%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET189-6 : 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 : n007.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 2.29s 13.94s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of clauses : 76 ( 24 unt; 21 nHn; 51 RR)
% Number of literals : 148 ( 34 equ; 61 neg)
% Maximal clause size : 4 ( 1 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 : 111 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_to_subclass_property6_1,negated_conjecture,
intersection(complement(y),x) = 'null$uclass' ).
cnf(prove_corollary_to_subclass_property6_2,negated_conjecture,
subclass(y,x) ).
cnf(prove_corollary_to_subclass_property6_3,negated_conjecture,
x != y ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$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(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(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$uclass',
inference(clausification,[status(esa)],[prove_corollary_to_subclass_property6_1]) ).
cnf(c1,plain,
subclass(y,x),
inference(clausification,[status(esa)],[prove_corollary_to_subclass_property6_2]) ).
cnf(c2,plain,
x != y,
inference(clausification,[status(esa)],[prove_corollary_to_subclass_property6_3]) ).
cnf(c3,plain,
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c4,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c5,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c6,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c9,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c23,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c24,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c25,plain,
( member(X0,intersection(X2,X1))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c26,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c27,plain,
( member(X0,X1)
| ~ member(X0,'universal$uclass')
| member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c30,plain,
restrict(X0,X1,X2) = intersection(X0,'cross$uproduct'(X1,X2)),
inference(clausification,[status(esa)],[restriction1]) ).
cnf(c32,plain,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c68,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(d0,plain,
( ~ subclass(x,y)
| y = x ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d1,plain,
( member('not$usubclass$uelement'(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d2,plain,
( ~ member(X0,x)
| ~ member(X0,complement(y))
| member(X0,'null$uclass') ),
inference(superposition,[status(thm)],[c0,c25]) ).
cnf(d3,plain,
( complement(X0) = 'null$uclass'
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[c26,c68]) ).
cnf(d4,plain,
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c68,c3]) ).
cnf(d5,plain,
( complement(X0) = 'null$uclass'
| ~ subclass(complement(X0),X0)
| complement(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
complement('universal$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( subclass(complement(X0),X1)
| ~ member('not$usubclass$uelement'(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c26,c4]) ).
cnf(d8,plain,
( subclass(complement(X0),X1)
| ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) ),
inference(resolution,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
subclass(complement('universal$uclass'),X0),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
subclass('null$uclass',X0),
inference(demodulation,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( ~ subclass(X0,'null$uclass')
| 'null$uclass' = X0 ),
inference(resolution,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c23,c4]) ).
cnf(d13,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d12,c5]) ).
cnf(d14,plain,
'null$uclass' = intersection('null$uclass',X0),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(superposition,[status(thm)],[d14,c30]) ).
cnf(d16,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d15,c32]) ).
cnf(d17,plain,
( complement('universal$uclass') = 'null$uclass'
| ~ subclass('null$uclass','universal$uclass') ),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d18,plain,
( ~ subclass('null$uclass','universal$uclass')
| 'null$uclass' = 'null$uclass' ),
inference(demodulation,[status(thm)],[d17,d6]) ).
cnf(d19,plain,
'null$uclass' = 'null$uclass',
inference(resolution,[status(thm)],[c6,d18]) ).
cnf(d20,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(resolution,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d20,c68]) ).
cnf(d22,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d20,d21]) ).
cnf(d23,plain,
( ~ member(X0,x)
| ~ member(X0,complement(y)) ),
inference(resolution,[status(thm)],[d22,d2]) ).
cnf(d24,plain,
( ~ member(X0,'universal$uclass')
| member(X0,y)
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[d23,c27]) ).
cnf(d25,plain,
( subclass(X0,X1)
| ~ subclass(X0,'universal$uclass')
| ~ member('not$usubclass$uelement'(X0,X1),x)
| member('not$usubclass$uelement'(X0,X1),y) ),
inference(resolution,[status(thm)],[d24,d1]) ).
cnf(d26,plain,
( ~ member('not$usubclass$uelement'(X0,X1),x)
| member('not$usubclass$uelement'(X0,X1),y)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[c6,d25]) ).
cnf(d27,plain,
( subclass(x,X0)
| member('not$usubclass$uelement'(x,X0),y)
| subclass(x,X0) ),
inference(resolution,[status(thm)],[d26,c4]) ).
cnf(d28,plain,
( subclass(x,y)
| subclass(x,y) ),
inference(resolution,[status(thm)],[d27,c5]) ).
cnf(d29,plain,
y = x,
inference(resolution,[status(thm)],[d28,d0]) ).
cnf(d30,plain,
y != y,
inference(demodulation,[status(thm)],[c2,d29]) ).
cnf(d31,plain,
( ~ subclass(X0,intersection(X0,X1))
| intersection(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d13,c9]) ).
cnf(d32,plain,
( subclass(X0,intersection(X1,X2))
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X2)
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c25,c5]) ).
cnf(d33,plain,
( subclass(X0,intersection(X0,X1))
| ~ member('not$usubclass$uelement'(X0,intersection(X0,X1)),X1)
| subclass(X0,intersection(X0,X1)) ),
inference(resolution,[status(thm)],[d32,c4]) ).
cnf(d34,plain,
( subclass(X0,intersection(X0,X0))
| subclass(X0,intersection(X0,X0)) ),
inference(resolution,[status(thm)],[d33,c4]) ).
cnf(d35,plain,
intersection(X0,X0) = X0,
inference(resolution,[status(thm)],[d34,d31]) ).
cnf(d36,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c24,c4]) ).
cnf(d37,plain,
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[d36,c5]) ).
cnf(d38,plain,
( ~ subclass(X1,intersection(X0,X1))
| intersection(X0,X1) = X1 ),
inference(resolution,[status(thm)],[d37,c9]) ).
cnf(d39,plain,
( intersection(X0,X0) = X0
| ~ subclass(X0,X0) ),
inference(superposition,[status(thm)],[d35,d38]) ).
cnf(d40,plain,
( ~ subclass(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d39,d35]) ).
cnf(d41,plain,
( subclass(X0,X0)
| subclass(X0,X0) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(d42,plain,
X0 = X0,
inference(resolution,[status(thm)],[d41,d40]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d42,d30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET189-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 07:16:38 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.29/13.94 % SZS status Unsatisfiable for theBenchmark.p
% 2.29/13.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------