%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM078-1 : 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 08:10:44 AM UTC 2026
% Result : Unsatisfiable 55.60s 21.36s
% Output : CNFRefutation 55.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of clauses : 63 ( 17 unt; 20 nHn; 39 RR)
% Number of literals : 125 ( 40 equ; 50 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 : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 96 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_2_to_well_ordering_property7_3,negated_conjecture,
member(u,intersection(u,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$uclass') ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(unordered_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(unordered_pair2,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection3,axiom,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(restriction1,axiom,
intersection(X0,'cross$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(c2,plain,
member(u,intersection(u,y)),
inference(clausification,[status(esa)],[prove_corollary_2_to_well_ordering_property7_3]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(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$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c9,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c10,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
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,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c23,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c25,plain,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c26,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c30,plain,
intersection(X0,'cross$uproduct'(X1,X2)) = restrict(X0,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(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$uclass') ),
inference(resolution,[status(thm)],[c3,c6]) ).
cnf(d1,plain,
member(u,'universal$uclass'),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c14,c11]) ).
cnf(d3,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c14,c10]) ).
cnf(d4,plain,
( singleton(X0) = 'null$uclass'
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[d3,c68]) ).
cnf(d5,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[d4,c68]) ).
cnf(d6,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| intersection(singleton(X0),X0) = 'null$uclass' ),
inference(superposition,[status(thm)],[d4,c69]) ).
cnf(d7,plain,
( singleton(X0) = 'null$uclass'
| ~ member(X1,X0)
| ~ member(X1,singleton(X0))
| member(X1,'null$uclass') ),
inference(superposition,[status(thm)],[d6,c25]) ).
cnf(d8,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),'universal$uclass') ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d9,plain,
( member(regular(X0),'universal$uclass')
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c68,d0]) ).
cnf(d10,plain,
( complement(X0) = 'null$uclass'
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[c26,c68]) ).
cnf(d11,plain,
( complement('universal$uclass') = 'null$uclass'
| complement('universal$uclass') = 'null$uclass' ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( ~ member(X0,'universal$uclass')
| ~ member(X0,'null$uclass') ),
inference(superposition,[status(thm)],[d11,c26]) ).
cnf(d13,plain,
( subclass('null$uclass',X0)
| ~ member('not$usubclass$uelement'('null$uclass',X0),'universal$uclass') ),
inference(resolution,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
( subclass('null$uclass',X0)
| subclass('null$uclass',X0) ),
inference(resolution,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
( ~ subclass(X0,'null$uclass')
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d14,c9]) ).
cnf(d16,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c23,c4]) ).
cnf(d17,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
intersection('null$uclass',X0) = 'null$uclass',
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
'null$uclass' = restrict('null$uclass',X0,X1),
inference(superposition,[status(thm)],[d18,c30]) ).
cnf(d20,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d19,c32]) ).
cnf(d21,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(equality_resolution,[status(thm)],[d20]) ).
cnf(d22,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d21,c68]) ).
cnf(d23,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d21,d22]) ).
cnf(d24,plain,
( ~ member(X1,singleton(X0))
| ~ member(X1,X0)
| singleton(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d23,d7]) ).
cnf(d25,plain,
( singleton(X0) = 'null$uclass'
| ~ member(X0,X0)
| singleton(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d24,d5]) ).
cnf(d26,plain,
( ~ member(X0,X0)
| ~ member(X0,'universal$uclass')
| member(X0,'null$uclass') ),
inference(superposition,[status(thm)],[d25,d2]) ).
cnf(d27,plain,
( ~ member(X0,'universal$uclass')
| ~ member(X0,X0) ),
inference(resolution,[status(thm)],[d23,d26]) ).
cnf(d28,plain,
~ member(u,u),
inference(resolution,[status(thm)],[d27,d1]) ).
cnf(d29,plain,
member(u,u),
inference(resolution,[status(thm)],[c23,c2]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d29,d28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM078-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.38 % Computer : n007.cluster.edu
% 0.07/0.38 % Model : x86_64 x86_64
% 0.07/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.38 % Memory : 8046.5625MB
% 0.07/0.38 % OS : Linux 6.8.0-71-generic
% 0.07/0.38 % CPULimit : 300
% 0.07/0.38 % WCLimit : 300
% 0.07/0.38 % DateTime : Sat Sep 26 01:57:54 UTC 2026
% 0.07/0.38 % CPUTime :
% 0.07/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.60/21.36 % SZS status Unsatisfiable for theBenchmark.p
% 55.60/21.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------