%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU311+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 : n002.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 08:41:38 AM UTC 2026
% Result : Theorem 22.73s 13.43s
% Output : CNFRefutation 22.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 128 ( 52 ~; 52 |; 10 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 1 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_subset_1,axiom,
! [X0] : ~ empty(powerset(X0)) ).
fof(s1_xboole_0__e2_37_1_1__pre_topc__1,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset('the$ucarrier'(X0))))
& 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in('set$udifference'('cast$uas$ucarrier$usubset'(X0),X3),X1)
& in(X3,powerset('the$ucarrier'(X0))) ) ) ) ).
fof(d2_subset_1,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ) ).
fof(l71_subset_1,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ) ).
fof(s3_subset_1__e2_37_1_1__pre_topc,conjecture,
! [X0,X1] :
( ( element(X1,powerset(powerset('the$ucarrier'(X0))))
& 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset('the$ucarrier'(X0)))
=> ( in(X3,X2)
<=> in('set$udifference'('cast$uas$ucarrier$usubset'(X0),X3),X1) ) )
& element(X2,powerset(powerset('the$ucarrier'(X0)))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(powerset('the$ucarrier'(X0))))
& 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset('the$ucarrier'(X0)))
=> ( in(X3,X2)
<=> in('set$udifference'('cast$uas$ucarrier$usubset'(X0),X3),X1) ) )
& element(X2,powerset(powerset('the$ucarrier'(X0)))) ) ),
inference(negate_conjecture,[status(cth)],[s3_subset_1__e2_37_1_1__pre_topc]) ).
cnf(c74,plain,
~ empty(powerset(X0)),
inference(clausification,[status(esa)],[fc1_subset_1]) ).
cnf(c75,plain,
( ~ 'topological$uspace'(X0)
| ~ in(X2,sK54(X0,X1))
| in(X2,powerset('the$ucarrier'(X0)))
| ~ element(X1,powerset(powerset('the$ucarrier'(X0))))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[s1_xboole_0__e2_37_1_1__pre_topc__1]) ).
cnf(c76,plain,
( in('set$udifference'('cast$uas$ucarrier$usubset'(X0),X2),X1)
| ~ 'topological$uspace'(X0)
| ~ in(X2,sK54(X0,X1))
| ~ element(X1,powerset(powerset('the$ucarrier'(X0))))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[s1_xboole_0__e2_37_1_1__pre_topc__1]) ).
cnf(c77,plain,
( ~ in(X1,powerset('the$ucarrier'(X0)))
| ~ 'topological$uspace'(X0)
| ~ in('set$udifference'('cast$uas$ucarrier$usubset'(X0),X1),X2)
| ~ element(X2,powerset(powerset('the$ucarrier'(X0))))
| in(X1,sK54(X0,X2))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[s1_xboole_0__e2_37_1_1__pre_topc__1]) ).
cnf(c78,plain,
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(clausification,[status(esa)],[d2_subset_1]) ).
cnf(c84,plain,
( element(X0,powerset(X1))
| in(sK62(X0,X1),X0) ),
inference(clausification,[status(esa)],[l71_subset_1]) ).
cnf(c85,plain,
( element(X0,powerset(X1))
| ~ in(sK62(X0,X1),X1) ),
inference(clausification,[status(esa)],[l71_subset_1]) ).
cnf(c91,plain,
'topological$uspace'(sK70),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c92,plain,
'top$ustr'(sK70),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c93,plain,
element(sK71,powerset(powerset('the$ucarrier'(sK70)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c94,plain,
( element(sK73(X0),powerset('the$ucarrier'(sK70)))
| ~ element(X0,powerset(powerset('the$ucarrier'(sK70)))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c96,plain,
( in('set$udifference'('cast$uas$ucarrier$usubset'(sK70),sK73(X0)),sK71)
| in(sK73(X0),X0)
| ~ element(X0,powerset(powerset('the$ucarrier'(sK70)))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c97,plain,
( ~ in(sK73(X0),X0)
| ~ in('set$udifference'('cast$uas$ucarrier$usubset'(sK70),sK73(X0)),sK71)
| ~ element(X0,powerset(powerset('the$ucarrier'(sK70)))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( in('set$udifference'('cast$uas$ucarrier$usubset'(sK70),X0),sK71)
| ~ in(X0,sK54(sK70,sK71))
| ~ 'top$ustr'(sK70)
| ~ 'topological$uspace'(sK70) ),
inference(resolution,[status(thm)],[c76,c93]) ).
cnf(d1,plain,
( in('set$udifference'('cast$uas$ucarrier$usubset'(sK70),X0),sK71)
| ~ in(X0,sK54(sK70,sK71))
| ~ 'top$ustr'(sK70) ),
inference(resolution,[status(thm)],[c91,d0]) ).
cnf(d2,plain,
( in('set$udifference'('cast$uas$ucarrier$usubset'(sK70),X0),sK71)
| ~ in(X0,sK54(sK70,sK71)) ),
inference(resolution,[status(thm)],[c92,d1]) ).
