%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET188-6 : 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 : n011.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 08:32:16 AM UTC 2026
% Result : Unsatisfiable 104.86s 22.60s
% Output : CNFRefutation 104.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of clauses : 57 ( 18 unt; 16 nHn; 38 RR)
% Number of literals : 114 ( 23 equ; 50 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 85 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_subclass_property6_1,negated_conjecture,
intersection(complement(y),x) = 'null$uclass' ).
cnf(prove_subclass_property6_2,negated_conjecture,
~ subclass(x,y) ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$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(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(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(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(c0,plain,
intersection(complement(y),x) = 'null$uclass',
inference(clausification,[status(esa)],[prove_subclass_property6_1]) ).
cnf(c1,plain,
~ subclass(x,y),
inference(clausification,[status(esa)],[prove_subclass_property6_2]) ).
cnf(c2,plain,
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c3,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c4,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c5,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c8,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c22,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c24,plain,
( member(X0,intersection(X2,X1))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c25,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c26,plain,
( member(X0,X1)
| ~ member(X0,'universal$uclass')
| member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c29,plain,
restrict(X0,X1,X2) = intersection(X0,'cross$uproduct'(X1,X2)),
inference(clausification,[status(esa)],[restriction1]) ).
cnf(c31,plain,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c67,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(d0,plain,
( member('not$usubclass$uelement'(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(d1,plain,
( ~ member(X0,x)
| ~ member(X0,complement(y))
| member(X0,'null$uclass') ),
inference(superposition,[status(thm)],[c0,c24]) ).
cnf(d2,plain,
( complement(X0) = 'null$uclass'
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[c25,c67]) ).
cnf(d3,plain,
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c67,c2]) ).
cnf(d4,plain,
( complement(X0) = 'null$uclass'
| ~ subclass(complement(X0),X0)
| complement(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
complement('universal$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( subclass(complement(X0),X1)
| ~ member('not$usubclass$uelement'(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c25,c3]) ).
cnf(d7,plain,
( subclass(complement(X0),X1)
| ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
subclass(complement('universal$uclass'),X0),
inference(resolution,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
subclass('null$uclass',X0),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( ~ subclass(X0,'null$uclass')
| 'null$uclass' = X0 ),
inference(resolution,[status(thm)],[d9,c8]) ).
cnf(d11,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c22,c3]) ).
cnf(d12,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d11,c4]) ).
cnf(d13,plain,
'null$uclass' = intersection('null$uclass',X0),
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(superposition,[status(thm)],[d13,c29]) ).
cnf(d15,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d14,c31]) ).
cnf(d16,plain,
( complement('universal$uclass') = 'null$uclass'
| ~ subclass('null$uclass','universal$uclass') ),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d17,plain,
( ~ subclass('null$uclass','universal$uclass')
| 'null$uclass' = 'null$uclass' ),
inference(demodulation,[status(thm)],[d16,d5]) ).
cnf(d18,plain,
'null$uclass' = 'null$uclass',
inference(resolution,[status(thm)],[c5,d17]) ).
cnf(d19,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(resolution,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d19,c67]) ).
cnf(d21,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d19,d20]) ).
cnf(d22,plain,
( ~ member(X0,x)
| ~ member(X0,complement(y)) ),
inference(resolution,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
( ~ member(X0,'universal$uclass')
| member(X0,y)
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[d22,c26]) ).
cnf(d24,plain,
( subclass(X0,X1)
| ~ subclass(X0,'universal$uclass')
| ~ member('not$usubclass$uelement'(X0,X1),x)
| member('not$usubclass$uelement'(X0,X1),y) ),
inference(resolution,[status(thm)],[d23,d0]) ).
cnf(d25,plain,
( ~ member('not$usubclass$uelement'(X0,X1),x)
| member('not$usubclass$uelement'(X0,X1),y)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[c5,d24]) ).
cnf(d26,plain,
( subclass(x,X0)
| member('not$usubclass$uelement'(x,X0),y)
| subclass(x,X0) ),
inference(resolution,[status(thm)],[d25,c3]) ).
cnf(d27,plain,
( subclass(x,y)
| subclass(x,y) ),
inference(resolution,[status(thm)],[d26,c4]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[c1,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET188-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:18:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 104.86/22.60 % SZS status Unsatisfiable for theBenchmark.p
% 104.86/22.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------