%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU144+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 : n006.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 08:41:00 AM UTC 2026
% Result : Theorem 16.71s 7.83s
% Output : CNFRefutation 16.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 53 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 15 ~; 19 |; 0 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 ( 1 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ) ).
fof(d1_xboole_0,axiom,
! [X0] :
( X0 = 'empty$uset'
<=> ! [X1] : ~ in(X1,X0) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(l1_zfmisc_1,lemma,
! [X0] : singleton(X0) != 'empty$uset' ).
fof(l2_zfmisc_1,conjecture,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
inference(negate_conjecture,[status(cth)],[l2_zfmisc_1]) ).
cnf(c8,plain,
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c15,plain,
( in(sK18(X0),X0)
| X0 = 'empty$uset' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c38,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c39,plain,
( in(sK34(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c40,plain,
( ~ in(sK34(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c74,plain,
singleton(X0) != 'empty$uset',
inference(clausification,[status(esa)],[l1_zfmisc_1]) ).
cnf(c121,plain,
( in(sK135,sK136)
| subset(singleton(sK135),sK136) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c122,plain,
( ~ subset(singleton(sK135),sK136)
| ~ in(sK135,sK136) ),
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(singleton(X0),X1)
| sK34(singleton(X0),X1) = X0 ),
inference(resolution,[status(thm)],[d0,c39]) ).
cnf(d2,plain,
( singleton(X0) = 'empty$uset'
| sK18(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[d0,c15]) ).
cnf(d3,plain,
sK18(singleton(X0)) = X0,
inference(resolution,[status(thm)],[c74,d2]) ).
cnf(d4,plain,
( in(sK135,sK136)
| ~ in(X0,singleton(sK135))
| in(X0,sK136) ),
inference(resolution,[status(thm)],[c38,c121]) ).
cnf(d5,plain,
( singleton(sK135) = 'empty$uset'
| in(sK135,sK136)
| in(sK18(singleton(sK135)),sK136) ),
inference(resolution,[status(thm)],[d4,c15]) ).
cnf(d6,plain,
( in(sK135,sK136)
| in(sK18(singleton(sK135)),sK136) ),
inference(resolution,[status(thm)],[c74,d5]) ).
cnf(d7,plain,
( in(sK135,sK136)
| in(sK135,sK136) ),
inference(demodulation,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
~ subset(singleton(sK135),sK136),
inference(resolution,[status(thm)],[d7,c122]) ).
cnf(d9,plain,
sK34(singleton(sK135),sK136) = sK135,
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( subset(singleton(sK135),sK136)
| ~ in(sK135,sK136) ),
inference(superposition,[status(thm)],[d9,c40]) ).
cnf(d11,plain,
subset(singleton(sK135),sK136),
inference(resolution,[status(thm)],[d7,d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d8,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU144+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n006.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 08:39:17 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.71/7.83 % SZS status Theorem for theBenchmark.p
% 16.71/7.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------