%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU154+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:41:03 AM UTC 2026
% Result : Theorem 16.25s 3.78s
% Output : CNFRefutation 16.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 49 ( 13 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 35 ( 14 ~; 10 |; 5 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 3 sgn 18 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ) ).
fof(l23_zfmisc_1,lemma,
! [X0,X1] :
( in(X0,X1)
=> 'set$uunion2'(singleton(X0),X1) = X1 ) ).
fof(l2_zfmisc_1,lemma,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ) ).
fof(t3_xboole_0,lemma,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ) ).
fof(t7_xboole_1,lemma,
! [X0,X1] : subset(X0,'set$uunion2'(X0,X1)) ).
fof(l28_zfmisc_1,conjecture,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
inference(negate_conjecture,[status(cth)],[l28_zfmisc_1]) ).
cnf(c3,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c8,plain,
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c81,plain,
( 'set$uunion2'(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[l23_zfmisc_1]) ).
cnf(c83,plain,
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(clausification,[status(esa)],[l2_zfmisc_1]) ).
cnf(c116,plain,
( in(sK122(X0,X1),X0)
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[t3_xboole_0]) ).
cnf(c117,plain,
( in(sK122(X0,X1),X1)
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[t3_xboole_0]) ).
cnf(c132,plain,
subset(X0,'set$uunion2'(X0,X1)),
inference(clausification,[status(esa)],[t7_xboole_1]) ).
cnf(c139,plain,
~ in(sK162,sK163),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c140,plain,
~ disjoint(singleton(sK162),sK163),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(d1,plain,
subset(X0,'set$uunion2'(X1,X0)),
inference(superposition,[status(thm)],[c3,c132]) ).
cnf(d2,plain,
in(X0,'set$uunion2'(X1,singleton(X0))),
inference(resolution,[status(thm)],[d1,c83]) ).
cnf(d3,plain,
( 'set$uunion2'(singleton(sK122(X0,X1)),X0) = X0
| disjoint(X0,X1) ),
inference(resolution,[status(thm)],[c116,c81]) ).
cnf(d4,plain,
( disjoint(X0,X1)
| 'set$uunion2'(X0,singleton(sK122(X0,X1))) = X0 ),
inference(demodulation,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
'set$uunion2'(singleton(sK162),singleton(sK122(singleton(sK162),sK163))) = singleton(sK162),
inference(resolution,[status(thm)],[d4,c140]) ).
cnf(d6,plain,
in(sK122(singleton(sK162),sK163),singleton(sK162)),
inference(superposition,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
sK122(singleton(sK162),sK163) = sK162,
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( disjoint(singleton(sK162),sK163)
| in(sK162,sK163) ),
inference(superposition,[status(thm)],[d7,c117]) ).
cnf(d9,plain,
disjoint(singleton(sK162),sK163),
inference(resolution,[status(thm)],[c139,d8]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c140,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU154+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n004.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 08:41:36 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.25/3.78 % SZS status Theorem for theBenchmark.p
% 16.25/3.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------