%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET138-6 : 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 : n001.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 08:32:09 AM UTC 2026
% Result : Unsatisfiable 17.05s 18.56s
% Output : CNFRefutation 17.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 14 unt; 5 nHn; 14 RR)
% Number of literals : 45 ( 6 equ; 19 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 : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_of_set_builder,axiom,
union(singleton(X0),X1) = 'set$ubuilder'(X0,X1) ).
cnf(prove_member_of_triple_kludge2_1,negated_conjecture,
member(u,'universal$uclass') ).
cnf(prove_member_of_triple_kludge2_4,negated_conjecture,
~ member(u,'set$ubuilder'(u,'set$ubuilder'(v,'set$ubuilder'(w,'null$uclass')))) ).
cnf(unordered_pair3,axiom,
( member(X0,'unordered$upair'(X1,X0))
| ~ member(X0,'universal$uclass') ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(complement2,axiom,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(union,axiom,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1) ).
cnf(c0,plain,
union(singleton(X0),X1) = 'set$ubuilder'(X0,X1),
inference(clausification,[status(esa)],[definition_of_set_builder]) ).
cnf(c1,plain,
member(u,'universal$uclass'),
inference(clausification,[status(esa)],[prove_member_of_triple_kludge2_1]) ).
cnf(c4,plain,
~ member(u,'set$ubuilder'(u,'set$ubuilder'(v,'set$ubuilder'(w,'null$uclass')))),
inference(clausification,[status(esa)],[prove_member_of_triple_kludge2_4]) ).
cnf(c14,plain,
( member(X0,'unordered$upair'(X1,X0))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair3]) ).
cnf(c16,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c25,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c28,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c29,plain,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c30,plain,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(clausification,[status(esa)],[union]) ).
cnf(d0,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c16,c14]) ).
cnf(d1,plain,
( ~ member(X2,'universal$uclass')
| member(X2,intersection(complement(X0),complement(X1)))
| member(X2,union(X0,X1)) ),
inference(superposition,[status(thm)],[c30,c29]) ).
cnf(d2,plain,
( member(X0,complement(X1))
| ~ member(X0,'universal$uclass')
| member(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[d1,c25]) ).
cnf(d3,plain,
( member(X2,complement(singleton(X0)))
| ~ member(X2,'universal$uclass')
| member(X2,'set$ubuilder'(X0,X1)) ),
inference(superposition,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
( member(u,complement(singleton(u)))
| ~ member(u,'universal$uclass') ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
member(u,complement(singleton(u))),
inference(resolution,[status(thm)],[c1,d4]) ).
cnf(d6,plain,
~ member(u,singleton(u)),
inference(resolution,[status(thm)],[d5,c28]) ).
cnf(d7,plain,
~ member(u,'universal$uclass'),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c1,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET138-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 07:18:13 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.05/18.56 % SZS status Unsatisfiable for theBenchmark.p
% 17.05/18.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------