%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU161+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:41:05 AM UTC 2026
% Result : Theorem 15.80s 14.01s
% Output : CNFRefutation 15.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% Number of atoms : 16 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 1 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(l23_zfmisc_1,lemma,
! [X0,X1] :
( in(X0,X1)
=> 'set$uunion2'(singleton(X0),X1) = X1 ) ).
fof(t46_zfmisc_1,conjecture,
! [X0,X1] :
( in(X0,X1)
=> 'set$uunion2'(singleton(X0),X1) = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> 'set$uunion2'(singleton(X0),X1) = X1 ),
inference(negate_conjecture,[status(cth)],[t46_zfmisc_1]) ).
cnf(c3,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c108,plain,
( 'set$uunion2'(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[l23_zfmisc_1]) ).
cnf(c181,plain,
in(sK208,sK209),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c182,plain,
'set$uunion2'(singleton(sK208),sK209) != sK209,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'set$uunion2'(singleton(sK208),sK209) = sK209,
inference(resolution,[status(thm)],[c108,c181]) ).
cnf(d1,plain,
'set$uunion2'(sK209,singleton(sK208)) = sK209,
inference(demodulation,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
'set$uunion2'(sK209,singleton(sK208)) != sK209,
inference(demodulation,[status(thm)],[c182,c3]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU161+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.39 % Computer : n016.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Sat Sep 26 08:47:41 UTC 2026
% 0.17/10.40 % CPUTime :
% 0.17/10.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.80/14.01 % SZS status Theorem for theBenchmark.p
% 15.80/14.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------