14/0.35 % CPUTime : % 28.14/28.30 % SZS status Unsatisfiable % 28.14/28.30 % SZS output start Proof % 28.14/28.30 The input problem is unsatisfiable because % 28.14/28.30 % 28.14/28.30 [1] the following set of Horn clauses is unsatisfiable: % 28.14/28.30 % 28.14/28.30 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)) % 28.14/28.30 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 28.14/28.30 apply(Y, f(Y)) = apply(f(Y), apply(Y, f(Y))) ==> \bottom % 28.14/28.30 % 28.14/28.30 This holds because % 28.14/28.30 % 28.14/28.30 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 28.14/28.30 % 28.14/28.30 E: % 28.14/28.30 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)) % 28.14/28.30 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 28.14/28.30 f1(apply(Y, f(Y)), Y) = true__ % 28.14/28.30 f1(apply(f(Y), apply(Y, f(Y))), Y) = false__ % 28.14/28.30 G: % 28.14/28.30 true__ = false__ % 28.14/28.30 % 28.14/28.30 This holds because % 28.14/28.30 % 28.14/28.30 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 28.14/28.30 % 28.14/28.30 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(apply(l, apply(l, X0)), Y1) % 28.14/28.30 apply(Y0, apply(apply(apply(l, l), X0), X0)) = apply(apply(l, Y0), apply(X0, X0)) % 28.14/28.30 apply(Y0, apply(apply(apply(l, l), Y1), Y1)) = apply(apply(l, apply(l, Y0)), Y1) % 28.14/28.30 apply(Y0, apply(apply(apply(s, X0), X0), X1)) = apply(apply(l, Y0), apply(X0, X1)) % 28.14/28.30 apply(Y0, apply(apply(apply(s, Y1), Y1), Y0)) = apply(apply(apply(s, l), Y1), Y0) % 28.14/28.30 apply(Y1, apply(apply(Y2, Y1), apply(Y2, Y1))) = apply(apply(apply(s, l), Y2), Y1) % 28.14/28.30 apply(apply(X0, apply(Y1, Y1)), apply(Y2, Y1)) = apply(apply(apply(s, apply(l, X0)), Y2), Y1) % 28.14/28.30 apply(apply(Y0, Y1), apply(X0, apply(Y1, Y1))) = apply(apply(apply(s, Y0), apply(l, X0)), Y1) % 28.14/28.30 apply(apply(Y0, Y1), apply(Y0, apply(Y1, Y1))) = apply(apply(apply(apply(s, s), l), Y0), Y1) % 28.14/28.30 apply(apply(apply(apply(l, s), X1), Y1), Y2) = apply(apply(apply(X1, X1), Y2), apply(Y1, Y2)) % 28.14/28.30 apply(apply(apply(apply(s, s), X2), Y0), Y2) = apply(apply(Y0, Y2), apply(apply(X2, Y0), Y2)) % 28.14/28.30 apply(apply(apply(l, apply(s, Y0)), X1), Y2) = apply(apply(Y0, Y2), apply(apply(X1, X1), Y2)) % 28.14/28.30 apply(apply(apply(l, l), X0), apply(Y1, Y1)) = apply(apply(l, apply(l, apply(X0, X0))), Y1) % 28.14/28.30 apply(apply(apply(l, l), X1), Y1) = apply(apply(X1, X1), apply(Y1, Y1)) % 28.14/28.30 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)) % 28.14/28.30 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 28.14/28.30 apply(Y0, apply(apply(apply(l, l), Y0), Y0)) -> apply(apply(l, Y0), apply(Y0, Y0)) % 28.14/28.30 f1(apply(Y, f(Y)), Y) -> true__ % 28.14/28.30 f1(apply(apply(apply(s, l), X1), f(apply(apply(s, X1), X1))), apply(apply(s, X1), X1)) -> false__ % 28.14/28.30 f1(apply(f(Y), apply(Y, f(Y))), Y) -> false__ % 28.14/28.30 true__ -> false__ % 28.14/28.30 with the LPO induced by % 28.14/28.30 apply > f1 > f > s > l > true__ > false__ % 28.14/28.30 % 28.14/28.30 % SZS output end Proof % 28.14/28.30 %------------------------------------------------------------------------------