%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET096-7 : 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 : n011.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 08:32:01 AM UTC 2026
% Result : Unsatisfiable 18.47s 2.80s
% Output : CNFRefutation 18.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 11 unt; 4 nHn; 24 RR)
% Number of literals : 45 ( 16 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(only_member_in_singleton,axiom,
( X0 = X1
| ~ member(X0,singleton(X1)) ) ).
cnf(property_of_singletons2,axiom,
( subclass(singleton(X0),X1)
| ~ member(X0,X1) ) ).
cnf(prove_two_subsets_of_singleton_1,negated_conjecture,
subclass(x,singleton(y)) ).
cnf(prove_two_subsets_of_singleton_2,negated_conjecture,
x != 'null$uclass' ).
cnf(prove_two_subsets_of_singleton_3,negated_conjecture,
singleton(y) != x ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(c33,plain,
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(clausification,[status(esa)],[only_member_in_singleton]) ).
cnf(c47,plain,
( subclass(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[property_of_singletons2]) ).
cnf(c48,plain,
subclass(x,singleton(y)),
inference(clausification,[status(esa)],[prove_two_subsets_of_singleton_1]) ).
cnf(c49,plain,
x != 'null$uclass',
inference(clausification,[status(esa)],[prove_two_subsets_of_singleton_2]) ).
cnf(c50,plain,
singleton(y) != x,
inference(clausification,[status(esa)],[prove_two_subsets_of_singleton_3]) ).
cnf(c51,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c57,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c116,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(d0,plain,
( ~ subclass(singleton(y),x)
| singleton(y) = x ),
inference(resolution,[status(thm)],[c57,c48]) ).
cnf(d1,plain,
~ subclass(singleton(y),x),
inference(resolution,[status(thm)],[c50,d0]) ).
cnf(d2,plain,
~ member(y,x),
inference(resolution,[status(thm)],[d1,c47]) ).
cnf(d3,plain,
( ~ member(X0,x)
| member(X0,singleton(y)) ),
inference(resolution,[status(thm)],[c51,c48]) ).
cnf(d4,plain,
( X0 = y
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[d3,c33]) ).
cnf(d5,plain,
( x = 'null$uclass'
| regular(x) = y ),
inference(resolution,[status(thm)],[d4,c116]) ).
cnf(d6,plain,
regular(x) = y,
inference(resolution,[status(thm)],[c49,d5]) ).
cnf(d7,plain,
( x = 'null$uclass'
| member(y,x) ),
inference(superposition,[status(thm)],[d6,c116]) ).
cnf(d8,plain,
member(y,x),
inference(resolution,[status(thm)],[c49,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET096-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:06:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.47/2.80 % SZS status Unsatisfiable for theBenchmark.p
% 18.47/2.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------