%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX200-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 07:04:32 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 32
% Syntax : Number of clauses : 87 ( 47 unt; 0 nHn; 51 RR)
% Number of literals : 148 ( 147 equ; 65 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 113 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_003,axiom,
aux2(Y,Y2,Xs,bfalse) = bfalse ).
cnf(axiom_005,axiom,
leqNat(s(Z),z) = bfalse ).
cnf(axiom_007,axiom,
merge(nil,Y) = Y ).
cnf(axiom_010,axiom,
ord(nil) = btrue ).
cnf(axiom_012,axiom,
ord(cons(Y,cons(Y2,Xs))) = aux2(Y,Y2,Xs,leqNat(Y,Y2)) ).
cnf(axiom_013,axiom,
impl(btrue,Q) = Q ).
cnf(axiom_015,axiom,
prop_merge_ord_not3(X,Y) = impl(eq2(ord(X),btrue),impl(eq2(ord(Y),bfalse),eq2(ord(merge(X,Y)),btrue))) ).
cnf(axiom_016,axiom,
eq2(bfalse,btrue) = bfalse ).
cnf(axiom_022,axiom,
eq2(X,X) = btrue ).
cnf(goal,negated_conjecture,
eq2(prop_merge_ord_not3(X,Y),bfalse) != btrue ).
cnf(refute_0_0,plain,
eq2(prop_merge_ord_not3(nil,cons(s(X_50),cons(z,X_51))),bfalse) != btrue,
inference(subst,[],[goal:[bind(X,$fot(nil)),bind(Y,$fot(cons(s(X_50),cons(z,X_51))))]]) ).
cnf(refute_0_1,plain,
prop_merge_ord_not3(nil,X_46) = impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(merge(nil,X_46)),btrue))),
inference(subst,[],[axiom_015:[bind(X,$fot(nil)),bind(Y,$fot(X_46))]]) ).
cnf(refute_0_2,plain,
merge(nil,X_46) = X_46,
inference(subst,[],[axiom_007:[bind(Y,$fot(X_46))]]) ).
cnf(refute_0_3,plain,
( merge(nil,X_46) != X_46
| prop_merge_ord_not3(nil,X_46) != impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(merge(nil,X_46)),btrue)))
| prop_merge_ord_not3(nil,X_46) = impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) ),
introduced(tautology,[equality,[$cnf( $equal(prop_merge_ord_not3(nil,X_46),impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(merge(nil,X_46)),btrue)))) ),[1,1,1,0,0],$fot(X_46)]]) ).
cnf(refute_0_4,plain,
( prop_merge_ord_not3(nil,X_46) != impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(merge(nil,X_46)),btrue)))
| prop_merge_ord_not3(nil,X_46) = impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) ),
inference(resolve,[$cnf( $equal(merge(nil,X_46),X_46) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
prop_merge_ord_not3(nil,X_46) = impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))),
inference(resolve,[$cnf( $equal(prop_merge_ord_not3(nil,X_46),impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(merge(nil,X_46)),btrue)))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
impl(btrue,impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) = impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)),
inference(subst,[],[axiom_013:[bind(Q,$fot(impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))))]]) ).
cnf(refute_0_7,plain,
eq2(btrue,btrue) = btrue,
inference(subst,[],[axiom_022:[bind(X,$fot(btrue))]]) ).
cnf(refute_0_8,plain,
eq2(ord(nil),btrue) = eq2(ord(nil),btrue),
introduced(tautology,[refl,[$fot(eq2(ord(nil),btrue))]]) ).
cnf(refute_0_9,plain,
( eq2(ord(nil),btrue) != eq2(ord(nil),btrue)
| ord(nil) != btrue
| eq2(ord(nil),btrue) = eq2(btrue,btrue) ),
introduced(tautology,[equality,[$cnf( $equal(eq2(ord(nil),btrue),eq2(ord(nil),btrue)) ),[1,0],$fot(btrue)]]) ).
