%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : SWX200-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 07:07:55 PM UTC 2026
% Result : Unsatisfiable 0.76s 1.15s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 26 ( 25 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 41 ( 10 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
eq2(prop_merge_ord_not3(X,Y),bfalse) != btrue,
file('theBenchmark.p',goal) ).
fof(e,plain,
! [X,Y] :
( true != false
& eq0(X,X) = true
& eq0(eq2(prop_merge_ord_not3(X,Y),bfalse),btrue) = false ),
inference(encode_existential,[status(esa)],[g0]) ).
cnf(g1,plain,
true != false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c1,axiom,
ord(nil) = btrue,
file('theBenchmark.p',axiom_010) ).
cnf(c2,plain,
eq0(X,X) = true,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c4,axiom,
eq2(X,X) = btrue,
file('theBenchmark.p',axiom_022) ).
cnf(c5,axiom,
merge(nil,X) = X,
file('theBenchmark.p',axiom_007) ).
cnf(c6,axiom,
impl(btrue,X) = X,
file('theBenchmark.p',axiom_013) ).
cnf(c10,axiom,
eq2(bfalse,btrue) = bfalse,
file('theBenchmark.p',axiom_016) ).
cnf(c14,axiom,
leqNat(s(X),z) = bfalse,
file('theBenchmark.p',axiom_005) ).
cnf(c15,axiom,
aux2(X,Y,Z,bfalse) = bfalse,
file('theBenchmark.p',axiom_003) ).
cnf(c16,axiom,
leqNat(s(X),s(Y)) = leqNat(X,Y),
file('theBenchmark.p',axiom_006) ).
cnf(c20,plain,
eq0(eq2(prop_merge_ord_not3(X,Y),bfalse),btrue) = false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c21,axiom,
ord(cons(X,cons(Y,Z))) = aux2(X,Y,Z,leqNat(X,Y)),
file('theBenchmark.p',axiom_012) ).
cnf(c22,plain,
aux2(X,Y,Z,leqNat(X,Y)) = ord(cons(X,cons(Y,Z))),
inference(equational,[status(thm)],[c21]) ).
cnf(c33,plain,
aux2(s(X),s(Y),Z,leqNat(X,Y)) = ord(cons(s(X),cons(s(Y),Z))),
inference(equational,[status(thm)],[c16,c22]) ).
cnf(c48,plain,
aux2(s(s(X)),s(s(Y)),Z,leqNat(X,Y)) = ord(cons(s(s(X)),cons(s(s(Y)),Z))),
inference(equational,[status(thm)],[c16,c33]) ).
cnf(c68,axiom,
prop_merge_ord_not3(X,Y) = impl(eq2(ord(X),btrue),impl(eq2(ord(Y),bfalse),eq2(ord(merge(X,Y)),btrue))),
file('theBenchmark.p',axiom_015) ).
cnf(c78,plain,
aux2(s(s(s(X))),s(s(s(Y))),Z,leqNat(X,Y)) = ord(cons(s(s(s(X))),cons(s(s(s(Y))),Z))),
inference(equational,[status(thm)],[c16,c48]) ).
cnf(c141,plain,
aux2(s(s(s(s(X)))),s(s(s(s(Y)))),Z,leqNat(X,Y)) = ord(cons(s(s(s(s(X)))),cons(s(s(s(s(Y)))),Z))),
inference(equational,[status(thm)],[c16,c78]) ).
cnf(c142,plain,
ord(cons(s(s(s(s(s(X))))),cons(s(s(s(s(z)))),Y))) = bfalse,
inference(equational,[status(thm)],[c14,c15,c141]) ).
cnf(c151,plain,
eq0(eq2(impl(eq2(ord(X),btrue),impl(eq2(ord(Y),bfalse),eq2(ord(merge(X,Y)),btrue))),bfalse),btrue) = false,
inference(equational,[status(thm)],[c20,c68]) ).
cnf(c154,plain,
eq0(eq2(impl(eq2(ord(X),bfalse),eq2(ord(X),btrue)),bfalse),btrue) = false,
inference(equational,[status(thm)],[c1,c4,c5,c6,c151]) ).
cnf(c155,plain,
true = false,
inference(equational,[status(thm)],[c2,c4,c6,c10,c142,c154]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c155]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX200-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_Leo-III %s %d THM
% 0.16/0.33 % Computer : n016.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 11:17:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.76/1.15 % SZS status Unsatisfiable
% 0.76/1.15 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------