%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET125-6 : 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 : n010.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 08:32:08 AM UTC 2026
% Result : Unsatisfiable 79.18s 37.41s
% Output : CNFRefutation 79.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 14 unt; 5 nHn; 16 RR)
% Number of literals : 47 ( 4 equ; 20 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_of_set_builder,axiom,
union(singleton(X0),X1) = 'set$ubuilder'(X0,X1) ).
cnf(prove_set_builder_alternate_defn3_1,negated_conjecture,
member(x,z) ).
cnf(prove_set_builder_alternate_defn3_2,negated_conjecture,
~ member(x,'set$ubuilder'(y,z)) ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(class_elements_are_sets,axiom,
subclass(X0,'universal$uclass') ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(complement2,axiom,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(union,axiom,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1) ).
cnf(c0,plain,
union(singleton(X0),X1) = 'set$ubuilder'(X0,X1),
inference(clausification,[status(esa)],[definition_of_set_builder]) ).
cnf(c1,plain,
member(x,z),
inference(clausification,[status(esa)],[prove_set_builder_alternate_defn3_1]) ).
cnf(c2,plain,
~ member(x,'set$ubuilder'(y,z)),
inference(clausification,[status(esa)],[prove_set_builder_alternate_defn3_2]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c6,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c24,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c26,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c27,plain,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$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(X2,'universal$uclass')
| member(X2,intersection(complement(X0),complement(X1)))
| member(X2,union(X0,X1)) ),
inference(superposition,[status(thm)],[c28,c27]) ).
cnf(d1,plain,
( member(X0,complement(X2))
| ~ member(X0,'universal$uclass')
| member(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[d0,c24]) ).
cnf(d2,plain,
( member(X2,complement(X1))
| ~ member(X2,'universal$uclass')
| member(X2,'set$ubuilder'(X0,X1)) ),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
( member(x,complement(z))
| ~ member(x,'universal$uclass') ),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c3,c6]) ).
cnf(d5,plain,
member(x,'universal$uclass'),
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
member(x,complement(z)),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
~ member(x,z),
inference(resolution,[status(thm)],[d6,c26]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c1,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET125-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/16.23 % Computer : n010.cluster.edu
% 0.10/16.23 % Model : x86_64 x86_64
% 0.10/16.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/16.23 % Memory : 8046.5625MB
% 0.10/16.23 % OS : Linux 6.8.0-71-generic
% 0.10/16.23 % CPULimit : 300
% 0.10/16.23 % WCLimit : 300
% 0.10/16.23 % DateTime : Sat Sep 26 07:12:08 UTC 2026
% 0.10/16.23 % CPUTime :
% 0.10/16.23 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 79.18/37.41 % SZS status Unsatisfiable for theBenchmark.p
% 79.18/37.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------