%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET068-7 : 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 : n012.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 15.44s 5.90s
% Output : CNFRefutation 15.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 16 unt; 12 nHn; 17 RR)
% Number of literals : 63 ( 19 equ; 19 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(null_class_is_subclass,axiom,
subclass('null$uclass',X0) ).
cnf(commutativity_of_unordered_pair,axiom,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0) ).
cnf(prove_singleton_in_unordered_pair2_1,negated_conjecture,
~ subclass(singleton(y),'unordered$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$upair'(X0,X0) = singleton(X0) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(c12,plain,
subclass('null$uclass',X0),
inference(clausification,[status(esa)],[null_class_is_subclass]) ).
cnf(c16,plain,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_unordered_pair]) ).
cnf(c17,plain,
~ subclass(singleton(y),'unordered$upair'(x,y)),
inference(clausification,[status(esa)],[prove_singleton_in_unordered_pair2_1]) ).
cnf(c18,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c19,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c20,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c21,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c25,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c26,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c29,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c83,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(d0,plain,
~ subclass(singleton(y),'unordered$upair'(y,x)),
inference(demodulation,[status(thm)],[c17,c16]) ).
cnf(d1,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(superposition,[status(thm)],[c29,c16]) ).
cnf(d2,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[d1,c25]) ).
cnf(d3,plain,
( subclass(singleton(X0),X1)
| 'not$usubclass$uelement'(singleton(X0),X1) = X0 ),
inference(resolution,[status(thm)],[d2,c19]) ).
cnf(d4,plain,
( subclass(singleton(X0),X1)
| subclass(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[d3,c20]) ).
cnf(d5,plain,
~ member(y,'unordered$upair'(y,x)),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
~ member(y,'universal$uclass'),
inference(resolution,[status(thm)],[d5,c26]) ).
cnf(d7,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c18,c21]) ).
cnf(d8,plain,
( X0 = 'null$uclass'
| member(regular(X0),'universal$uclass') ),
inference(resolution,[status(thm)],[d7,c83]) ).
cnf(d9,plain,
( singleton(X0) = 'null$uclass'
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[d2,c83]) ).
cnf(d10,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( member(y,'universal$uclass')
| ~ subclass('null$uclass','unordered$upair'(y,x)) ),
inference(superposition,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
member(y,'universal$uclass'),
inference(resolution,[status(thm)],[c12,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET068-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/3.84 % Computer : n012.cluster.edu
% 0.03/3.84 % Model : x86_64 x86_64
% 0.03/3.84 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/3.84 % Memory : 8046.5625MB
% 0.03/3.84 % OS : Linux 6.8.0-71-generic
% 0.03/3.84 % CPULimit : 300
% 0.03/3.84 % WCLimit : 300
% 0.03/3.84 % DateTime : Sat Sep 26 07:01:56 UTC 2026
% 0.03/3.84 % CPUTime :
% 0.03/3.84 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.44/5.90 % SZS status Unsatisfiable for theBenchmark.p
% 15.44/5.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------