%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU341+1 : 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 : n009.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 08:41:43 AM UTC 2026
% Result : Theorem 14.36s 2.79s
% Output : CNFRefutation 14.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 111 ( 9 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 132 ( 53 ~; 48 |; 12 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 4 sgn 17 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_connsp_2,axiom,
! [X0] :
( ( 'top$ustr'(X0)
& 'topological$uspace'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,'the$ucarrier'(X0))
=> ! [X2] :
( element(X2,powerset('the$ucarrier'(X0)))
=> ( 'point$uneighbourhood'(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ) ).
fof(rc2_subset_1,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ) ).
fof(t4_subset,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ) ).
fof(t55_tops_1,axiom,
! [X0] :
( ( 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> ! [X1] :
( 'top$ustr'(X1)
=> ! [X2] :
( element(X2,powerset('the$ucarrier'(X0)))
=> ! [X3] :
( element(X3,powerset('the$ucarrier'(X1)))
=> ( ( interior(X0,X2) = X2
=> 'open$usubset'(X2,X0) )
& ( 'open$usubset'(X3,X1)
=> interior(X1,X3) = X3 ) ) ) ) ) ) ).
fof(t5_connsp_2,conjecture,
! [X0] :
( ( 'top$ustr'(X0)
& 'topological$uspace'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> ( ( in(X2,X1)
& 'open$usubset'(X1,X0) )
=> 'point$uneighbourhood'(X1,X0,X2) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'top$ustr'(X0)
& 'topological$uspace'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> ( ( in(X2,X1)
& 'open$usubset'(X1,X0) )
=> 'point$uneighbourhood'(X1,X0,X2) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t5_connsp_2]) ).
cnf(c44,plain,
( ~ element(X2,powerset('the$ucarrier'(X0)))
| ~ 'topological$uspace'(X0)
| ~ element(X1,'the$ucarrier'(X0))
| 'point$uneighbourhood'(X2,X0,X1)
| ~ 'top$ustr'(X0)
| ~ in(X1,interior(X0,X2))
| 'empty$ucarrier'(X0) ),
inference(clausification,[status(esa)],[d1_connsp_2]) ).
cnf(c67,plain,
element(sK51(X0),powerset(X0)),
inference(clausification,[status(esa)],[rc2_subset_1]) ).
cnf(c74,plain,
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t4_subset]) ).
cnf(c75,plain,
( interior(X2,X1) = X1
| ~ 'top$ustr'(X2)
| ~ 'top$ustr'(X0)
| ~ element(X3,powerset('the$ucarrier'(X0)))
| ~ 'open$usubset'(X1,X2)
| ~ element(X1,powerset('the$ucarrier'(X2)))
| ~ 'topological$uspace'(X0) ),
inference(clausification,[status(esa)],[t55_tops_1]) ).
cnf(c81,plain,
~ 'empty$ucarrier'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c82,plain,
'topological$uspace'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c83,plain,
'top$ustr'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c84,plain,
element(sK76,powerset('the$ucarrier'(sK75))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c86,plain,
'open$usubset'(sK76,sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c87,plain,
in(sK77,sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c88,plain,
~ 'point$uneighbourhood'(sK76,sK75,sK77),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( element(X0,'the$ucarrier'(sK75))
| ~ in(X0,sK76) ),
inference(resolution,[status(thm)],[c74,c84]) ).
cnf(d1,plain,
( ~ 'open$usubset'(sK76,sK75)
| ~ 'topological$uspace'(X1)
| ~ 'top$ustr'(X1)
| ~ 'top$ustr'(sK75)
| ~ element(X0,powerset('the$ucarrier'(X1)))
| interior(sK75,sK76) = sK76 ),
inference(resolution,[status(thm)],[c75,c84]) ).
cnf(d2,plain,
( ~ 'open$usubset'(sK76,sK75)
| ~ 'topological$uspace'(X1)
| ~ 'top$ustr'(X1)
| ~ element(X0,powerset('the$ucarrier'(X1)))
| interior(sK75,sK76) = sK76 ),
inference(resolution,[status(thm)],[c83,d1]) ).
cnf(d3,plain,
( ~ 'topological$uspace'(X1)
| ~ 'top$ustr'(X1)
| ~ element(X0,powerset('the$ucarrier'(X1)))
| interior(sK75,sK76) = sK76 ),
inference(resolution,[status(thm)],[c86,d2]) ).
cnf(d4,plain,
( ~ 'topological$uspace'(X0)
| ~ 'top$ustr'(X0)
| interior(sK75,sK76) = sK76 ),
inference(resolution,[status(thm)],[d3,c67]) ).
cnf(d5,plain,
( ~ 'top$ustr'(sK75)
| interior(sK75,sK76) = sK76 ),
inference(resolution,[status(thm)],[d4,c82]) ).
cnf(d6,plain,
interior(sK75,sK76) = sK76,
inference(resolution,[status(thm)],[c83,d5]) ).
cnf(d7,plain,
( 'empty$ucarrier'(sK75)
| ~ 'topological$uspace'(sK75)
| 'point$uneighbourhood'(sK76,sK75,X0)
| ~ 'top$ustr'(sK75)
| ~ element(X0,'the$ucarrier'(sK75))
| ~ in(X0,interior(sK75,sK76)) ),
inference(resolution,[status(thm)],[c44,c84]) ).
cnf(d8,plain,
( ~ 'topological$uspace'(sK75)
| 'point$uneighbourhood'(sK76,sK75,X0)
| ~ 'top$ustr'(sK75)
| ~ element(X0,'the$ucarrier'(sK75))
| ~ in(X0,interior(sK75,sK76)) ),
inference(resolution,[status(thm)],[c81,d7]) ).
cnf(d9,plain,
( 'point$uneighbourhood'(sK76,sK75,X0)
| ~ 'top$ustr'(sK75)
| ~ element(X0,'the$ucarrier'(sK75))
| ~ in(X0,interior(sK75,sK76)) ),
inference(resolution,[status(thm)],[c82,d8]) ).
cnf(d10,plain,
( 'point$uneighbourhood'(sK76,sK75,X0)
| ~ element(X0,'the$ucarrier'(sK75))
| ~ in(X0,interior(sK75,sK76)) ),
inference(resolution,[status(thm)],[c83,d9]) ).
cnf(d11,plain,
( 'point$uneighbourhood'(sK76,sK75,X0)
| ~ element(X0,'the$ucarrier'(sK75))
| ~ in(X0,sK76) ),
inference(demodulation,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( ~ in(X0,sK76)
| 'point$uneighbourhood'(sK76,sK75,X0)
| ~ in(X0,sK76) ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
~ in(sK77,sK76),
inference(resolution,[status(thm)],[d12,c88]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[c87,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 09:15:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.36/2.79 % SZS status Theorem for theBenchmark.p
% 14.36/2.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------