%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET096-6 : 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 : n015.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 08:32:01 AM UTC 2026
% Result : Unsatisfiable 14.13s 3.72s
% Output : CNFRefutation 14.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 34 ( 14 unt; 12 nHn; 27 RR)
% Number of literals : 63 ( 26 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_two_subsets_of_singleton_1,negated_conjecture,
subclass(x,singleton(y)) ).
cnf(prove_two_subsets_of_singleton_2,negated_conjecture,
x != 'null$uclass' ).
cnf(prove_two_subsets_of_singleton_3,negated_conjecture,
singleton(y) != x ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ) ).
cnf(not_subclass_members2,axiom,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ) ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(unordered_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
subclass(x,singleton(y)),
inference(clausification,[status(esa)],[prove_two_subsets_of_singleton_1]) ).
cnf(c1,plain,
x != 'null$uclass',
inference(clausification,[status(esa)],[prove_two_subsets_of_singleton_2]) ).
cnf(c2,plain,
singleton(y) != x,
inference(clausification,[status(esa)],[prove_two_subsets_of_singleton_3]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c4,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c5,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c9,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c10,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c14,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c68,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(d0,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c14,c10]) ).
cnf(d1,plain,
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c68,c3]) ).
cnf(d2,plain,
( regular(X0) = X1
| ~ subclass(X0,singleton(X1))
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( regular(x) = y
| x = 'null$uclass' ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
regular(x) = y,
inference(resolution,[status(thm)],[c1,d3]) ).
cnf(d5,plain,
( x = 'null$uclass'
| member(y,x) ),
inference(superposition,[status(thm)],[d4,c68]) ).
cnf(d6,plain,
member(y,x),
inference(resolution,[status(thm)],[c1,d5]) ).
cnf(d7,plain,
( ~ subclass(singleton(y),x)
| singleton(y) = x ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d8,plain,
~ subclass(singleton(y),x),
inference(resolution,[status(thm)],[c2,d7]) ).
cnf(d9,plain,
( subclass(singleton(X0),X1)
| 'not$usubclass$uelement'(singleton(X0),X1) = X0 ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d10,plain,
'not$usubclass$uelement'(singleton(y),x) = y,
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( subclass(singleton(y),x)
| ~ member(y,x) ),
inference(superposition,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
~ member(y,x),
inference(resolution,[status(thm)],[d8,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET096-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 07:09:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.13/3.72 % SZS status Unsatisfiable for theBenchmark.p
% 14.13/3.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------