cnf(d3,plain,
( ~ in(sK73(X0),X0)
| ~ element(X0,powerset(powerset('the$ucarrier'(sK70))))
| ~ in(sK73(X0),sK54(sK70,sK71)) ),
inference(resolution,[status(thm)],[d2,c97]) ).
cnf(d4,plain,
( ~ in(X0,sK54(sK70,sK71))
| in(X0,powerset('the$ucarrier'(sK70)))
| ~ 'top$ustr'(sK70)
| ~ 'topological$uspace'(sK70) ),
inference(resolution,[status(thm)],[c75,c93]) ).
cnf(d5,plain,
( ~ in(X0,sK54(sK70,sK71))
| in(X0,powerset('the$ucarrier'(sK70)))
| ~ 'top$ustr'(sK70) ),
inference(resolution,[status(thm)],[c91,d4]) ).
cnf(d6,plain,
( ~ in(X0,sK54(sK70,sK71))
| in(X0,powerset('the$ucarrier'(sK70))) ),
inference(resolution,[status(thm)],[c92,d5]) ).
cnf(d7,plain,
( element(sK54(sK70,sK71),powerset(X0))
| in(sK62(sK54(sK70,sK71),X0),powerset('the$ucarrier'(sK70))) ),
inference(resolution,[status(thm)],[d6,c84]) ).
cnf(d8,plain,
( element(sK54(sK70,sK71),powerset(powerset('the$ucarrier'(sK70))))
| element(sK54(sK70,sK71),powerset(powerset('the$ucarrier'(sK70)))) ),
inference(resolution,[status(thm)],[d7,c85]) ).
cnf(d9,plain,
( in(sK73(sK54(sK70,sK71)),sK54(sK70,sK71))
| in('set$udifference'('cast$uas$ucarrier$usubset'(sK70),sK73(sK54(sK70,sK71))),sK71) ),
inference(resolution,[status(thm)],[d8,c96]) ).
cnf(d10,plain,
( in(sK73(sK54(sK70,sK71)),sK54(sK70,sK71))
| ~ in(sK73(sK54(sK70,sK71)),powerset('the$ucarrier'(sK70)))
| ~ 'top$ustr'(sK70)
| ~ 'topological$uspace'(sK70)
| ~ element(sK71,powerset(powerset('the$ucarrier'(sK70))))
| in(sK73(sK54(sK70,sK71)),sK54(sK70,sK71)) ),
inference(resolution,[status(thm)],[d9,c77]) ).
cnf(d11,plain,
( in(sK73(sK54(sK70,sK71)),sK54(sK70,sK71))
| ~ in(sK73(sK54(sK70,sK71)),powerset('the$ucarrier'(sK70)))
| ~ 'top$ustr'(sK70)
| ~ element(sK71,powerset(powerset('the$ucarrier'(sK70)))) ),
inference(resolution,[status(thm)],[c91,d10]) ).
cnf(d12,plain,
( in(sK73(sK54(sK70,sK71)),sK54(sK70,sK71))
| ~ in(sK73(sK54(sK70,sK71)),powerset('the$ucarrier'(sK70)))
| ~ element(sK71,powerset(powerset('the$ucarrier'(sK70)))) ),
inference(resolution,[status(thm)],[c92,d11]) ).
cnf(d13,plain,
( in(sK73(sK54(sK70,sK71)),sK54(sK70,sK71))
| ~ in(sK73(sK54(sK70,sK71)),powerset('the$ucarrier'(sK70))) ),
inference(resolution,[status(thm)],[c93,d12]) ).
cnf(d14,plain,
element(sK73(sK54(sK70,sK71)),powerset('the$ucarrier'(sK70))),
inference(resolution,[status(thm)],[d8,c94]) ).
cnf(d15,plain,
( in(sK73(sK54(sK70,sK71)),powerset('the$ucarrier'(sK70)))
| empty(powerset('the$ucarrier'(sK70))) ),
inference(resolution,[status(thm)],[d14,c78]) ).
cnf(d16,plain,
in(sK73(sK54(sK70,sK71)),powerset('the$ucarrier'(sK70))),
inference(resolution,[status(thm)],[c74,d15]) ).
cnf(d17,plain,
in(sK73(sK54(sK70,sK71)),sK54(sK70,sK71)),
inference(resolution,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
( ~ in(sK73(sK54(sK70,sK71)),sK54(sK70,sK71))
| ~ element(sK54(sK70,sK71),powerset(powerset('the$ucarrier'(sK70)))) ),
inference(resolution,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
~ in(sK73(sK54(sK70,sK71)),sK54(sK70,sK71)),
inference(resolution,[status(thm)],[d8,d18]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d17,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU311+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/10.65 % Computer : n002.cluster.edu
% 0.17/10.65 % Model : x86_64 x86_64
% 0.17/10.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.65 % Memory : 8046.5625MB
% 0.17/10.65 % OS : Linux 6.8.0-71-generic
% 0.17/10.65 % CPULimit : 300
% 0.17/10.65 % WCLimit : 300
% 0.17/10.65 % DateTime : Sat Sep 26 09:12:46 UTC 2026
% 0.17/10.65 % CPUTime :
% 0.17/10.65 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.73/13.43 % SZS status Theorem for theBenchmark.p
% 22.73/13.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------