%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 07:04:33 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of clauses : 46 ( 26 unt; 0 nHn; 36 RR)
% Number of literals : 77 ( 76 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
impl(btrue,Q) = Q ).
cnf(axiom_002,axiom,
x2(z,Y) = Y ).
cnf(axiom_004,axiom,
plus_not_idem(X) = impl(eq(x2(X,X),X),eq2(btrue,bfalse)) ).
cnf(axiom_006,axiom,
eq2(btrue,bfalse) = bfalse ).
cnf(axiom_010,axiom,
eq(X,X) = btrue ).
cnf(axiom_011,axiom,
eq2(X,X) = btrue ).
cnf(goal,negated_conjecture,
eq2(plus_not_idem(X),bfalse) != btrue ).
cnf(refute_0_0,plain,
eq2(plus_not_idem(z),bfalse) != btrue,
inference(subst,[],[goal:[bind(X,$fot(z))]]) ).
cnf(refute_0_1,plain,
impl(eq(x2(X,X),X),eq2(btrue,bfalse)) = impl(eq(x2(X,X),X),eq2(btrue,bfalse)),
introduced(tautology,[refl,[$fot(impl(eq(x2(X,X),X),eq2(btrue,bfalse)))]]) ).
cnf(refute_0_2,plain,
( eq2(btrue,bfalse) != bfalse
| impl(eq(x2(X,X),X),eq2(btrue,bfalse)) != impl(eq(x2(X,X),X),eq2(btrue,bfalse))
| impl(eq(x2(X,X),X),eq2(btrue,bfalse)) = impl(eq(x2(X,X),X),bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(impl(eq(x2(X,X),X),eq2(btrue,bfalse)),impl(eq(x2(X,X),X),eq2(btrue,bfalse))) ),[1,1],$fot(bfalse)]]) ).
cnf(refute_0_3,plain,
( eq2(btrue,bfalse) != bfalse
| impl(eq(x2(X,X),X),eq2(btrue,bfalse)) = impl(eq(x2(X,X),X),bfalse) ),
inference(resolve,[$cnf( $equal(impl(eq(x2(X,X),X),eq2(btrue,bfalse)),impl(eq(x2(X,X),X),eq2(btrue,bfalse))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
impl(eq(x2(X,X),X),eq2(btrue,bfalse)) = impl(eq(x2(X,X),X),bfalse),
inference(resolve,[$cnf( $equal(eq2(btrue,bfalse),bfalse) )],[axiom_006,refute_0_3]) ).
cnf(refute_0_5,plain,
( impl(eq(x2(X,X),X),eq2(btrue,bfalse)) != impl(eq(x2(X,X),X),bfalse)
| plus_not_idem(X) != impl(eq(x2(X,X),X),eq2(btrue,bfalse))
| plus_not_idem(X) = impl(eq(x2(X,X),X),bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(plus_not_idem(X),impl(eq(x2(X,X),X),eq2(btrue,bfalse))) ),[1],$fot(impl(eq(x2(X,X),X),bfalse))]]) ).
cnf(refute_0_6,plain,
( plus_not_idem(X) != impl(eq(x2(X,X),X),eq2(btrue,bfalse))
| plus_not_idem(X) = impl(eq(x2(X,X),X),bfalse) ),
inference(resolve,[$cnf( $equal(impl(eq(x2(X,X),X),eq2(btrue,bfalse)),impl(eq(x2(X,X),X),bfalse)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
plus_not_idem(X) = impl(eq(x2(X,X),X),bfalse),
inference(resolve,[$cnf( $equal(plus_not_idem(X),impl(eq(x2(X,X),X),eq2(btrue,bfalse))) )],[axiom_004,refute_0_6]) ).
cnf(refute_0_8,plain,
plus_not_idem(z) = impl(eq(x2(z,z),z),bfalse),
inference(subst,[],[refute_0_7:[bind(X,$fot(z))]]) ).
cnf(refute_0_9,plain,
x2(z,z) = z,
inference(subst,[],[axiom_002:[bind(Y,$fot(z))]]) ).
cnf(refute_0_10,plain,
( plus_not_idem(z) != impl(eq(x2(z,z),z),bfalse)
| x2(z,z) != z
| plus_not_idem(z) = impl(eq(z,z),bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(plus_not_idem(z),impl(eq(x2(z,z),z),bfalse)) ),[1,0,0],$fot(z)]]) ).
cnf(refute_0_11,plain,
( plus_not_idem(z) != impl(eq(x2(z,z),z),bfalse)
| plus_not_idem(z) = impl(eq(z,z),bfalse) ),
inference(resolve,[$cnf( $equal(x2(z,z),z) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
plus_not_idem(z) = impl(eq(z,z),bfalse),
inference(resolve,[$cnf( $equal(plus_not_idem(z),impl(eq(x2(z,z),z),bfalse)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
impl(btrue,bfalse) = bfalse,
inference(subst,[],[axiom:[bind(Q,$fot(bfalse))]]) ).
