%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX186-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n002.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 07:04:30 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 26
% Syntax : Number of clauses : 64 ( 36 unt; 0 nHn; 43 RR)
% Number of literals : 107 ( 106 equ; 49 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 : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 99 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
impl(btrue,Q) = Q ).
cnf(axiom_002,axiom,
drop(s(Z),nil) = nil ).
cnf(axiom_003,axiom,
drop(s(Z),cons(X2,X3)) = drop(Z,X3) ).
cnf(axiom_005,axiom,
prop_drop_inj2(X,Y,Z) = impl(eq(drop(X,Y),drop(X,Z)),eq(Y,Z)) ).
cnf(axiom_011,axiom,
eq(X,X) = btrue ).
cnf(axiom_013,axiom,
eq3(X,X) = btrue ).
cnf(axiom_016,axiom,
eq(nil,cons(X,Y)) = bfalse ).
cnf(goal,negated_conjecture,
eq3(prop_drop_inj2(X,Y,Z),bfalse) != btrue ).
cnf(refute_0_0,plain,
eq3(prop_drop_inj2(s(X_38),nil,cons(X_36,X_37)),bfalse) != btrue,
inference(subst,[],[goal:[bind(X,$fot(s(X_38))),bind(Y,$fot(nil)),bind(Z,$fot(cons(X_36,X_37)))]]) ).
cnf(refute_0_1,plain,
prop_drop_inj2(s(Z),nil,X_23) = impl(eq(drop(s(Z),nil),drop(s(Z),X_23)),eq(nil,X_23)),
inference(subst,[],[axiom_005:[bind(X,$fot(s(Z))),bind(Y,$fot(nil)),bind(Z,$fot(X_23))]]) ).
cnf(refute_0_2,plain,
( drop(s(Z),nil) != nil
| prop_drop_inj2(s(Z),nil,X_23) != impl(eq(drop(s(Z),nil),drop(s(Z),X_23)),eq(nil,X_23))
| prop_drop_inj2(s(Z),nil,X_23) = impl(eq(nil,drop(s(Z),X_23)),eq(nil,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(prop_drop_inj2(s(Z),nil,X_23),impl(eq(drop(s(Z),nil),drop(s(Z),X_23)),eq(nil,X_23))) ),[1,0,0],$fot(nil)]]) ).
cnf(refute_0_3,plain,
( prop_drop_inj2(s(Z),nil,X_23) != impl(eq(drop(s(Z),nil),drop(s(Z),X_23)),eq(nil,X_23))
| prop_drop_inj2(s(Z),nil,X_23) = impl(eq(nil,drop(s(Z),X_23)),eq(nil,X_23)) ),
inference(resolve,[$cnf( $equal(drop(s(Z),nil),nil) )],[axiom_002,refute_0_2]) ).
cnf(refute_0_4,plain,
prop_drop_inj2(s(Z),nil,X_23) = impl(eq(nil,drop(s(Z),X_23)),eq(nil,X_23)),
inference(resolve,[$cnf( $equal(prop_drop_inj2(s(Z),nil,X_23),impl(eq(drop(s(Z),nil),drop(s(Z),X_23)),eq(nil,X_23))) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
prop_drop_inj2(s(X_34),nil,cons(X,Y)) = impl(eq(nil,drop(s(X_34),cons(X,Y))),eq(nil,cons(X,Y))),
inference(subst,[],[refute_0_4:[bind(Z,$fot(X_34)),bind(X_23,$fot(cons(X,Y)))]]) ).
cnf(refute_0_6,plain,
( eq(nil,cons(X,Y)) != bfalse
| prop_drop_inj2(s(X_34),nil,cons(X,Y)) != impl(eq(nil,drop(s(X_34),cons(X,Y))),eq(nil,cons(X,Y)))
| prop_drop_inj2(s(X_34),nil,cons(X,Y)) = impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(prop_drop_inj2(s(X_34),nil,cons(X,Y)),impl(eq(nil,drop(s(X_34),cons(X,Y))),eq(nil,cons(X,Y)))) ),[1,1],$fot(bfalse)]]) ).
cnf(refute_0_7,plain,
( prop_drop_inj2(s(X_34),nil,cons(X,Y)) != impl(eq(nil,drop(s(X_34),cons(X,Y))),eq(nil,cons(X,Y)))
| prop_drop_inj2(s(X_34),nil,cons(X,Y)) = impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse) ),
inference(resolve,[$cnf( $equal(eq(nil,cons(X,Y)),bfalse) )],[axiom_016,refute_0_6]) ).
