%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET071-6 : 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 : n009.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 08:31:53 AM UTC 2026
% Result : Unsatisfiable 110.09s 30.30s
% Output : CNFRefutation 110.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 24
% Syntax : Number of clauses : 103 ( 31 unt; 31 nHn; 67 RR)
% Number of literals : 204 ( 63 equ; 79 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 154 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_null_unordered_pair_1,negated_conjecture,
'unordered$upair'(x,y) != 'null$uclass' ).
cnf(prove_null_unordered_pair_2,negated_conjecture,
~ member(x,'universal$uclass') ).
cnf(prove_null_unordered_pair_3,negated_conjecture,
~ member(y,'universal$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(unordered_pair2,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(ordered_pair,axiom,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1) ).
cnf(cartesian_product2,axiom,
( member(X1,X3)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(cartesian_product3,axiom,
( member('ordered$upair'(X0,X2),'cross$uproduct'(X1,X3))
| ~ member(X2,X3)
| ~ member(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$uclass' ) ).
cnf(inductive1,axiom,
( member('null$uclass',X0)
| ~ inductive(X0) ) ).
cnf(omega_is_inductive1,axiom,
inductive(omega) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(regularity2,axiom,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
'unordered$upair'(x,y) != 'null$uclass',
inference(clausification,[status(esa)],[prove_null_unordered_pair_1]) ).
cnf(c1,plain,
~ member(x,'universal$uclass'),
inference(clausification,[status(esa)],[prove_null_unordered_pair_2]) ).
cnf(c2,plain,
~ member(y,'universal$uclass'),
inference(clausification,[status(esa)],[prove_null_unordered_pair_3]) ).
cnf(c3,plain,
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c4,plain,
( subclass(X0,X1)
| member('not$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(c10,plain,
( X2 = X1
| ~ member(X1,'unordered$upair'(X0,X2))
| X0 = X1 ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c11,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c14,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c15,plain,
'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))),
inference(clausification,[status(esa)],[ordered_pair]) ).
cnf(c17,plain,
( member(X1,X3)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[cartesian_product2]) ).
cnf(c18,plain,
( member('ordered$upair'(X2,X0),'cross$uproduct'(X3,X1))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[cartesian_product3]) ).
cnf(c23,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c25,plain,
( member(X0,intersection(X2,X1))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c26,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c27,plain,
( member(X0,X1)
| ~ member(X0,'universal$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(c49,plain,
( member('null$uclass',X0)
| ~ inductive(X0) ),
inference(clausification,[status(esa)],[inductive1]) ).
cnf(c52,plain,
inductive(omega),
inference(clausification,[status(esa)],[omega_is_inductive1]) ).
cnf(c68,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(c69,plain,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity2]) ).
cnf(d0,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c3,c6]) ).
cnf(d1,plain,
( ~ inductive(X0)
| member('null$uclass','universal$uclass') ),
inference(resolution,[status(thm)],[d0,c49]) ).
cnf(d2,plain,
member('null$uclass','universal$uclass'),
inference(resolution,[status(thm)],[d1,c52]) ).
cnf(d3,plain,
( member(regular(X0),'universal$uclass')
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c68,d0]) ).
cnf(d4,plain,
( X0 = X1
| X0 = X1
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c14,c10]) ).
cnf(d5,plain,
( singleton(X0) = 'null$uclass'
| X0 = regular(singleton(X0)) ),
inference(resolution,[status(thm)],[d4,c68]) ).
cnf(d6,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
singleton(x) = 'null$uclass',
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
'ordered$upair'(singleton(X0),X0) = 'unordered$upair'(singleton(singleton(X0)),singleton(singleton(X0))),
inference(superposition,[status(thm)],[c14,c15]) ).
cnf(d9,plain,
'ordered$upair'(singleton(X0),X0) = singleton(singleton(singleton(X0))),
inference(demodulation,[status(thm)],[d8,c14]) ).
cnf(d10,plain,
'ordered$upair'('null$uclass',x) = singleton(singleton(singleton(x))),
inference(superposition,[status(thm)],[d7,d9]) ).
cnf(d11,plain,
'ordered$upair'('null$uclass',x) = singleton(singleton('null$uclass')),
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( ~ member('null$uclass',X0)
| ~ member(x,X1)
| member(singleton(singleton('null$uclass')),'cross$uproduct'(X0,X1)) ),
inference(superposition,[status(thm)],[d11,c18]) ).
cnf(d13,plain,
( member(X0,X2)
| ~ member(singleton(singleton(singleton(X0))),'cross$uproduct'(X1,X2)) ),
inference(superposition,[status(thm)],[d9,c17]) ).
cnf(d14,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[d5,c68]) ).
cnf(d15,plain,
( X0 = 'null$uclass'
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| member(X1,'null$uclass') ),
inference(superposition,[status(thm)],[c69,c25]) ).
cnf(d16,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),'universal$uclass') ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d17,plain,
( complement(X0) = 'null$uclass'
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[c26,c68]) ).
cnf(d18,plain,
( complement('universal$uclass') = 'null$uclass'
| complement('universal$uclass') = 'null$uclass' ),
inference(resolution,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
( ~ member(X0,'universal$uclass')
| ~ member(X0,'null$uclass') ),
inference(superposition,[status(thm)],[d18,c26]) ).
