%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU188+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 : n010.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 08:41:12 AM UTC 2026
% Result : Theorem 18.83s 3.27s
% Output : CNFRefutation 18.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 9 unt; 0 def)
% Number of atoms : 90 ( 35 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 87 ( 33 ~; 41 |; 2 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 8 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X0] :
( X0 = 'empty$uset'
<=> ! [X1] : ~ in(X1,X0) ) ).
fof(d5_relat_1,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = 'relation$urng'(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in('ordered$upair'(X3,X2),X0) ) ) ) ).
fof(fc1_xboole_0,axiom,
empty('empty$uset') ).
fof(fc5_relat_1,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty('relation$udom'(X0)) ) ).
fof(fc6_relat_1,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty('relation$urng'(X0)) ) ).
fof(t6_boole,axiom,
! [X0] :
( empty(X0)
=> X0 = 'empty$uset' ) ).
fof(t64_relat_1,conjecture,
! [X0] :
( relation(X0)
=> ( ( 'relation$urng'(X0) = 'empty$uset'
| 'relation$udom'(X0) = 'empty$uset' )
=> X0 = 'empty$uset' ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ( 'relation$urng'(X0) = 'empty$uset'
| 'relation$udom'(X0) = 'empty$uset' )
=> X0 = 'empty$uset' ) ),
inference(negate_conjecture,[status(cth)],[t64_relat_1]) ).
cnf(c31,plain,
( ~ in(X1,X0)
| X0 != 'empty$uset' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c123,plain,
( ~ in('ordered$upair'(X3,X2),X0)
| in(X2,X1)
| X1 != 'relation$urng'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d5_relat_1]) ).
cnf(c125,plain,
( in('ordered$upair'(sK109(X0,X1),sK107(X0,X1)),X0)
| in(sK107(X0,X1),X1)
| X1 = 'relation$urng'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d5_relat_1]) ).
cnf(c172,plain,
empty('empty$uset'),
inference(clausification,[status(esa)],[fc1_xboole_0]) ).
cnf(c182,plain,
( ~ empty('relation$udom'(X0))
| ~ relation(X0)
| empty(X0) ),
inference(clausification,[status(esa)],[fc5_relat_1]) ).
cnf(c183,plain,
( ~ empty('relation$urng'(X0))
| ~ relation(X0)
| empty(X0) ),
inference(clausification,[status(esa)],[fc6_relat_1]) ).
cnf(c314,plain,
( X0 = 'empty$uset'
| ~ empty(X0) ),
inference(clausification,[status(esa)],[t6_boole]) ).
cnf(c331,plain,
relation(sK404),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c332,plain,
( 'relation$urng'(sK404) = 'empty$uset'
| 'relation$udom'(sK404) = 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c333,plain,
sK404 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ in(X0,'empty$uset'),
inference(equality_resolution,[status(thm)],[c31]) ).
cnf(d1,plain,
( 'relation$udom'(sK404) = 'empty$uset'
| ~ relation(sK404)
| ~ in('ordered$upair'(X2,X1),sK404)
| in(X1,X0)
| X0 != 'empty$uset' ),
inference(superposition,[status(thm)],[c332,c123]) ).
cnf(d2,plain,
( ~ in('ordered$upair'(X2,X1),sK404)
| in(X1,X0)
| 'relation$udom'(sK404) = 'empty$uset'
| X0 != 'empty$uset' ),
inference(resolution,[status(thm)],[c331,d1]) ).
cnf(d3,plain,
( ~ in('ordered$upair'(X1,X0),sK404)
| in(X0,'empty$uset')
| 'relation$udom'(sK404) = 'empty$uset' ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
( ~ in('ordered$upair'(X0,X1),sK404)
| 'relation$udom'(sK404) = 'empty$uset' ),
inference(resolution,[status(thm)],[d0,d3]) ).
cnf(d5,plain,
( ~ relation(sK404)
| in(sK107(sK404,X0),X0)
| X0 = 'relation$urng'(sK404)
| 'relation$udom'(sK404) = 'empty$uset' ),
inference(resolution,[status(thm)],[d4,c125]) ).
cnf(d6,plain,
( in(sK107(sK404,X0),X0)
| 'relation$udom'(sK404) = 'empty$uset'
| X0 = 'relation$urng'(sK404) ),
inference(resolution,[status(thm)],[c331,d5]) ).
cnf(d7,plain,
( 'relation$udom'(sK404) = 'empty$uset'
| 'empty$uset' = 'relation$urng'(sK404) ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( 'relation$udom'(sK404) = 'empty$uset'
| ~ relation(sK404)
| empty(sK404)
| ~ empty('empty$uset') ),
inference(superposition,[status(thm)],[d7,c183]) ).
cnf(d9,plain,
( empty(sK404)
| ~ empty('empty$uset')
| 'relation$udom'(sK404) = 'empty$uset' ),
inference(resolution,[status(thm)],[c331,d8]) ).
cnf(d10,plain,
( empty(sK404)
| 'relation$udom'(sK404) = 'empty$uset' ),
inference(resolution,[status(thm)],[c172,d9]) ).
cnf(d11,plain,
( sK404 = 'empty$uset'
| 'relation$udom'(sK404) = 'empty$uset' ),
inference(resolution,[status(thm)],[d10,c314]) ).
cnf(d12,plain,
'relation$udom'(sK404) = 'empty$uset',
inference(resolution,[status(thm)],[c333,d11]) ).
cnf(d13,plain,
( ~ relation(sK404)
| empty(sK404)
| ~ empty('empty$uset') ),
inference(superposition,[status(thm)],[d12,c182]) ).
cnf(d14,plain,
( empty(sK404)
| ~ empty('empty$uset') ),
inference(resolution,[status(thm)],[c331,d13]) ).
cnf(d15,plain,
empty(sK404),
inference(resolution,[status(thm)],[c172,d14]) ).
cnf(d16,plain,
sK404 = 'empty$uset',
inference(resolution,[status(thm)],[d15,c314]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[c333,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU188+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
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:47:30 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.83/3.27 % SZS status Theorem for theBenchmark.p
% 18.83/3.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------