%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWX233-1 : TPTP v9.3.0. Released v9.3.0. % 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 : 300s % DateTime : Tue May 5 07:04:57 PM UTC 2026 % Result : Unsatisfiable 0.19s 0.40s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX233-1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.13 % Command : moca.sh %s % 0.17/0.34 % Computer : n020.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue May 5 13:07:04 EDT 2026 % 0.17/0.34 % CPUTime : % 0.19/0.40 % SZS status Unsatisfiable % 0.19/0.40 % SZS output start Proof % 0.19/0.40 The input problem is unsatisfiable because % 0.19/0.40 % 0.19/0.40 [1] the following set of Horn clauses is unsatisfiable: % 0.19/0.40 % 0.19/0.40 aux(Z, btrue) = bfalse % 0.19/0.40 aux(Z, bfalse) = btrue % 0.19/0.40 h(nil) = nil % 0.19/0.40 h(cons(Y, Xs)) = Xs % 0.19/0.40 g(btrue) = bfalse % 0.19/0.40 g(bfalse) = btrue % 0.19/0.40 f(nil) = btrue % 0.19/0.40 f(cons(Y, Z)) = aux(Z, f(Z)) % 0.19/0.40 prop1(X) = eq(f(X), bfalse) % 0.19/0.40 eq(bfalse, btrue) = bfalse % 0.19/0.40 eq(btrue, bfalse) = bfalse % 0.19/0.40 eq(X, X) = btrue % 0.19/0.40 eq(prop1(X), bfalse) = btrue ==> \bottom % 0.19/0.40 % 0.19/0.40 This holds because % 0.19/0.40 % 0.19/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.19/0.40 % 0.19/0.40 E: % 0.19/0.40 aux(Z, bfalse) = btrue % 0.19/0.40 aux(Z, btrue) = bfalse % 0.19/0.40 eq(X, X) = btrue % 0.19/0.40 eq(bfalse, btrue) = bfalse % 0.19/0.40 eq(btrue, bfalse) = bfalse % 0.19/0.40 f(cons(Y, Z)) = aux(Z, f(Z)) % 0.19/0.40 f(nil) = btrue % 0.19/0.40 f1(btrue) = false__ % 0.19/0.40 f1(eq(prop1(X), bfalse)) = true__ % 0.19/0.40 g(bfalse) = btrue % 0.19/0.40 g(btrue) = bfalse % 0.19/0.40 h(cons(Y, Xs)) = Xs % 0.19/0.40 h(nil) = nil % 0.19/0.40 prop1(X) = eq(f(X), bfalse) % 0.19/0.40 G: % 0.19/0.40 true__ = false__ % 0.19/0.40 % 0.19/0.40 This holds because % 0.19/0.40 % 0.19/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.19/0.40 % 0.19/0.40 % 0.19/0.40 aux(Y0, f(nil)) -> g(f(nil)) % 0.19/0.40 aux(Y0, g(f(nil))) -> f(nil) % 0.19/0.40 aux(Z, bfalse) -> btrue % 0.19/0.40 aux(Z, btrue) -> bfalse % 0.19/0.40 bfalse -> g(btrue) % 0.19/0.40 btrue -> f(nil) % 0.19/0.40 eq(X, X) -> btrue % 0.19/0.40 eq(bfalse, btrue) -> bfalse % 0.19/0.40 eq(btrue, bfalse) -> bfalse % 0.19/0.40 eq(f(nil), g(f(nil))) -> g(f(nil)) % 0.19/0.40 eq(g(f(nil)), f(nil)) -> g(f(nil)) % 0.19/0.40 f(cons(Y, Z)) -> aux(Z, f(Z)) % 0.19/0.40 f1(btrue) -> false__ % 0.19/0.40 f1(eq(eq(aux(X1, f(X1)), g(f(nil))), g(f(nil)))) -> true__ % 0.19/0.40 f1(eq(eq(f(Y0), g(f(nil))), g(f(nil)))) -> true__ % 0.19/0.40 f1(eq(prop1(X), bfalse)) -> true__ % 0.19/0.40 f1(f(nil)) -> false__ % 0.19/0.40 g(bfalse) -> btrue % 0.19/0.40 g(g(f(nil))) -> f(nil) % 0.19/0.40 h(cons(Y, Xs)) -> Xs % 0.19/0.40 h(nil) -> nil % 0.19/0.40 prop1(X) -> eq(f(X), bfalse) % 0.19/0.40 true__ -> false__ % 0.19/0.40 with the LPO induced by % 0.19/0.40 f1 > cons > prop1 > eq > aux > bfalse > btrue > nil > f > g > h > true__ > false__ % 0.19/0.40 % 0.19/0.40 % SZS output end Proof % 0.19/0.40 %------------------------------------------------------------------------------