%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU146+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 : n011.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 08:41:01 AM UTC 2026
% Result : Theorem 16.63s 2.60s
% Output : CNFRefutation 16.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 110 ( 62 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 96 ( 29 ~; 55 |; 2 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 43 ( 3 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ) ).
fof(d1_xboole_0,axiom,
! [X0] :
( X0 = 'empty$uset'
<=> ! [X1] : ~ in(X1,X0) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(d8_xboole_0,axiom,
! [X0,X1] :
( 'proper$usubset'(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [X0,X1] : ~ 'proper$usubset'(X0,X0) ).
fof(l2_zfmisc_1,lemma,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ) ).
fof(reflexivity_r1_tarski,axiom,
! [X0,X1] : subset(X0,X0) ).
fof(t2_xboole_1,lemma,
! [X0] : subset('empty$uset',X0) ).
fof(l4_zfmisc_1,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = 'empty$uset' ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = 'empty$uset' ) ),
inference(negate_conjecture,[status(cth)],[l4_zfmisc_1]) ).
cnf(c7,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[d10_xboole_0]) ).
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$uset' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c38,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c67,plain,
( X0 = X1
| ~ subset(X0,X1)
| 'proper$usubset'(X0,X1) ),
inference(clausification,[status(esa)],[d8_xboole_0]) ).
cnf(c73,plain,
~ 'proper$usubset'(X0,X0),
inference(clausification,[status(esa)],[irreflexivity_r2_xboole_0]) ).
cnf(c76,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(clausification,[status(esa)],[l2_zfmisc_1]) ).
cnf(c82,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(c96,plain,
subset('empty$uset',X0),
inference(clausification,[status(esa)],[t2_xboole_1]) ).
cnf(c124,plain,
( sK140 = singleton(sK141)
| sK140 = 'empty$uset'
| subset(sK140,singleton(sK141)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c125,plain,
( ~ subset(sK140,singleton(sK141))
| sK140 != 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c127,plain,
( ~ subset(sK140,singleton(sK141))
| sK140 != singleton(sK141) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( sK140 = 'empty$uset'
| sK140 = singleton(sK141)
| 'proper$usubset'(sK140,singleton(sK141))
| sK140 = singleton(sK141) ),
inference(resolution,[status(thm)],[c67,c124]) ).
cnf(d1,plain,
( sK140 = 'empty$uset'
| sK140 = singleton(sK141)
| ~ subset(singleton(sK141),sK140)
| singleton(sK141) = sK140 ),
inference(resolution,[status(thm)],[c7,c124]) ).
cnf(d2,plain,
( sK140 = 'empty$uset'
| sK140 = singleton(sK141)
| singleton(sK141) = sK140
| ~ in(sK141,sK140) ),
inference(resolution,[status(thm)],[c76,d1]) ).
cnf(d3,plain,
( sK140 = 'empty$uset'
| sK140 = singleton(sK141)
| ~ in(X0,sK140)
| in(X0,singleton(sK141)) ),
inference(resolution,[status(thm)],[c38,c124]) ).
cnf(d4,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(d5,plain,
( ~ in(X0,sK140)
| sK140 = 'empty$uset'
| sK140 = singleton(sK141)
| X0 = sK141 ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( sK140 = 'empty$uset'
| sK140 = 'empty$uset'
| sK140 = singleton(sK141)
| sK18(sK140) = sK141 ),
inference(resolution,[status(thm)],[d5,c15]) ).
cnf(d7,plain,
( sK140 = 'empty$uset'
| sK140 = singleton(sK141)
| sK140 = 'empty$uset'
| in(sK141,sK140) ),
inference(superposition,[status(thm)],[d6,c15]) ).
cnf(d8,plain,
( sK140 = 'empty$uset'
| sK140 = singleton(sK141)
| singleton(sK141) = sK140
| sK140 = 'empty$uset'
| sK140 = singleton(sK141) ),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( sK140 = 'empty$uset'
| sK140 = singleton(sK141)
| sK140 = 'empty$uset'
| sK140 = singleton(sK141)
| 'proper$usubset'(sK140,sK140) ),
inference(superposition,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
( sK140 = 'empty$uset'
| sK140 = singleton(sK141) ),
inference(resolution,[status(thm)],[c73,d9]) ).
cnf(d11,plain,
( sK140 = 'empty$uset'
| ~ subset(sK140,singleton(sK141))
| sK140 != sK140 ),
inference(superposition,[status(thm)],[d10,c127]) ).
cnf(d12,plain,
( ~ subset(sK140,singleton(sK141))
| sK140 = 'empty$uset' ),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
( sK140 = 'empty$uset'
| singleton(sK141) = sK140
| sK140 != sK140 ),
inference(equality_factoring,[status(thm)],[d8]) ).
cnf(d14,plain,
( sK140 = 'empty$uset'
| singleton(sK141) = sK140 ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
( sK140 = 'empty$uset'
| sK140 = 'empty$uset'
| ~ subset(sK140,sK140) ),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
sK140 = 'empty$uset',
inference(resolution,[status(thm)],[c82,d15]) ).
cnf(d17,plain,
~ subset(sK140,singleton(sK141)),
inference(resolution,[status(thm)],[d16,c125]) ).
cnf(d18,plain,
~ subset('empty$uset',singleton(sK141)),
inference(demodulation,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c96,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+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
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:40:29 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.63/2.60 % SZS status Theorem for theBenchmark.p
% 16.63/2.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------