cnf(d20,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),'null$uclass') ),
inference(resolution,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
( subclass('null$uclass',X0)
| subclass('null$uclass',X0) ),
inference(resolution,[status(thm)],[d20,c4]) ).
cnf(d22,plain,
( ~ subclass(X0,'null$uclass')
| 'null$uclass' = X0 ),
inference(resolution,[status(thm)],[d21,c9]) ).
cnf(d23,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c23,c4]) ).
cnf(d24,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d23,c5]) ).
cnf(d25,plain,
'null$uclass' = intersection('null$uclass',X0),
inference(resolution,[status(thm)],[d24,d22]) ).
cnf(d26,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(superposition,[status(thm)],[d25,c30]) ).
cnf(d27,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d26,c32]) ).
cnf(d28,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(equality_resolution,[status(thm)],[d27]) ).
cnf(d29,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d28,c68]) ).
cnf(d30,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d28,d29]) ).
cnf(d31,plain,
( ~ member(X1,regular(X0))
| ~ member(X1,X0)
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d30,d15]) ).
cnf(d32,plain,
( singleton(X0) = 'null$uclass'
| ~ member(X1,singleton(X0))
| singleton(X0) = 'null$uclass'
| ~ member(X1,X0) ),
inference(superposition,[status(thm)],[d5,d31]) ).
cnf(d33,plain,
( singleton(X0) = 'null$uclass'
| ~ member(X0,X0)
| singleton(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d32,d14]) ).
cnf(d34,plain,
( singleton('universal$uclass') = 'null$uclass'
| singleton('universal$uclass') = 'null$uclass' ),
inference(resolution,[status(thm)],[d33,d6]) ).
cnf(d35,plain,
( member('universal$uclass',X1)
| ~ member(singleton(singleton('null$uclass')),'cross$uproduct'(X0,X1)) ),
inference(superposition,[status(thm)],[d34,d13]) ).
cnf(d36,plain,
( ~ member('null$uclass',X1)
| ~ member(x,X0)
| member('universal$uclass',X0) ),
inference(resolution,[status(thm)],[d35,d12]) ).
cnf(d37,plain,
( member('universal$uclass',X0)
| ~ member(x,X0) ),
inference(resolution,[status(thm)],[d36,d2]) ).
cnf(d38,plain,
( subclass(X0,complement(X1))
| ~ member('not$usubclass$uelement'(X0,complement(X1)),'universal$uclass')
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[c27,c5]) ).
cnf(d39,plain,
( subclass(X0,complement(X1))
| subclass(X0,complement(X1))
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[d38,d16]) ).
cnf(d40,plain,
( ~ member('not$usubclass$uelement'(X0,complement(complement(X1))),X1)
| subclass(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[d39,c26]) ).
cnf(d41,plain,
( subclass(X0,complement(complement(X0)))
| subclass(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[d40,c4]) ).
cnf(d42,plain,
( ~ member(X0,X1)
| member(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[d41,c3]) ).
cnf(d43,plain,
( member('universal$uclass',complement(complement(X0)))
| ~ member(x,X0) ),
inference(resolution,[status(thm)],[d42,d37]) ).
cnf(d44,plain,
( member('universal$uclass','universal$uclass')
| ~ member(x,X0) ),
inference(resolution,[status(thm)],[d43,d0]) ).
cnf(d45,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c14,c11]) ).
cnf(d46,plain,
( ~ member('universal$uclass','universal$uclass')
| member('universal$uclass','null$uclass') ),
inference(superposition,[status(thm)],[d34,d45]) ).
cnf(d47,plain,
~ member('universal$uclass','universal$uclass'),
inference(resolution,[status(thm)],[d30,d46]) ).
cnf(d48,plain,
~ member(x,X0),
inference(resolution,[status(thm)],[d47,d44]) ).
cnf(d49,plain,
( X0 = regular('unordered$upair'(X0,X1))
| X1 = regular('unordered$upair'(X0,X1))
| 'unordered$upair'(X0,X1) = 'null$uclass' ),
inference(resolution,[status(thm)],[c68,c10]) ).
cnf(d50,plain,
( 'unordered$upair'(X0,X1) = 'null$uclass'
| X0 = regular('unordered$upair'(X0,X1))
| 'unordered$upair'(X0,X1) = 'null$uclass'
| member(X1,'universal$uclass') ),
inference(superposition,[status(thm)],[d49,d3]) ).
cnf(d51,plain,
( 'unordered$upair'(X0,y) = 'null$uclass'
| X0 = regular('unordered$upair'(X0,y)) ),
inference(resolution,[status(thm)],[d50,c2]) ).
cnf(d52,plain,
( 'unordered$upair'(X0,y) = 'null$uclass'
| 'unordered$upair'(X0,y) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(superposition,[status(thm)],[d51,d3]) ).
cnf(d53,plain,
'unordered$upair'(x,y) = 'null$uclass',
inference(resolution,[status(thm)],[d52,d48]) ).
cnf(d54,plain,
$false,
inference(resolution,[status(thm)],[c0,d53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET071-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n009.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 07:02:15 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 110.09/30.30 % SZS status Unsatisfiable for theBenchmark.p
% 110.09/30.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------