%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET080-6 : 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 : n017.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 08:31:56 AM UTC 2026
% Result : Unsatisfiable 22.33s 3.53s
% Output : CNFRefutation 22.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 11 unt; 0 nHn; 14 RR)
% Number of literals : 31 ( 2 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_null_class_in_its_singleton_1,negated_conjecture,
~ member('null$uclass',singleton('null$uclass')) ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(class_elements_are_sets,axiom,
subclass(X0,'universal$uclass') ).
cnf(unordered_pair2,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(inductive1,axiom,
( member('null$uclass',X0)
| ~ inductive(X0) ) ).
cnf(omega_is_inductive1,axiom,
inductive(omega) ).
cnf(c0,plain,
~ member('null$uclass',singleton('null$uclass')),
inference(clausification,[status(esa)],[prove_null_class_in_its_singleton_1]) ).
cnf(c1,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c4,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c9,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c12,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c47,plain,
( member('null$uclass',X0)
| ~ inductive(X0) ),
inference(clausification,[status(esa)],[inductive1]) ).
cnf(c50,plain,
inductive(omega),
inference(clausification,[status(esa)],[omega_is_inductive1]) ).
cnf(d0,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c9]) ).
cnf(d1,plain,
~ member('null$uclass','universal$uclass'),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d3,plain,
( ~ inductive(X0)
| member('null$uclass','universal$uclass') ),
inference(resolution,[status(thm)],[d2,c47]) ).
cnf(d4,plain,
member('null$uclass','universal$uclass'),
inference(resolution,[status(thm)],[d3,c50]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET080-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45 % Computer : n017.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.45 % WCLimit : 300
% 0.21/0.45 % DateTime : Sat Sep 26 06:59:18 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.33/3.53 % SZS status Unsatisfiable for theBenchmark.p
% 22.33/3.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------