cnf(refute_0_10,plain,
( ord(nil) != btrue
| eq2(ord(nil),btrue) = eq2(btrue,btrue) ),
inference(resolve,[$cnf( $equal(eq2(ord(nil),btrue),eq2(ord(nil),btrue)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
eq2(ord(nil),btrue) = eq2(btrue,btrue),
inference(resolve,[$cnf( $equal(ord(nil),btrue) )],[axiom_010,refute_0_10]) ).
cnf(refute_0_12,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_14,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( eq2(btrue,btrue) != btrue
| eq2(ord(nil),btrue) != eq2(btrue,btrue)
| eq2(ord(nil),btrue) = btrue ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(eq2(ord(nil),btrue))),bind(Y0,$fot(eq2(btrue,btrue))),bind(Z0,$fot(btrue))]]) ).
cnf(refute_0_18,plain,
( eq2(btrue,btrue) != btrue
| eq2(ord(nil),btrue) = btrue ),
inference(resolve,[$cnf( $equal(eq2(ord(nil),btrue),eq2(btrue,btrue)) )],[refute_0_11,refute_0_17]) ).
cnf(refute_0_19,plain,
eq2(ord(nil),btrue) = btrue,
inference(resolve,[$cnf( $equal(eq2(btrue,btrue),btrue) )],[refute_0_7,refute_0_18]) ).
cnf(refute_0_20,plain,
impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) = impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))),
introduced(tautology,[refl,[$fot(impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))))]]) ).
cnf(refute_0_21,plain,
( eq2(ord(nil),btrue) != btrue
| impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) != impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)))
| impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) = impl(btrue,impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) ),
introduced(tautology,[equality,[$cnf( $equal(impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))),impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)))) ),[1,0],$fot(btrue)]]) ).
cnf(refute_0_22,plain,
( eq2(ord(nil),btrue) != btrue
| impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) = impl(btrue,impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) ),
inference(resolve,[$cnf( $equal(impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))),impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) = impl(btrue,impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))),
inference(resolve,[$cnf( $equal(eq2(ord(nil),btrue),btrue) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( impl(btrue,impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) != impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))
| impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) != impl(btrue,impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)))
| impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) = impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))))),bind(Y0,$fot(impl(btrue,impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))))),bind(Z0,$fot(impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))))]]) ).
cnf(refute_0_25,plain,
( impl(btrue,impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) != impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))
| impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) = impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)) ),
inference(resolve,[$cnf( $equal(impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))),impl(btrue,impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) = impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)),
inference(resolve,[$cnf( $equal(impl(btrue,impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) )],[refute_0_6,refute_0_25]) ).
cnf(refute_0_27,plain,
( impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) != impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))
| prop_merge_ord_not3(nil,X_46) != impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)))
| prop_merge_ord_not3(nil,X_46) = impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)) ),
introduced(tautology,[equality,[$cnf( $equal(prop_merge_ord_not3(nil,X_46),impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)))) ),[1],$fot(impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)))]]) ).
cnf(refute_0_28,plain,
( prop_merge_ord_not3(nil,X_46) != impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)))
| prop_merge_ord_not3(nil,X_46) = impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)) ),
inference(resolve,[$cnf( $equal(impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
prop_merge_ord_not3(nil,X_46) = impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)),
inference(resolve,[$cnf( $equal(prop_merge_ord_not3(nil,X_46),impl(eq2(ord(nil),btrue),impl(eq2(ord(X_46),bfalse),eq2(ord(X_46),btrue)))) )],[refute_0_5,refute_0_28]) ).
cnf(refute_0_30,plain,
prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) = impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(ord(cons(s(Z),cons(z,X_24))),btrue)),
inference(subst,[],[refute_0_29:[bind(X_46,$fot(cons(s(Z),cons(z,X_24))))]]) ).
cnf(refute_0_31,plain,
ord(cons(s(Z),cons(z,X_24))) = aux2(s(Z),z,X_24,leqNat(s(Z),z)),
inference(subst,[],[axiom_012:[bind(Xs,$fot(X_24)),bind(Y,$fot(s(Z))),bind(Y2,$fot(z))]]) ).