cnf(refute_0_14,plain,
eq(z,z) = btrue,
inference(subst,[],[axiom_010:[bind(X,$fot(z))]]) ).
cnf(refute_0_15,plain,
impl(eq(z,z),bfalse) = impl(eq(z,z),bfalse),
introduced(tautology,[refl,[$fot(impl(eq(z,z),bfalse))]]) ).
cnf(refute_0_16,plain,
( eq(z,z) != btrue
| impl(eq(z,z),bfalse) != impl(eq(z,z),bfalse)
| impl(eq(z,z),bfalse) = impl(btrue,bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(impl(eq(z,z),bfalse),impl(eq(z,z),bfalse)) ),[1,0],$fot(btrue)]]) ).
cnf(refute_0_17,plain,
( eq(z,z) != btrue
| impl(eq(z,z),bfalse) = impl(btrue,bfalse) ),
inference(resolve,[$cnf( $equal(impl(eq(z,z),bfalse),impl(eq(z,z),bfalse)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
impl(eq(z,z),bfalse) = impl(btrue,bfalse),
inference(resolve,[$cnf( $equal(eq(z,z),btrue) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_20,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_21,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( impl(btrue,bfalse) != bfalse
| impl(eq(z,z),bfalse) != impl(btrue,bfalse)
| impl(eq(z,z),bfalse) = bfalse ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(impl(eq(z,z),bfalse))),bind(Y0,$fot(impl(btrue,bfalse))),bind(Z,$fot(bfalse))]]) ).
cnf(refute_0_25,plain,
( impl(btrue,bfalse) != bfalse
| impl(eq(z,z),bfalse) = bfalse ),
inference(resolve,[$cnf( $equal(impl(eq(z,z),bfalse),impl(btrue,bfalse)) )],[refute_0_18,refute_0_24]) ).
cnf(refute_0_26,plain,
impl(eq(z,z),bfalse) = bfalse,
inference(resolve,[$cnf( $equal(impl(btrue,bfalse),bfalse) )],[refute_0_13,refute_0_25]) ).
cnf(refute_0_27,plain,
( impl(eq(z,z),bfalse) != bfalse
| plus_not_idem(z) != impl(eq(z,z),bfalse)
| plus_not_idem(z) = bfalse ),
introduced(tautology,[equality,[$cnf( $equal(plus_not_idem(z),impl(eq(z,z),bfalse)) ),[1],$fot(bfalse)]]) ).
cnf(refute_0_28,plain,
( plus_not_idem(z) != impl(eq(z,z),bfalse)
| plus_not_idem(z) = bfalse ),
inference(resolve,[$cnf( $equal(impl(eq(z,z),bfalse),bfalse) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
plus_not_idem(z) = bfalse,
inference(resolve,[$cnf( $equal(plus_not_idem(z),impl(eq(z,z),bfalse)) )],[refute_0_12,refute_0_28]) ).
cnf(refute_0_30,plain,
( eq2(bfalse,bfalse) != btrue
| plus_not_idem(z) != bfalse
| eq2(plus_not_idem(z),bfalse) = btrue ),
introduced(tautology,[equality,[$cnf( ~ $equal(eq2(plus_not_idem(z),bfalse),btrue) ),[0,0],$fot(bfalse)]]) ).
cnf(refute_0_31,plain,
( eq2(bfalse,bfalse) != btrue
| eq2(plus_not_idem(z),bfalse) = btrue ),
inference(resolve,[$cnf( $equal(plus_not_idem(z),bfalse) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
eq2(bfalse,bfalse) != btrue,
inference(resolve,[$cnf( $equal(eq2(plus_not_idem(z),bfalse),btrue) )],[refute_0_31,refute_0_0]) ).
cnf(refute_0_33,plain,
eq2(bfalse,bfalse) = btrue,
inference(subst,[],[axiom_011:[bind(X,$fot(bfalse))]]) ).
cnf(refute_0_34,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_35,plain,
( btrue != btrue
| eq2(bfalse,bfalse) = btrue ),
inference(resolve,[$cnf( $equal(eq2(bfalse,bfalse),btrue) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
btrue != btrue,
inference(resolve,[$cnf( $equal(eq2(bfalse,bfalse),btrue) )],[refute_0_35,refute_0_32]) ).
cnf(refute_0_37,plain,
btrue = btrue,
introduced(tautology,[refl,[$fot(btrue)]]) ).
cnf(refute_0_38,plain,
$false,
inference(resolve,[$cnf( $equal(btrue,btrue) )],[refute_0_37,refute_0_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.16/0.34 % Computer : n027.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 11:34:19 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------