%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET067-6 : 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 : n020.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 08:31:52 AM UTC 2026
% Result : Unsatisfiable 36.03s 5.06s
% Output : CNFRefutation 36.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 41 ( 12 unt; 17 nHn; 24 RR)
% Number of literals : 82 ( 22 equ; 31 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_singleton_in_unordered_pair1_1,negated_conjecture,
~ subclass(singleton(x),'unordered$upair'(x,y)) ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$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(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(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
~ subclass(singleton(x),'unordered$upair'(x,y)),
inference(clausification,[status(esa)],[prove_singleton_in_unordered_pair1_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$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c9,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c12,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c24,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c66,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(d0,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d1,plain,
( singleton(X0) = 'null$uclass'
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[d0,c66]) ).
cnf(d2,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[d1,c66]) ).
cnf(d3,plain,
( member(X0,X1)
| ~ subclass(singleton(X0),X1)
| singleton(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
( member(X0,'universal$uclass')
| singleton(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( member(x,'universal$uclass')
| ~ subclass('null$uclass','unordered$upair'(x,y)) ),
inference(superposition,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( subclass(singleton(X0),X1)
| 'not$usubclass$uelement'(singleton(X0),X1) = X0 ),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d7,plain,
( subclass(singleton(X0),X1)
| subclass(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
~ member(x,'unordered$upair'(x,y)),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
~ member(x,'universal$uclass'),
inference(resolution,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
~ subclass('null$uclass','unordered$upair'(x,y)),
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
( complement(X0) = 'null$uclass'
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[c24,c66]) ).
cnf(d12,plain,
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c66,c1]) ).
cnf(d13,plain,
( complement(X0) = 'null$uclass'
| ~ subclass(complement(X0),X0)
| complement(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
complement('universal$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d13,c4]) ).
cnf(d15,plain,
( ~ member(X0,'universal$uclass')
| ~ member(X0,'null$uclass') ),
inference(superposition,[status(thm)],[d14,c24]) ).
cnf(d16,plain,
( subclass('null$uclass',X0)
| ~ member('not$usubclass$uelement'('null$uclass',X0),'universal$uclass') ),
inference(resolution,[status(thm)],[d15,c2]) ).
cnf(d17,plain,
( member('not$usubclass$uelement'(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d18,plain,
( subclass('null$uclass',X0)
| subclass('null$uclass',X0)
| ~ subclass('null$uclass','universal$uclass') ),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
subclass('null$uclass',X0),
inference(resolution,[status(thm)],[c4,d18]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d19,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET067-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.58 % Computer : n020.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Sat Sep 26 07:03:06 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.03/5.06 % SZS status Unsatisfiable for theBenchmark.p
% 36.03/5.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------