cnf(refute_0_32,plain,
( leqNat(s(Z),z) != bfalse
| ord(cons(s(Z),cons(z,X_24))) != aux2(s(Z),z,X_24,leqNat(s(Z),z))
| ord(cons(s(Z),cons(z,X_24))) = aux2(s(Z),z,X_24,bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(ord(cons(s(Z),cons(z,X_24))),aux2(s(Z),z,X_24,leqNat(s(Z),z))) ),[1,3],$fot(bfalse)]]) ).
cnf(refute_0_33,plain,
( ord(cons(s(Z),cons(z,X_24))) != aux2(s(Z),z,X_24,leqNat(s(Z),z))
| ord(cons(s(Z),cons(z,X_24))) = aux2(s(Z),z,X_24,bfalse) ),
inference(resolve,[$cnf( $equal(leqNat(s(Z),z),bfalse) )],[axiom_005,refute_0_32]) ).
cnf(refute_0_34,plain,
ord(cons(s(Z),cons(z,X_24))) = aux2(s(Z),z,X_24,bfalse),
inference(resolve,[$cnf( $equal(ord(cons(s(Z),cons(z,X_24))),aux2(s(Z),z,X_24,leqNat(s(Z),z))) )],[refute_0_31,refute_0_33]) ).
cnf(refute_0_35,plain,
aux2(s(Z),z,X_24,bfalse) = bfalse,
inference(subst,[],[axiom_003:[bind(Xs,$fot(X_24)),bind(Y,$fot(s(Z))),bind(Y2,$fot(z))]]) ).
cnf(refute_0_36,plain,
( aux2(s(Z),z,X_24,bfalse) != bfalse
| ord(cons(s(Z),cons(z,X_24))) != aux2(s(Z),z,X_24,bfalse)
| ord(cons(s(Z),cons(z,X_24))) = bfalse ),
introduced(tautology,[equality,[$cnf( $equal(ord(cons(s(Z),cons(z,X_24))),aux2(s(Z),z,X_24,bfalse)) ),[1],$fot(bfalse)]]) ).
cnf(refute_0_37,plain,
( ord(cons(s(Z),cons(z,X_24))) != aux2(s(Z),z,X_24,bfalse)
| ord(cons(s(Z),cons(z,X_24))) = bfalse ),
inference(resolve,[$cnf( $equal(aux2(s(Z),z,X_24,bfalse),bfalse) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
ord(cons(s(Z),cons(z,X_24))) = bfalse,
inference(resolve,[$cnf( $equal(ord(cons(s(Z),cons(z,X_24))),aux2(s(Z),z,X_24,bfalse)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( ord(cons(s(Z),cons(z,X_24))) != bfalse
| prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) != impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(ord(cons(s(Z),cons(z,X_24))),btrue))
| prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) = impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) ),
introduced(tautology,[equality,[$cnf( $equal(prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))),impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(ord(cons(s(Z),cons(z,X_24))),btrue))) ),[1,1,0],$fot(bfalse)]]) ).
cnf(refute_0_40,plain,
( prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) != impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(ord(cons(s(Z),cons(z,X_24))),btrue))
| prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) = impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) ),
inference(resolve,[$cnf( $equal(ord(cons(s(Z),cons(z,X_24))),bfalse) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) = impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)),
inference(resolve,[$cnf( $equal(prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))),impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(ord(cons(s(Z),cons(z,X_24))),btrue))) )],[refute_0_30,refute_0_40]) ).
cnf(refute_0_42,plain,
impl(btrue,bfalse) = bfalse,
inference(subst,[],[axiom_013:[bind(Q,$fot(bfalse))]]) ).
cnf(refute_0_43,plain,
impl(btrue,eq2(bfalse,btrue)) = impl(btrue,eq2(bfalse,btrue)),
introduced(tautology,[refl,[$fot(impl(btrue,eq2(bfalse,btrue)))]]) ).
cnf(refute_0_44,plain,
( eq2(bfalse,btrue) != bfalse
| impl(btrue,eq2(bfalse,btrue)) != impl(btrue,eq2(bfalse,btrue))
| impl(btrue,eq2(bfalse,btrue)) = impl(btrue,bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(impl(btrue,eq2(bfalse,btrue)),impl(btrue,eq2(bfalse,btrue))) ),[1,1],$fot(bfalse)]]) ).
