%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:12:39 AM UTC 2026
% Result : Theorem 16.60s 4.15s
% Output : CNFRefutation 16.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 18 unt; 0 def)
% Number of atoms : 88 ( 8 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 79 ( 30 ~; 28 |; 14 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 24 ( 3 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_ordinal1,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( 'transfinite$usequence'(X0)
<=> ordinal('relation$udom'(X0)) ) ) ).
fof(d8_ordinal1,axiom,
! [X0,X1] :
( ( 'transfinite$usequence'(X1)
& function(X1)
& relation(X1) )
=> ( 'transfinite$usequence$uof'(X1,X0)
<=> subset('relation$urng'(X1),X0) ) ) ).
fof(fc12_relat_1,axiom,
( 'relation$uempty$uyielding'('empty$uset')
& relation('empty$uset')
& empty('empty$uset') ) ).
fof(fc2_ordinal1,axiom,
( ordinal('empty$uset')
& 'epsilon$uconnected'('empty$uset')
& 'epsilon$utransitive'('empty$uset')
& empty('empty$uset')
& 'one$uto$uone'('empty$uset')
& function('empty$uset')
& 'relation$uempty$uyielding'('empty$uset')
& relation('empty$uset') ) ).
fof(fc7_relat_1,axiom,
! [X0] :
( empty(X0)
=> ( relation('relation$udom'(X0))
& empty('relation$udom'(X0)) ) ) ).
fof(fc8_relat_1,axiom,
! [X0] :
( empty(X0)
=> ( relation('relation$urng'(X0))
& empty('relation$urng'(X0)) ) ) ).
fof(rc1_xboole_0,axiom,
? [X0] : empty(X0) ).
fof(t2_xboole_1,axiom,
! [X0] : subset('empty$uset',X0) ).
fof(t6_boole,axiom,
! [X0] :
( empty(X0)
=> X0 = 'empty$uset' ) ).
fof(t45_ordinal1,conjecture,
! [X0] : 'transfinite$usequence$uof'('empty$uset',X0) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : 'transfinite$usequence$uof'('empty$uset',X0),
inference(negate_conjecture,[status(cth)],[t45_ordinal1]) ).
cnf(c21,plain,
( ~ ordinal('relation$udom'(X0))
| 'transfinite$usequence'(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d7_ordinal1]) ).
cnf(c23,plain,
( ~ 'transfinite$usequence'(X0)
| ~ function(X0)
| ~ subset('relation$urng'(X0),X1)
| 'transfinite$usequence$uof'(X0,X1)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d8_ordinal1]) ).
cnf(c29,plain,
empty('empty$uset'),
inference(clausification,[status(esa)],[fc12_relat_1]) ).
cnf(c30,plain,
relation('empty$uset'),
inference(clausification,[status(esa)],[fc12_relat_1]) ).
cnf(c36,plain,
function('empty$uset'),
inference(clausification,[status(esa)],[fc2_ordinal1]) ).
cnf(c41,plain,
ordinal('empty$uset'),
inference(clausification,[status(esa)],[fc2_ordinal1]) ).
cnf(c47,plain,
( empty('relation$udom'(X0))
| ~ empty(X0) ),
inference(clausification,[status(esa)],[fc7_relat_1]) ).
cnf(c49,plain,
( empty('relation$urng'(X0))
| ~ empty(X0) ),
inference(clausification,[status(esa)],[fc8_relat_1]) ).
cnf(c58,plain,
empty(sK39),
inference(clausification,[status(esa)],[rc1_xboole_0]) ).
cnf(c93,plain,
subset('empty$uset',X0),
inference(clausification,[status(esa)],[t2_xboole_1]) ).
cnf(c100,plain,
( X0 = 'empty$uset'
| ~ empty(X0) ),
inference(clausification,[status(esa)],[t6_boole]) ).
cnf(c103,plain,
~ 'transfinite$usequence$uof'('empty$uset',sK71),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ empty(X0)
| 'relation$urng'(X0) = 'empty$uset' ),
inference(resolution,[status(thm)],[c100,c49]) ).
cnf(d1,plain,
'relation$urng'('empty$uset') = 'empty$uset',
inference(resolution,[status(thm)],[d0,c29]) ).
cnf(d2,plain,
( 'transfinite$usequence$uof'('empty$uset',X0)
| ~ 'transfinite$usequence'('empty$uset')
| ~ relation('empty$uset')
| ~ function('empty$uset')
| ~ subset('empty$uset',X0) ),
inference(superposition,[status(thm)],[d1,c23]) ).
cnf(d3,plain,
( ~ subset('empty$uset',X0)
| 'transfinite$usequence$uof'('empty$uset',X0)
| ~ 'transfinite$usequence'('empty$uset')
| ~ function('empty$uset') ),
inference(resolution,[status(thm)],[c30,d2]) ).
cnf(d4,plain,
( ~ subset('empty$uset',X0)
| 'transfinite$usequence$uof'('empty$uset',X0)
| ~ 'transfinite$usequence'('empty$uset') ),
inference(resolution,[status(thm)],[c36,d3]) ).
cnf(d5,plain,
( 'transfinite$usequence$uof'('empty$uset',X0)
| ~ 'transfinite$usequence'('empty$uset') ),
inference(resolution,[status(thm)],[c93,d4]) ).
cnf(d6,plain,
sK39 = 'empty$uset',
inference(resolution,[status(thm)],[c100,c58]) ).
cnf(d7,plain,
( ~ empty(X0)
| 'relation$udom'(X0) = 'empty$uset' ),
inference(resolution,[status(thm)],[c100,c47]) ).
cnf(d8,plain,
'relation$udom'(sK39) = 'empty$uset',
inference(resolution,[status(thm)],[d7,c58]) ).
cnf(d9,plain,
'relation$udom'('empty$uset') = 'empty$uset',
inference(demodulation,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( 'transfinite$usequence'('empty$uset')
| ~ relation('empty$uset')
| ~ function('empty$uset')
| ~ ordinal('empty$uset') ),
inference(superposition,[status(thm)],[d9,c21]) ).
cnf(d11,plain,
( 'transfinite$usequence'('empty$uset')
| ~ ordinal('empty$uset')
| ~ function('empty$uset') ),
inference(resolution,[status(thm)],[c30,d10]) ).
cnf(d12,plain,
( 'transfinite$usequence'('empty$uset')
| ~ ordinal('empty$uset') ),
inference(resolution,[status(thm)],[c36,d11]) ).
cnf(d13,plain,
'transfinite$usequence'('empty$uset'),
inference(resolution,[status(thm)],[c41,d12]) ).
cnf(d14,plain,
'transfinite$usequence$uof'('empty$uset',X0),
inference(resolution,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,c103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n019.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 02:39:33 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.60/4.15 % SZS status Theorem for theBenchmark.p
% 16.60/4.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------