%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n010.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 : 300s % DateTime : Tue May 5 07:04:55 PM UTC 2026 % Result : Unsatisfiable 0.18s 0.39s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : moca.sh %s % 0.16/0.33 % Computer : n010.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue May 5 11:34:21 EDT 2026 % 0.16/0.34 % CPUTime : % 0.18/0.39 % SZS status Unsatisfiable % 0.18/0.39 % SZS output start Proof % 0.18/0.39 The input problem is unsatisfiable because % 0.18/0.39 % 0.18/0.39 [1] the following set of Horn clauses is unsatisfiable: % 0.18/0.39 % 0.18/0.39 impl(btrue, Q) = Q % 0.18/0.39 impl(bfalse, Q) = btrue % 0.18/0.39 x2(z, Y) = Y % 0.18/0.39 x2(s(N), Y) = s(x2(N, Y)) % 0.18/0.39 plus_not_idem(X) = impl(eq(x2(X, X), X), eq2(btrue, bfalse)) % 0.18/0.39 eq2(bfalse, btrue) = bfalse % 0.18/0.39 eq2(btrue, bfalse) = bfalse % 0.18/0.39 eq(s(X), s(Y)) = eq(X, Y) % 0.18/0.39 eq(z, s(X)) = bfalse % 0.18/0.39 eq(s(X), z) = bfalse % 0.18/0.39 eq(X, X) = btrue % 0.18/0.39 eq2(X, X) = btrue % 0.18/0.39 eq2(plus_not_idem(X), bfalse) = btrue ==> \bottom % 0.18/0.39 % 0.18/0.39 This holds because % 0.18/0.39 % 0.18/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.18/0.39 % 0.18/0.39 E: % 0.18/0.39 eq(X, X) = btrue % 0.18/0.39 eq(s(X), s(Y)) = eq(X, Y) % 0.18/0.39 eq(s(X), z) = bfalse % 0.18/0.39 eq(z, s(X)) = bfalse % 0.18/0.39 eq2(X, X) = btrue % 0.18/0.39 eq2(bfalse, btrue) = bfalse % 0.18/0.39 eq2(btrue, bfalse) = bfalse % 0.18/0.39 f1(btrue) = false__ % 0.18/0.39 f1(eq2(plus_not_idem(X), bfalse)) = true__ % 0.18/0.39 impl(bfalse, Q) = btrue % 0.18/0.39 impl(btrue, Q) = Q % 0.18/0.39 plus_not_idem(X) = impl(eq(x2(X, X), X), eq2(btrue, bfalse)) % 0.18/0.39 x2(s(N), Y) = s(x2(N, Y)) % 0.18/0.39 x2(z, Y) = Y % 0.18/0.39 G: % 0.18/0.39 true__ = false__ % 0.18/0.39 % 0.18/0.39 This holds because % 0.18/0.39 % 0.18/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.18/0.39 % 0.18/0.39 % 0.18/0.39 eq(X, X) -> btrue % 0.18/0.39 eq(s(X), s(Y)) -> eq(X, Y) % 0.18/0.39 eq(s(X), z) -> bfalse % 0.18/0.39 eq(z, s(X)) -> bfalse % 0.18/0.39 eq2(X, X) -> btrue % 0.18/0.39 eq2(bfalse, btrue) -> bfalse % 0.18/0.39 eq2(btrue, bfalse) -> bfalse % 0.18/0.39 f1(btrue) -> false__ % 0.18/0.39 f1(eq2(impl(eq(x2(X0, s(X0)), X0), bfalse), bfalse)) -> true__ % 0.18/0.39 f1(eq2(impl(eq(x2(Y0, Y0), Y0), bfalse), bfalse)) -> true__ % 0.18/0.39 f1(eq2(plus_not_idem(X), bfalse)) -> true__ % 0.18/0.39 impl(bfalse, Q) -> btrue % 0.18/0.39 impl(btrue, Q) -> Q % 0.18/0.39 plus_not_idem(X) -> impl(eq(x2(X, X), X), eq2(btrue, bfalse)) % 0.18/0.39 true__ -> false__ % 0.18/0.39 x2(s(N), Y) -> s(x2(N, Y)) % 0.18/0.39 x2(z, Y) -> Y % 0.18/0.39 with the LPO induced by % 0.18/0.39 f1 > plus_not_idem > eq2 > x2 > s > bfalse > eq > btrue > z > impl > true__ > false__ % 0.18/0.39 % 0.18/0.39 % SZS output end Proof % 0.18/0.39 %------------------------------------------------------------------------------