%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWX205-1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n004.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 07:04:54 PM UTC 2026 % Result : Unknown 0.55s 0.73s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWX205-1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : moca.sh %s % 0.14/0.33 % Computer : n004.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Tue May 5 11:32:02 EDT 2026 % 0.14/0.33 % CPUTime : % 0.55/0.73 % SZS status Satisfiable % 0.55/0.73 % SZS output start Proof % 0.55/0.73 The input problem is satisfiable because % 0.55/0.73 % 0.55/0.73 [1] the following set of Horn clauses is satisfiable: % 0.55/0.73 % 0.55/0.73 impl(btrue, Q) = Q % 0.55/0.73 impl(bfalse, Q) = btrue % 0.55/0.73 plus_ninf(X) = impl(eq(s(X), X), eq2(btrue, bfalse)) % 0.55/0.73 eq2(bfalse, btrue) = bfalse % 0.55/0.73 eq2(btrue, bfalse) = bfalse % 0.55/0.73 eq(s(X), s(Y)) = eq(X, Y) % 0.55/0.73 eq(z, s(X)) = bfalse % 0.55/0.73 eq(s(X), z) = bfalse % 0.55/0.73 eq(X, X) = btrue % 0.55/0.73 eq2(X, X) = btrue % 0.55/0.73 eq2(plus_ninf(X), bfalse) = btrue ==> \bottom % 0.55/0.73 % 0.55/0.73 This holds because % 0.55/0.73 % 0.55/0.73 [2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)): % 0.55/0.73 % 0.55/0.73 E: % 0.55/0.73 eq(X, X) = btrue % 0.55/0.73 eq(s(X), s(Y)) = eq(X, Y) % 0.55/0.73 eq(s(X), z) = bfalse % 0.55/0.73 eq(z, s(X)) = bfalse % 0.55/0.73 eq2(X, X) = btrue % 0.55/0.73 eq2(bfalse, btrue) = bfalse % 0.55/0.73 eq2(btrue, bfalse) = bfalse % 0.55/0.73 f1(btrue) = true__ % 0.55/0.73 f1(eq2(plus_ninf(X), bfalse)) = false__ % 0.55/0.73 impl(bfalse, Q) = btrue % 0.55/0.73 impl(btrue, Q) = Q % 0.55/0.73 plus_ninf(X) = impl(eq(s(X), X), eq2(btrue, bfalse)) % 0.55/0.73 G: % 0.55/0.73 true__ = false__ % 0.55/0.73 % 0.55/0.73 This holds because % 0.55/0.73 % 0.55/0.73 [3] the following ground-complete ordered TRS entails E but does not entail G: % 0.55/0.73 % 0.55/0.73 % 0.55/0.73 eq(X, X) -> btrue % 0.55/0.73 eq(s(X), s(Y)) -> eq(X, Y) % 0.55/0.73 eq(s(X), z) -> bfalse % 0.55/0.73 eq(z, s(X)) -> bfalse % 0.55/0.73 eq2(X, X) -> btrue % 0.55/0.73 eq2(bfalse, btrue) -> bfalse % 0.55/0.73 eq2(btrue, bfalse) -> bfalse % 0.55/0.73 f1(bfalse) -> false__ % 0.55/0.73 f1(btrue) -> true__ % 0.55/0.73 f1(eq2(impl(eq(s(Y0), Y0), bfalse), bfalse)) -> false__ % 0.55/0.73 impl(bfalse, Q) -> btrue % 0.55/0.73 impl(btrue, Q) -> Q % 0.55/0.73 plus_ninf(X) -> impl(eq(s(X), X), bfalse) % 0.55/0.73 with the LPO induced by % 0.55/0.73 plus_ninf > s > bfalse > eq > eq2 > btrue > z > impl > f1 > false__ > true__ % 0.55/0.73 % 0.55/0.73 % SZS output end Proof % 0.55/0.73 %------------------------------------------------------------------------------