%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU230+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 : n002.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 08:41:22 AM UTC 2026
% Result : Theorem 40.51s 10.69s
% Output : CNFRefutation 40.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 13 unt; 0 def)
% Number of atoms : 17 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 20 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(d1_ordinal1,axiom,
! [X0] : succ(X0) = 'set$uunion2'(X0,singleton(X0)) ).
fof(l2_zfmisc_1,lemma,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ) ).
fof(t7_xboole_1,lemma,
! [X0,X1] : subset(X0,'set$uunion2'(X0,X1)) ).
fof(t10_ordinal1,conjecture,
! [X0] : in(X0,succ(X0)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : in(X0,succ(X0)),
inference(negate_conjecture,[status(cth)],[t10_ordinal1]) ).
cnf(c8,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c107,plain,
succ(X0) = 'set$uunion2'(X0,singleton(X0)),
inference(clausification,[status(esa)],[d1_ordinal1]) ).
cnf(c355,plain,
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(clausification,[status(esa)],[l2_zfmisc_1]) ).
cnf(c563,plain,
subset(X0,'set$uunion2'(X0,X1)),
inference(clausification,[status(esa)],[t7_xboole_1]) ).
cnf(c587,plain,
~ in(sK644,succ(sK644)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset(X0,'set$uunion2'(X1,X0)),
inference(superposition,[status(thm)],[c8,c563]) ).
cnf(d1,plain,
subset(singleton(X0),succ(X0)),
inference(superposition,[status(thm)],[c107,d0]) ).
cnf(d2,plain,
in(X0,succ(X0)),
inference(resolution,[status(thm)],[c355,d1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,c587]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.47 % Computer : n002.cluster.edu
% 0.19/5.47 % Model : x86_64 x86_64
% 0.19/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.47 % Memory : 8046.5625MB
% 0.19/5.47 % OS : Linux 6.8.0-71-generic
% 0.19/5.47 % CPULimit : 300
% 0.19/5.47 % WCLimit : 300
% 0.19/5.47 % DateTime : Sat Sep 26 08:57:57 UTC 2026
% 0.19/5.48 % CPUTime :
% 0.19/5.48 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.51/10.69 % SZS status Theorem for theBenchmark.p
% 40.51/10.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------