%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET016-6 : 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 : n018.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 08:31:35 AM UTC 2026
% Result : Unsatisfiable 32.55s 6.03s
% Output : CNFRefutation 32.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 18 unt; 8 nHn; 21 RR)
% Number of literals : 55 ( 26 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_ordered_pair_determines_components1_1,negated_conjecture,
'ordered$upair'(w,x) = 'ordered$upair'(y,z) ).
cnf(prove_ordered_pair_determines_components1_2,negated_conjecture,
member(w,'universal$uclass') ).
cnf(prove_ordered_pair_determines_components1_3,negated_conjecture,
w != y ).
cnf(unordered_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(unordered_pair2,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(unordered_pair3,axiom,
( member(X0,'unordered$upair'(X1,X0))
| ~ member(X0,'universal$uclass') ) ).
cnf(unordered_pairs_in_universal,axiom,
member('unordered$upair'(X0,X1),'universal$uclass') ).
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(c0,plain,
'ordered$upair'(w,x) = 'ordered$upair'(y,z),
inference(clausification,[status(esa)],[prove_ordered_pair_determines_components1_1]) ).
cnf(c1,plain,
member(w,'universal$uclass'),
inference(clausification,[status(esa)],[prove_ordered_pair_determines_components1_2]) ).
cnf(c2,plain,
w != y,
inference(clausification,[status(esa)],[prove_ordered_pair_determines_components1_3]) ).
cnf(c10,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c11,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c12,plain,
( member(X0,'unordered$upair'(X1,X0))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair3]) ).
cnf(c13,plain,
member('unordered$upair'(X0,X1),'universal$uclass'),
inference(clausification,[status(esa)],[unordered_pairs_in_universal]) ).
cnf(c14,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c15,plain,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1),
inference(clausification,[status(esa)],[ordered_pair]) ).
cnf(d0,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c14,c12]) ).
cnf(d1,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c14,c10]) ).
cnf(d2,plain,
( X2 = singleton(X0)
| X2 = 'unordered$upair'(X0,singleton(X1))
| ~ member(X2,'ordered$upair'(X0,X1)) ),
inference(superposition,[status(thm)],[c15,c10]) ).
cnf(d3,plain,
( ~ member(singleton(X0),'universal$uclass')
| member(singleton(X0),'ordered$upair'(X0,X1)) ),
inference(superposition,[status(thm)],[c15,c11]) ).
cnf(d4,plain,
member(singleton(X0),'universal$uclass'),
inference(superposition,[status(thm)],[c14,c13]) ).
cnf(d5,plain,
member(singleton(X0),'ordered$upair'(X0,X1)),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
member(singleton(y),'ordered$upair'(w,x)),
inference(superposition,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
( singleton(y) = singleton(w)
| singleton(y) = 'unordered$upair'(w,singleton(x)) ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( singleton(y) = singleton(w)
| ~ member(w,'universal$uclass')
| member(w,singleton(y)) ),
inference(superposition,[status(thm)],[d7,c11]) ).
cnf(d9,plain,
( member(w,singleton(y))
| singleton(y) = singleton(w) ),
inference(resolution,[status(thm)],[c1,d8]) ).
cnf(d10,plain,
( w = y
| singleton(y) = singleton(w) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
singleton(y) = singleton(w),
inference(resolution,[status(thm)],[c2,d10]) ).
cnf(d12,plain,
( X0 = y
| ~ member(X0,singleton(w)) ),
inference(superposition,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( ~ member(w,'universal$uclass')
| w = y ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
w = y,
inference(resolution,[status(thm)],[c1,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[c2,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.55 % Computer : n018.cluster.edu
% 0.11/0.55 % Model : x86_64 x86_64
% 0.11/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.55 % Memory : 8046.5625MB
% 0.11/0.55 % OS : Linux 6.8.0-71-generic
% 0.11/0.55 % CPULimit : 300
% 0.11/0.55 % WCLimit : 300
% 0.11/0.55 % DateTime : Sat Sep 26 06:53:23 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.55/6.03 % SZS status Unsatisfiable for theBenchmark.p
% 32.55/6.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------