%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET103-6 : 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 : 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 08:32:03 AM UTC 2026
% Result : Unsatisfiable 34.24s 4.79s
% Output : CNFRefutation 34.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 13 unt; 8 nHn; 12 RR)
% Number of literals : 41 ( 21 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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 : 30 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
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$uclass') ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(class_elements_are_sets,axiom,
subclass(X0,'universal$uclass') ).
cnf(unordered_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(ordered_pair,axiom,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
'unordered$upair'(singleton(x),'unordered$upair'(x,'null$uclass')) != 'ordered$upair'(x,y),
inference(clausification,[status(esa)],[prove_property_1_of_ordered_pair_1]) ).
cnf(c1,plain,
~ member(y,'universal$uclass'),
inference(clausification,[status(esa)],[prove_property_1_of_ordered_pair_2]) ).
cnf(c2,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c5,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c9,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c13,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c14,plain,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1),
inference(clausification,[status(esa)],[ordered_pair]) ).
cnf(c67,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(d0,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c2,c5]) ).
cnf(d1,plain,
( member(regular(X0),'universal$uclass')
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c67,d0]) ).
cnf(d2,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c13,c9]) ).
cnf(d3,plain,
( singleton(X0) = 'null$uclass'
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[d2,c67]) ).
cnf(d4,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
singleton(y) = 'null$uclass',
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,'null$uclass')) = 'ordered$upair'(X0,y),
inference(superposition,[status(thm)],[d5,c14]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET103-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.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
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 07:08:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.24/4.79 % SZS status Unsatisfiable for theBenchmark.p
% 34.24/4.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------