cnf(refute_0_8,plain,
prop_drop_inj2(s(X_34),nil,cons(X,Y)) = impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse),
inference(resolve,[$cnf( $equal(prop_drop_inj2(s(X_34),nil,cons(X,Y)),impl(eq(nil,drop(s(X_34),cons(X,Y))),eq(nil,cons(X,Y)))) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
drop(s(X_34),cons(X,Y)) = drop(X_34,Y),
inference(subst,[],[axiom_003:[bind(X2,$fot(X)),bind(X3,$fot(Y)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_10,plain,
eq(nil,drop(s(X_34),cons(X,Y))) = eq(nil,drop(s(X_34),cons(X,Y))),
introduced(tautology,[refl,[$fot(eq(nil,drop(s(X_34),cons(X,Y))))]]) ).
cnf(refute_0_11,plain,
( drop(s(X_34),cons(X,Y)) != drop(X_34,Y)
| eq(nil,drop(s(X_34),cons(X,Y))) != eq(nil,drop(s(X_34),cons(X,Y)))
| eq(nil,drop(s(X_34),cons(X,Y))) = eq(nil,drop(X_34,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(eq(nil,drop(s(X_34),cons(X,Y))),eq(nil,drop(s(X_34),cons(X,Y)))) ),[1,1],$fot(drop(X_34,Y))]]) ).
cnf(refute_0_12,plain,
( drop(s(X_34),cons(X,Y)) != drop(X_34,Y)
| eq(nil,drop(s(X_34),cons(X,Y))) = eq(nil,drop(X_34,Y)) ),
inference(resolve,[$cnf( $equal(eq(nil,drop(s(X_34),cons(X,Y))),eq(nil,drop(s(X_34),cons(X,Y)))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
eq(nil,drop(s(X_34),cons(X,Y))) = eq(nil,drop(X_34,Y)),
inference(resolve,[$cnf( $equal(drop(s(X_34),cons(X,Y)),drop(X_34,Y)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse) = impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse),
introduced(tautology,[refl,[$fot(impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse))]]) ).
cnf(refute_0_15,plain,
( eq(nil,drop(s(X_34),cons(X,Y))) != eq(nil,drop(X_34,Y))
| impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse) != impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse)
| impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse) = impl(eq(nil,drop(X_34,Y)),bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse),impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse)) ),[1,0],$fot(eq(nil,drop(X_34,Y)))]]) ).
cnf(refute_0_16,plain,
( eq(nil,drop(s(X_34),cons(X,Y))) != eq(nil,drop(X_34,Y))
| impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse) = impl(eq(nil,drop(X_34,Y)),bfalse) ),
inference(resolve,[$cnf( $equal(impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse),impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse) = impl(eq(nil,drop(X_34,Y)),bfalse),
inference(resolve,[$cnf( $equal(eq(nil,drop(s(X_34),cons(X,Y))),eq(nil,drop(X_34,Y))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse) != impl(eq(nil,drop(X_34,Y)),bfalse)
| prop_drop_inj2(s(X_34),nil,cons(X,Y)) != impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse)
| prop_drop_inj2(s(X_34),nil,cons(X,Y)) = impl(eq(nil,drop(X_34,Y)),bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(prop_drop_inj2(s(X_34),nil,cons(X,Y)),impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse)) ),[1],$fot(impl(eq(nil,drop(X_34,Y)),bfalse))]]) ).
cnf(refute_0_19,plain,
( prop_drop_inj2(s(X_34),nil,cons(X,Y)) != impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse)
| prop_drop_inj2(s(X_34),nil,cons(X,Y)) = impl(eq(nil,drop(X_34,Y)),bfalse) ),
inference(resolve,[$cnf( $equal(impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse),impl(eq(nil,drop(X_34,Y)),bfalse)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
prop_drop_inj2(s(X_34),nil,cons(X,Y)) = impl(eq(nil,drop(X_34,Y)),bfalse),
inference(resolve,[$cnf( $equal(prop_drop_inj2(s(X_34),nil,cons(X,Y)),impl(eq(nil,drop(s(X_34),cons(X,Y))),bfalse)) )],[refute_0_8,refute_0_19]) ).
cnf(refute_0_21,plain,
prop_drop_inj2(s(X_38),nil,cons(X_36,X_37)) = impl(eq(nil,drop(X_38,X_37)),bfalse),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(X_34,$fot(X_38))]]) ).
