%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU152+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 : n015.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 15.75s 2.47s
% Output : CNFRefutation 15.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 39 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 9 ~; 6 |; 0 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(l2_zfmisc_1,lemma,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ) ).
fof(l32_xboole_1,lemma,
! [X0,X1] :
( 'set$udifference'(X0,X1) = 'empty$uset'
<=> subset(X0,X1) ) ).
fof(t12_xboole_1,lemma,
! [X0,X1] :
( subset(X0,X1)
=> 'set$uunion2'(X0,X1) = X1 ) ).
fof(t36_xboole_1,lemma,
! [X0,X1] : subset('set$udifference'(X0,X1),X0) ).
fof(t4_boole,axiom,
! [X0] : 'set$udifference'('empty$uset',X0) = 'empty$uset' ).
fof(l23_zfmisc_1,conjecture,
! [X0,X1] :
( in(X0,X1)
=> 'set$uunion2'(singleton(X0),X1) = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> 'set$uunion2'(singleton(X0),X1) = X1 ),
inference(negate_conjecture,[status(cth)],[l23_zfmisc_1]) ).
cnf(c3,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c82,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(clausification,[status(esa)],[l2_zfmisc_1]) ).
cnf(c83,plain,
( subset(X0,X1)
| 'set$udifference'(X0,X1) != 'empty$uset' ),
inference(clausification,[status(esa)],[l32_xboole_1]) ).
cnf(c84,plain,
( ~ subset(X0,X1)
| 'set$udifference'(X0,X1) = 'empty$uset' ),
inference(clausification,[status(esa)],[l32_xboole_1]) ).
cnf(c94,plain,
( 'set$uunion2'(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t12_xboole_1]) ).
cnf(c109,plain,
subset('set$udifference'(X0,X1),X0),
inference(clausification,[status(esa)],[t36_xboole_1]) ).
cnf(c121,plain,
'set$udifference'('empty$uset',X0) = 'empty$uset',
inference(clausification,[status(esa)],[t4_boole]) ).
cnf(c137,plain,
in(sK158,sK159),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c138,plain,
'set$uunion2'(singleton(sK158),sK159) != sK159,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X0,X1)
| 'set$udifference'(singleton(X0),X1) = 'empty$uset' ),
inference(resolution,[status(thm)],[c84,c82]) ).
cnf(d1,plain,
'set$udifference'(singleton(sK158),sK159) = 'empty$uset',
inference(resolution,[status(thm)],[d0,c137]) ).
cnf(d2,plain,
( subset(singleton(sK158),sK159)
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[d1,c83]) ).
cnf(d3,plain,
'set$udifference'('set$udifference'(X0,X1),X0) = 'empty$uset',
inference(resolution,[status(thm)],[c84,c109]) ).
cnf(d4,plain,
'set$udifference'('empty$uset',singleton(sK158)) = 'empty$uset',
inference(superposition,[status(thm)],[d1,d3]) ).
cnf(d5,plain,
'empty$uset' = 'empty$uset',
inference(demodulation,[status(thm)],[d4,c121]) ).
cnf(d6,plain,
subset(singleton(sK158),sK159),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
'set$uunion2'(singleton(sK158),sK159) = sK159,
inference(resolution,[status(thm)],[d6,c94]) ).
cnf(d8,plain,
'set$uunion2'(sK159,singleton(sK158)) = sK159,
inference(demodulation,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
'set$uunion2'(sK159,singleton(sK158)) != sK159,
inference(demodulation,[status(thm)],[c138,c3]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU152+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.39 % Computer : n015.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sat Sep 26 08:44:29 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.75/2.47 % SZS status Theorem for theBenchmark.p
% 15.75/2.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------