%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 08:31:57 AM UTC 2026
% Result : Theorem 18.30s 4.78s
% Output : CNFRefutation 18.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 33 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 25 ( 8 ~; 10 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 7 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [X0,X1,X2] :
( member(X0,'unordered$upair'(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,'universal$uclass') ) ) ).
fof(singleton_set_defn,axiom,
! [X0] : singleton(X0) = 'unordered$upair'(X0,X0) ).
fof(regularity,axiom,
! [X0] :
( X0 != 'null$uclass'
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,'universal$uclass') ) ) ).
fof(singleton_is_null_class,conjecture,
! [X0] :
( ~ member(X0,'universal$uclass')
=> singleton(X0) = 'null$uclass' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ~ member(X0,'universal$uclass')
=> singleton(X0) = 'null$uclass' ),
inference(negate_conjecture,[status(cth)],[singleton_is_null_class]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_defn]) ).
cnf(c12,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set_defn]) ).
cnf(c83,plain,
( member(sK85(X0),'universal$uclass')
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity]) ).
cnf(c84,plain,
( member(sK85(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity]) ).
cnf(c89,plain,
~ member(sK90,'universal$uclass'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
singleton(sK90) != 'null$uclass',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d1,plain,
( singleton(X0) = 'null$uclass'
| sK85(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[d0,c84]) ).
cnf(d2,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(superposition,[status(thm)],[d1,c83]) ).
cnf(d3,plain,
singleton(sK90) = 'null$uclass',
inference(resolution,[status(thm)],[d2,c89]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c90,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n018.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sat Sep 26 07:06:21 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.30/4.78 % SZS status Theorem for theBenchmark.p
% 18.30/4.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------