%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET151-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 08:32:11 AM UTC 2026
% Result : Unsatisfiable 16.27s 3.14s
% Output : CNFRefutation 16.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 52 ( 18 unt; 18 nHn; 30 RR)
% Number of literals : 97 ( 27 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 83 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_complement_of_null_class_1,negated_conjecture,
complement('null$uclass') != 'universal$uclass' ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ) ).
cnf(not_subclass_members2,axiom,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ) ).
cnf(class_elements_are_sets,axiom,
subclass(X0,'universal$uclass') ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection3,axiom,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ) ).
cnf(complement2,axiom,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(restriction1,axiom,
intersection(X0,'cross$uproduct'(X1,X2)) = restrict(X0,X1,X2) ).
cnf(domain1,axiom,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(regularity2,axiom,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
complement('null$uclass') != 'universal$uclass',
inference(clausification,[status(esa)],[prove_complement_of_null_class_1]) ).
cnf(c2,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c3,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c4,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c7,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c21,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c22,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c23,plain,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c25,plain,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c28,plain,
intersection(X0,'cross$uproduct'(X1,X2)) = restrict(X0,X1,X2),
inference(clausification,[status(esa)],[restriction1]) ).
cnf(c30,plain,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c66,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(c67,plain,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity2]) ).
cnf(d0,plain,
( ~ subclass('universal$uclass',X0)
| 'universal$uclass' = X0 ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d1,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c21,c2]) ).
cnf(d2,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
subclass(restrict(X0,X1,X2),X0),
inference(superposition,[status(thm)],[c28,d2]) ).
cnf(d4,plain,
( X0 = 'null$uclass'
| subclass('null$uclass',X0) ),
inference(superposition,[status(thm)],[c67,d2]) ).
cnf(d5,plain,
( ~ subclass(X0,'null$uclass')
| X0 = 'null$uclass'
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d6,c30]) ).
cnf(d8,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d8,c66]) ).
cnf(d10,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d8,d9]) ).
cnf(d11,plain,
( subclass(X0,complement(X1))
| ~ member('not$usubclass$uelement'(X0,complement(X1)),'universal$uclass')
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[c25,c3]) ).
cnf(d12,plain,
( subclass('universal$uclass',complement(X0))
| member('not$usubclass$uelement'('universal$uclass',complement(X0)),X0)
| subclass('universal$uclass',complement(X0)) ),
inference(resolution,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
subclass('universal$uclass',complement('null$uclass')),
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
'universal$uclass' = complement('null$uclass'),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
'universal$uclass' != 'universal$uclass',
inference(demodulation,[status(thm)],[c0,d14]) ).
cnf(d16,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c22,c2]) ).
cnf(d17,plain,
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[d16,c3]) ).
cnf(d18,plain,
( ~ subclass(X0,intersection(X1,X0))
| X0 = intersection(X1,X0) ),
inference(resolution,[status(thm)],[d17,c7]) ).
cnf(d19,plain,
( subclass(X0,intersection(X1,X2))
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X2)
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c23,c3]) ).
cnf(d20,plain,
( subclass(X0,intersection(X0,X1))
| ~ member('not$usubclass$uelement'(X0,intersection(X0,X1)),X1)
| subclass(X0,intersection(X0,X1)) ),
inference(resolution,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
( subclass(X0,intersection(X0,X0))
| subclass(X0,intersection(X0,X0)) ),
inference(resolution,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
X0 = intersection(X0,X0),
inference(resolution,[status(thm)],[d21,d18]) ).
cnf(d23,plain,
'universal$uclass' = intersection('universal$uclass','universal$uclass'),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d24,plain,
'universal$uclass' = 'universal$uclass',
inference(demodulation,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d24,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET151-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 07:13:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.27/3.14 % SZS status Unsatisfiable for theBenchmark.p
% 16.27/3.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------