cnf(refute_0_45,plain,
( eq2(bfalse,btrue) != bfalse
| impl(btrue,eq2(bfalse,btrue)) = impl(btrue,bfalse) ),
inference(resolve,[$cnf( $equal(impl(btrue,eq2(bfalse,btrue)),impl(btrue,eq2(bfalse,btrue))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
impl(btrue,eq2(bfalse,btrue)) = impl(btrue,bfalse),
inference(resolve,[$cnf( $equal(eq2(bfalse,btrue),bfalse) )],[axiom_016,refute_0_45]) ).
cnf(refute_0_47,plain,
eq2(bfalse,bfalse) = btrue,
inference(subst,[],[axiom_022:[bind(X,$fot(bfalse))]]) ).
cnf(refute_0_48,plain,
eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) = eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),
introduced(tautology,[refl,[$fot(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse))]]) ).
cnf(refute_0_49,plain,
( eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) != eq2(ord(cons(s(Z),cons(z,X_24))),bfalse)
| ord(cons(s(Z),cons(z,X_24))) != bfalse
| eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) = eq2(bfalse,bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(ord(cons(s(Z),cons(z,X_24))),bfalse)) ),[1,0],$fot(bfalse)]]) ).
cnf(refute_0_50,plain,
( ord(cons(s(Z),cons(z,X_24))) != bfalse
| eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) = eq2(bfalse,bfalse) ),
inference(resolve,[$cnf( $equal(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(ord(cons(s(Z),cons(z,X_24))),bfalse)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) = eq2(bfalse,bfalse),
inference(resolve,[$cnf( $equal(ord(cons(s(Z),cons(z,X_24))),bfalse) )],[refute_0_38,refute_0_50]) ).
cnf(refute_0_52,plain,
( eq2(bfalse,bfalse) != btrue
| eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) != eq2(bfalse,bfalse)
| eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) = btrue ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse))),bind(Y0,$fot(eq2(bfalse,bfalse))),bind(Z0,$fot(btrue))]]) ).
cnf(refute_0_53,plain,
( eq2(bfalse,bfalse) != btrue
| eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) = btrue ),
inference(resolve,[$cnf( $equal(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,bfalse)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) = btrue,
inference(resolve,[$cnf( $equal(eq2(bfalse,bfalse),btrue) )],[refute_0_47,refute_0_53]) ).
cnf(refute_0_55,plain,
impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) = impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)),
introduced(tautology,[refl,[$fot(impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)))]]) ).
cnf(refute_0_56,plain,
( eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) != btrue
| impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) != impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue))
| impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) = impl(btrue,eq2(bfalse,btrue)) ),
introduced(tautology,[equality,[$cnf( $equal(impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)),impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue))) ),[1,0],$fot(btrue)]]) ).
cnf(refute_0_57,plain,
( eq2(ord(cons(s(Z),cons(z,X_24))),bfalse) != btrue
| impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) = impl(btrue,eq2(bfalse,btrue)) ),
inference(resolve,[$cnf( $equal(impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)),impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) = impl(btrue,eq2(bfalse,btrue)),
inference(resolve,[$cnf( $equal(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),btrue) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
( impl(btrue,eq2(bfalse,btrue)) != impl(btrue,bfalse)
| impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) != impl(btrue,eq2(bfalse,btrue))
| impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) = impl(btrue,bfalse) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)))),bind(Y0,$fot(impl(btrue,eq2(bfalse,btrue)))),bind(Z0,$fot(impl(btrue,bfalse)))]]) ).
cnf(refute_0_60,plain,
( impl(btrue,eq2(bfalse,btrue)) != impl(btrue,bfalse)
| impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) = impl(btrue,bfalse) ),
inference(resolve,[$cnf( $equal(impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)),impl(btrue,eq2(bfalse,btrue))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) = impl(btrue,bfalse),
inference(resolve,[$cnf( $equal(impl(btrue,eq2(bfalse,btrue)),impl(btrue,bfalse)) )],[refute_0_46,refute_0_60]) ).