cnf(refute_0_22,plain,
( eq3(impl(eq(nil,drop(X_38,X_37)),bfalse),bfalse) != btrue
| prop_drop_inj2(s(X_38),nil,cons(X_36,X_37)) != impl(eq(nil,drop(X_38,X_37)),bfalse)
| eq3(prop_drop_inj2(s(X_38),nil,cons(X_36,X_37)),bfalse) = btrue ),
introduced(tautology,[equality,[$cnf( ~ $equal(eq3(prop_drop_inj2(s(X_38),nil,cons(X_36,X_37)),bfalse),btrue) ),[0,0],$fot(impl(eq(nil,drop(X_38,X_37)),bfalse))]]) ).
cnf(refute_0_23,plain,
( eq3(impl(eq(nil,drop(X_38,X_37)),bfalse),bfalse) != btrue
| eq3(prop_drop_inj2(s(X_38),nil,cons(X_36,X_37)),bfalse) = btrue ),
inference(resolve,[$cnf( $equal(prop_drop_inj2(s(X_38),nil,cons(X_36,X_37)),impl(eq(nil,drop(X_38,X_37)),bfalse)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
eq3(impl(eq(nil,drop(X_38,X_37)),bfalse),bfalse) != btrue,
inference(resolve,[$cnf( $equal(eq3(prop_drop_inj2(s(X_38),nil,cons(X_36,X_37)),bfalse),btrue) )],[refute_0_23,refute_0_0]) ).
cnf(refute_0_25,plain,
eq3(impl(eq(nil,drop(s(Z),nil)),bfalse),bfalse) != btrue,
inference(subst,[],[refute_0_24:[bind(X_37,$fot(nil)),bind(X_38,$fot(s(Z)))]]) ).
cnf(refute_0_26,plain,
( drop(s(Z),nil) != nil
| eq3(impl(eq(nil,nil),bfalse),bfalse) != btrue
| eq3(impl(eq(nil,drop(s(Z),nil)),bfalse),bfalse) = btrue ),
introduced(tautology,[equality,[$cnf( ~ $equal(eq3(impl(eq(nil,drop(s(Z),nil)),bfalse),bfalse),btrue) ),[0,0,0,1],$fot(nil)]]) ).
cnf(refute_0_27,plain,
( eq3(impl(eq(nil,nil),bfalse),bfalse) != btrue
| eq3(impl(eq(nil,drop(s(Z),nil)),bfalse),bfalse) = btrue ),
inference(resolve,[$cnf( $equal(drop(s(Z),nil),nil) )],[axiom_002,refute_0_26]) ).
cnf(refute_0_28,plain,
eq3(impl(eq(nil,nil),bfalse),bfalse) != btrue,
inference(resolve,[$cnf( $equal(eq3(impl(eq(nil,drop(s(Z),nil)),bfalse),bfalse),btrue) )],[refute_0_27,refute_0_25]) ).
cnf(refute_0_29,plain,
eq3(bfalse,bfalse) = btrue,
inference(subst,[],[axiom_013:[bind(X,$fot(bfalse))]]) ).
cnf(refute_0_30,plain,
impl(btrue,bfalse) = bfalse,
inference(subst,[],[axiom:[bind(Q,$fot(bfalse))]]) ).
cnf(refute_0_31,plain,
eq(nil,nil) = btrue,
inference(subst,[],[axiom_011:[bind(X,$fot(nil))]]) ).
cnf(refute_0_32,plain,
impl(eq(nil,nil),bfalse) = impl(eq(nil,nil),bfalse),
introduced(tautology,[refl,[$fot(impl(eq(nil,nil),bfalse))]]) ).
cnf(refute_0_33,plain,
( eq(nil,nil) != btrue
| impl(eq(nil,nil),bfalse) != impl(eq(nil,nil),bfalse)
| impl(eq(nil,nil),bfalse) = impl(btrue,bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(impl(eq(nil,nil),bfalse),impl(eq(nil,nil),bfalse)) ),[1,0],$fot(btrue)]]) ).
cnf(refute_0_34,plain,
( eq(nil,nil) != btrue
| impl(eq(nil,nil),bfalse) = impl(btrue,bfalse) ),
inference(resolve,[$cnf( $equal(impl(eq(nil,nil),bfalse),impl(eq(nil,nil),bfalse)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
impl(eq(nil,nil),bfalse) = impl(btrue,bfalse),
inference(resolve,[$cnf( $equal(eq(nil,nil),btrue) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_37,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_38,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_40,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( impl(btrue,bfalse) != bfalse
| impl(eq(nil,nil),bfalse) != impl(btrue,bfalse)
| impl(eq(nil,nil),bfalse) = bfalse ),
inference(subst,[],[refute_0_40:[bind(X0,$fot(impl(eq(nil,nil),bfalse))),bind(Y0,$fot(impl(btrue,bfalse))),bind(Z0,$fot(bfalse))]]) ).
