%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX233-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 07:04:38 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.35s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 14 unt; 0 nHn; 20 RR)
% Number of literals : 34 ( 33 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 3 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_006,axiom,
f(nil) = btrue ).
cnf(axiom_008,axiom,
prop1(X) = eq(f(X),bfalse) ).
cnf(axiom_010,axiom,
eq(btrue,bfalse) = bfalse ).
cnf(axiom_011,axiom,
eq(X,X) = btrue ).
cnf(goal,negated_conjecture,
eq(prop1(X),bfalse) != btrue ).
cnf(refute_0_0,plain,
eq(prop1(nil),bfalse) != btrue,
inference(subst,[],[goal:[bind(X,$fot(nil))]]) ).
cnf(refute_0_1,plain,
prop1(nil) = eq(f(nil),bfalse),
inference(subst,[],[axiom_008:[bind(X,$fot(nil))]]) ).
cnf(refute_0_2,plain,
( f(nil) != btrue
| prop1(nil) != eq(f(nil),bfalse)
| prop1(nil) = eq(btrue,bfalse) ),
introduced(tautology,[equality,[$cnf( $equal(prop1(nil),eq(f(nil),bfalse)) ),[1,0],$fot(btrue)]]) ).
cnf(refute_0_3,plain,
( prop1(nil) != eq(f(nil),bfalse)
| prop1(nil) = eq(btrue,bfalse) ),
inference(resolve,[$cnf( $equal(f(nil),btrue) )],[axiom_006,refute_0_2]) ).
cnf(refute_0_4,plain,
prop1(nil) = eq(btrue,bfalse),
inference(resolve,[$cnf( $equal(prop1(nil),eq(f(nil),bfalse)) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( eq(btrue,bfalse) != bfalse
| prop1(nil) != eq(btrue,bfalse)
| prop1(nil) = bfalse ),
introduced(tautology,[equality,[$cnf( $equal(prop1(nil),eq(btrue,bfalse)) ),[1],$fot(bfalse)]]) ).
cnf(refute_0_6,plain,
( prop1(nil) != eq(btrue,bfalse)
| prop1(nil) = bfalse ),
inference(resolve,[$cnf( $equal(eq(btrue,bfalse),bfalse) )],[axiom_010,refute_0_5]) ).
cnf(refute_0_7,plain,
prop1(nil) = bfalse,
inference(resolve,[$cnf( $equal(prop1(nil),eq(btrue,bfalse)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( eq(bfalse,bfalse) != btrue
| prop1(nil) != bfalse
| eq(prop1(nil),bfalse) = btrue ),
introduced(tautology,[equality,[$cnf( ~ $equal(eq(prop1(nil),bfalse),btrue) ),[0,0],$fot(bfalse)]]) ).
cnf(refute_0_9,plain,
( eq(bfalse,bfalse) != btrue
| eq(prop1(nil),bfalse) = btrue ),
inference(resolve,[$cnf( $equal(prop1(nil),bfalse) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
eq(bfalse,bfalse) != btrue,
inference(resolve,[$cnf( $equal(eq(prop1(nil),bfalse),btrue) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
eq(bfalse,bfalse) = btrue,
inference(subst,[],[axiom_011:[bind(X,$fot(bfalse))]]) ).
cnf(refute_0_12,plain,
( btrue != btrue
| eq(bfalse,bfalse) != btrue
| eq(bfalse,bfalse) = btrue ),
introduced(tautology,[equality,[$cnf( $equal(eq(bfalse,bfalse),btrue) ),[1],$fot(btrue)]]) ).
cnf(refute_0_13,plain,
( btrue != btrue
| eq(bfalse,bfalse) = btrue ),
inference(resolve,[$cnf( $equal(eq(bfalse,bfalse),btrue) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
btrue != btrue,
inference(resolve,[$cnf( $equal(eq(bfalse,bfalse),btrue) )],[refute_0_13,refute_0_10]) ).
cnf(refute_0_15,plain,
btrue = btrue,
introduced(tautology,[refl,[$fot(btrue)]]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( $equal(btrue,btrue) )],[refute_0_15,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX233-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 13:06:43 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35
% 0.20/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.35
%------------------------------------------------------------------------------