cnf(refute_0_62,plain,
( impl(btrue,bfalse) != bfalse
| impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) != impl(btrue,bfalse)
| impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) = bfalse ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)))),bind(Y0,$fot(impl(btrue,bfalse))),bind(Z0,$fot(bfalse))]]) ).
cnf(refute_0_63,plain,
( impl(btrue,bfalse) != bfalse
| impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) = bfalse ),
inference(resolve,[$cnf( $equal(impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)),impl(btrue,bfalse)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) = bfalse,
inference(resolve,[$cnf( $equal(impl(btrue,bfalse),bfalse) )],[refute_0_42,refute_0_63]) ).
cnf(refute_0_65,plain,
( impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)) != bfalse
| prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) != impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue))
| prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) = bfalse ),
introduced(tautology,[equality,[$cnf( $equal(prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))),impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue))) ),[1],$fot(bfalse)]]) ).
cnf(refute_0_66,plain,
( prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) != impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue))
| prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) = bfalse ),
inference(resolve,[$cnf( $equal(impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue)),bfalse) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))) = bfalse,
inference(resolve,[$cnf( $equal(prop_merge_ord_not3(nil,cons(s(Z),cons(z,X_24))),impl(eq2(ord(cons(s(Z),cons(z,X_24))),bfalse),eq2(bfalse,btrue))) )],[refute_0_41,refute_0_66]) ).
cnf(refute_0_68,plain,
prop_merge_ord_not3(nil,cons(s(X_50),cons(z,X_51))) = bfalse,
inference(subst,[],[refute_0_67:[bind(Z,$fot(X_50)),bind(X_24,$fot(X_51))]]) ).
cnf(refute_0_69,plain,
( eq2(bfalse,bfalse) != btrue
| prop_merge_ord_not3(nil,cons(s(X_50),cons(z,X_51))) != bfalse
| eq2(prop_merge_ord_not3(nil,cons(s(X_50),cons(z,X_51))),bfalse) = btrue ),
introduced(tautology,[equality,[$cnf( ~ $equal(eq2(prop_merge_ord_not3(nil,cons(s(X_50),cons(z,X_51))),bfalse),btrue) ),[0,0],$fot(bfalse)]]) ).
cnf(refute_0_70,plain,
( eq2(bfalse,bfalse) != btrue
| eq2(prop_merge_ord_not3(nil,cons(s(X_50),cons(z,X_51))),bfalse) = btrue ),
inference(resolve,[$cnf( $equal(prop_merge_ord_not3(nil,cons(s(X_50),cons(z,X_51))),bfalse) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
eq2(bfalse,bfalse) != btrue,
inference(resolve,[$cnf( $equal(eq2(prop_merge_ord_not3(nil,cons(s(X_50),cons(z,X_51))),bfalse),btrue) )],[refute_0_70,refute_0_0]) ).
cnf(refute_0_72,plain,
( btrue != btrue
| eq2(bfalse,bfalse) != btrue
| eq2(bfalse,bfalse) = btrue ),
introduced(tautology,[equality,[$cnf( $equal(eq2(bfalse,bfalse),btrue) ),[1],$fot(btrue)]]) ).
cnf(refute_0_73,plain,
( btrue != btrue
| eq2(bfalse,bfalse) = btrue ),
inference(resolve,[$cnf( $equal(eq2(bfalse,bfalse),btrue) )],[refute_0_47,refute_0_72]) ).
cnf(refute_0_74,plain,
btrue != btrue,
inference(resolve,[$cnf( $equal(eq2(bfalse,bfalse),btrue) )],[refute_0_73,refute_0_71]) ).
cnf(refute_0_75,plain,
btrue = btrue,
introduced(tautology,[refl,[$fot(btrue)]]) ).
cnf(refute_0_76,plain,
$false,
inference(resolve,[$cnf( $equal(btrue,btrue) )],[refute_0_75,refute_0_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX200-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 11:15:40 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.40
% 0.20/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.42
%------------------------------------------------------------------------------