%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET166-6 : 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 : n003.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 08:32:13 AM UTC 2026
% Result : Unsatisfiable 2.72s 14.37s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 49 ( 15 unt; 12 nHn; 33 RR)
% Number of literals : 95 ( 6 equ; 45 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 : 76 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_members_of_union1_1,negated_conjecture,
member(x,union(y,z)) ).
cnf(prove_members_of_union1_2,negated_conjecture,
~ member(x,y) ).
cnf(prove_members_of_union1_3,negated_conjecture,
~ member(x,z) ).
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$uclass') ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection3,axiom,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(complement2,axiom,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(union,axiom,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1) ).
cnf(c0,plain,
member(x,union(y,z)),
inference(clausification,[status(esa)],[prove_members_of_union1_1]) ).
cnf(c1,plain,
~ member(x,y),
inference(clausification,[status(esa)],[prove_members_of_union1_2]) ).
cnf(c2,plain,
~ member(x,z),
inference(clausification,[status(esa)],[prove_members_of_union1_3]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c4,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c5,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c6,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c9,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c23,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c25,plain,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c26,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c27,plain,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c28,plain,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(clausification,[status(esa)],[union]) ).
cnf(d0,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d1,plain,
member(x,'universal$uclass'),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( member(X0,complement(X2))
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[d0,c27]) ).
cnf(d3,plain,
( member(x,complement(X0))
| member(x,X0) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c23,c4]) ).
cnf(d5,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( ~ subclass(X0,intersection(X0,X1))
| X0 = intersection(X0,X1) ),
inference(resolution,[status(thm)],[d5,c9]) ).
cnf(d7,plain,
( subclass(X0,intersection(X1,X2))
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X2)
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c25,c5]) ).
cnf(d8,plain,
( subclass(X0,intersection(X0,X1))
| subclass(X0,intersection(X0,X1))
| ~ member('not$usubclass$uelement'(X0,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
( subclass(X0,intersection(X0,X0))
| subclass(X0,intersection(X0,X0)) ),
inference(resolution,[status(thm)],[d8,c4]) ).
cnf(d10,plain,
X0 = intersection(X0,X0),
inference(resolution,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( ~ member(X0,X1)
| member(X0,intersection(X1,X1)) ),
inference(resolution,[status(thm)],[d9,c3]) ).
cnf(d12,plain,
( member(X1,X0)
| ~ member(X1,X0) ),
inference(demodulation,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( member(x,complement(X0))
| member(x,X0) ),
inference(resolution,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
( member(x,complement(X0))
| member(x,X0) ),
inference(resolution,[status(thm)],[d12,d13]) ).
cnf(d15,plain,
( ~ member(X2,intersection(complement(X0),complement(X1)))
| ~ member(X2,union(X0,X1)) ),
inference(superposition,[status(thm)],[c28,c26]) ).
cnf(d16,plain,
( ~ member(X0,complement(X2))
| ~ member(X0,complement(X1))
| ~ member(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[d15,c25]) ).
cnf(d17,plain,
( ~ member(x,complement(y))
| ~ member(x,complement(z)) ),
inference(resolution,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
( ~ member(x,complement(z))
| ~ member(x,complement(y)) ),
inference(resolution,[status(thm)],[d12,d17]) ).
cnf(d19,plain,
( member(x,z)
| ~ member(x,complement(y)) ),
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
~ member(x,complement(y)),
inference(resolution,[status(thm)],[c2,d19]) ).
cnf(d21,plain,
member(x,y),
inference(resolution,[status(thm)],[d20,d14]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[c1,d21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET166-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n003.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 07:16:53 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.72/14.37 % SZS status Unsatisfiable for theBenchmark.p
% 2.72/14.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------