%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET510-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 08:32:42 AM UTC 2026
% Result : Unsatisfiable 33.10s 13.89s
% Output : CNFRefutation 33.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 50 ( 14 unt; 22 nHn; 30 RR)
% Number of literals : 107 ( 44 equ; 39 neg)
% Maximal clause size : 5 ( 2 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 : 85 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_to_singleton_is_null_class_1,negated_conjecture,
singleton('universal$uclass') != 'null$uclass' ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
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$uclass') ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(unordered_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection3,axiom,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ) ).
cnf(restriction1,axiom,
intersection(X0,'cross$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,
singleton('universal$uclass') != 'null$uclass',
inference(clausification,[status(esa)],[prove_corollary_to_singleton_is_null_class_1]) ).
cnf(c1,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
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$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c7,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c12,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c21,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c23,plain,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c28,plain,
intersection(X0,'cross$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,
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c66,c1]) ).
cnf(d1,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d2,plain,
( singleton(X0) = 'null$uclass'
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[d1,c66]) ).
cnf(d3,plain,
( singleton(X0) = 'null$uclass'
| ~ subclass(singleton(X0),X1)
| singleton(X0) = 'null$uclass'
| member(X0,X1) ),
inference(superposition,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( member(X0,'universal$uclass')
| singleton(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[d2,c66]) ).
cnf(d6,plain,
( X0 = 'null$uclass'
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| member(X1,'null$uclass') ),
inference(superposition,[status(thm)],[c67,c23]) ).
cnf(d7,plain,
( singleton(X0) = 'null$uclass'
| member(X1,'null$uclass')
| ~ member(X1,singleton(X0))
| singleton(X0) = 'null$uclass'
| ~ member(X1,X0) ),
inference(superposition,[status(thm)],[d2,d6]) ).
cnf(d8,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c21,c2]) ).
cnf(d9,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
subclass(restrict(X0,X1,X2),X0),
inference(superposition,[status(thm)],[c28,d9]) ).
cnf(d11,plain,
( X0 = 'null$uclass'
| subclass('null$uclass',X0) ),
inference(superposition,[status(thm)],[c67,d9]) ).
cnf(d12,plain,
( ~ subclass(X0,'null$uclass')
| X0 = 'null$uclass'
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d11,c7]) ).
cnf(d13,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d13,c30]) ).
cnf(d15,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d15,c66]) ).
cnf(d17,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d15,d16]) ).
cnf(d18,plain,
( ~ member(X1,singleton(X0))
| ~ member(X1,X0)
| singleton(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d17,d7]) ).
cnf(d19,plain,
( singleton(X0) = 'null$uclass'
| ~ member(X0,X0)
| singleton(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
( singleton('universal$uclass') = 'null$uclass'
| singleton('universal$uclass') = 'null$uclass' ),
inference(resolution,[status(thm)],[d19,d4]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[c0,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET510-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n001.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sat Sep 26 07:56:48 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.10/13.89 % SZS status Unsatisfiable for theBenchmark.p
% 33.10/13.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------