cnf(refute_0_42,plain,
( impl(btrue,bfalse) != bfalse
| impl(eq(nil,nil),bfalse) = bfalse ),
inference(resolve,[$cnf( $equal(impl(eq(nil,nil),bfalse),impl(btrue,bfalse)) )],[refute_0_35,refute_0_41]) ).
cnf(refute_0_43,plain,
impl(eq(nil,nil),bfalse) = bfalse,
inference(resolve,[$cnf( $equal(impl(btrue,bfalse),bfalse) )],[refute_0_30,refute_0_42]) ).
cnf(refute_0_44,plain,
eq3(impl(eq(nil,nil),bfalse),bfalse) = eq3(impl(eq(nil,nil),bfalse),bfalse),
introduced(tautology,[refl,[$fot(eq3(impl(eq(nil,nil),bfalse),bfalse))]]) ).
cnf(refute_0_45,plain,
( eq3(impl(eq(nil,nil),bfalse),bfalse) != eq3(impl(eq(nil,nil),bfalse),bfalse)
| impl(eq(nil,nil),bfalse) != bfalse
| eq3(impl(eq(nil,nil),bfalse),bfalse) = eq3(bfalse,bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(eq3(impl(eq(nil,nil),bfalse),bfalse),eq3(impl(eq(nil,nil),bfalse),bfalse)) ),[1,0],$fot(bfalse)]]) ).
cnf(refute_0_46,plain,
( impl(eq(nil,nil),bfalse) != bfalse
| eq3(impl(eq(nil,nil),bfalse),bfalse) = eq3(bfalse,bfalse) ),
inference(resolve,[$cnf( $equal(eq3(impl(eq(nil,nil),bfalse),bfalse),eq3(impl(eq(nil,nil),bfalse),bfalse)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
eq3(impl(eq(nil,nil),bfalse),bfalse) = eq3(bfalse,bfalse),
inference(resolve,[$cnf( $equal(impl(eq(nil,nil),bfalse),bfalse) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( eq3(bfalse,bfalse) != btrue
| eq3(impl(eq(nil,nil),bfalse),bfalse) != eq3(bfalse,bfalse)
| eq3(impl(eq(nil,nil),bfalse),bfalse) = btrue ),
inference(subst,[],[refute_0_40:[bind(X0,$fot(eq3(impl(eq(nil,nil),bfalse),bfalse))),bind(Y0,$fot(eq3(bfalse,bfalse))),bind(Z0,$fot(btrue))]]) ).
cnf(refute_0_49,plain,
( eq3(bfalse,bfalse) != btrue
| eq3(impl(eq(nil,nil),bfalse),bfalse) = btrue ),
inference(resolve,[$cnf( $equal(eq3(impl(eq(nil,nil),bfalse),bfalse),eq3(bfalse,bfalse)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
eq3(impl(eq(nil,nil),bfalse),bfalse) = btrue,
inference(resolve,[$cnf( $equal(eq3(bfalse,bfalse),btrue) )],[refute_0_29,refute_0_49]) ).
cnf(refute_0_51,plain,
( btrue != btrue
| eq3(impl(eq(nil,nil),bfalse),bfalse) != btrue
| eq3(impl(eq(nil,nil),bfalse),bfalse) = btrue ),
introduced(tautology,[equality,[$cnf( $equal(eq3(impl(eq(nil,nil),bfalse),bfalse),btrue) ),[1],$fot(btrue)]]) ).
cnf(refute_0_52,plain,
( btrue != btrue
| eq3(impl(eq(nil,nil),bfalse),bfalse) = btrue ),
inference(resolve,[$cnf( $equal(eq3(impl(eq(nil,nil),bfalse),bfalse),btrue) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
btrue != btrue,
inference(resolve,[$cnf( $equal(eq3(impl(eq(nil,nil),bfalse),bfalse),btrue) )],[refute_0_52,refute_0_28]) ).
cnf(refute_0_54,plain,
btrue = btrue,
introduced(tautology,[refl,[$fot(btrue)]]) ).
cnf(refute_0_55,plain,
$false,
inference(resolve,[$cnf( $equal(btrue,btrue) )],[refute_0_54,refute_0_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX186-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.14/0.33 % Computer : n002.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 09:39:01 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.37
% 0.19/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.38
%------------------------------------------------------------------------------