%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET103-7 : 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 : n008.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 08:32:03 AM UTC 2026
% Result : Unsatisfiable 50.07s 10.34s
% Output : CNFRefutation 50.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 21 unt; 2 nHn; 14 RR)
% Number of literals : 29 ( 18 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(null_class_is_a_set,axiom,
member('null$uclass','universal$uclass') ).
cnf(commutativity_of_unordered_pair,axiom,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0) ).
cnf(singletons_are_sets,axiom,
member(singleton(X0),'universal$uclass') ).
cnf(singleton_is_null_class,axiom,
( singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ) ).
cnf(member_of_singleton_is_unique,axiom,
( 'member$uof'(singleton(X0)) = X0
| ~ member(X0,'universal$uclass') ) ).
cnf(prove_property_1_of_ordered_pair_1,negated_conjecture,
'unordered$upair'(singleton(x),'unordered$upair'(x,'null$uclass')) != 'ordered$upair'(x,y) ).
cnf(prove_property_1_of_ordered_pair_2,negated_conjecture,
~ member(y,'universal$uclass') ).
cnf(ordered_pair,axiom,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1) ).
cnf(c15,plain,
member('null$uclass','universal$uclass'),
inference(clausification,[status(esa)],[null_class_is_a_set]) ).
cnf(c16,plain,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_unordered_pair]) ).
cnf(c28,plain,
member(singleton(X0),'universal$uclass'),
inference(clausification,[status(esa)],[singletons_are_sets]) ).
cnf(c34,plain,
( singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[singleton_is_null_class]) ).
cnf(c42,plain,
( 'member$uof'(singleton(X0)) = X0
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[member_of_singleton_is_unique]) ).
cnf(c56,plain,
'ordered$upair'(x,y) != 'unordered$upair'(singleton(x),'unordered$upair'(x,'null$uclass')),
inference(clausification,[status(esa)],[prove_property_1_of_ordered_pair_1]) ).
cnf(c57,plain,
~ member(y,'universal$uclass'),
inference(clausification,[status(esa)],[prove_property_1_of_ordered_pair_2]) ).
cnf(c70,plain,
'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))),
inference(clausification,[status(esa)],[ordered_pair]) ).
cnf(d0,plain,
'ordered$upair'(x,y) != 'unordered$upair'(singleton(x),'unordered$upair'('null$uclass',x)),
inference(demodulation,[status(thm)],[c56,c16]) ).
cnf(d1,plain,
'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(singleton(X1),X0)),
inference(superposition,[status(thm)],[c16,c70]) ).
cnf(d2,plain,
'member$uof'(singleton('null$uclass')) = 'null$uclass',
inference(resolution,[status(thm)],[c42,c15]) ).
cnf(d3,plain,
'member$uof'(singleton(singleton(X0))) = singleton(X0),
inference(resolution,[status(thm)],[c42,c28]) ).
cnf(d4,plain,
singleton(y) = 'null$uclass',
inference(resolution,[status(thm)],[c34,c57]) ).
cnf(d5,plain,
'member$uof'(singleton('null$uclass')) = singleton(y),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'null$uclass' = singleton(y),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
'ordered$upair'(X0,y) = 'unordered$upair'(singleton(X0),'unordered$upair'('null$uclass',X0)),
inference(superposition,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET103-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 07:08:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.07/10.34 % SZS status Unsatisfiable for theBenchmark.p
% 50.07/10.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------