%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET097+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 : Theorem 13.74s 6.95s
% Output : CNFRefutation 13.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 9 unt; 0 def)
% Number of atoms : 103 ( 27 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 98 ( 37 ~; 46 |; 8 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 4 sgn 18 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(class_elements_are_sets,axiom,
! [X0] : subclass(X0,'universal$uclass') ).
fof(extensionality,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ) ).
fof(unordered_pair_defn,axiom,
! [X0,X1,X2] :
( member(X0,'unordered$upair'(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,'universal$uclass') ) ) ).
fof(singleton_set_defn,axiom,
! [X0] : singleton(X0) = 'unordered$upair'(X0,X0) ).
fof(intersection,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
fof(complement,axiom,
! [X0,X1] :
( member(X1,complement(X0))
<=> ( ~ member(X1,X0)
& member(X1,'universal$uclass') ) ) ).
fof(regularity,axiom,
! [X0] :
( X0 != 'null$uclass'
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,'universal$uclass') ) ) ).
fof(number_of_elements_in_class,conjecture,
! [X0] :
( ? [X2] :
( ? [X3] : member(X3,intersection(complement(singleton(X2)),X0))
& member(X2,X0) )
| ? [X1] : singleton(X1) = X0
| X0 = 'null$uclass' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ? [X2] :
( ? [X3] : member(X3,intersection(complement(singleton(X2)),X0))
& member(X2,X0) )
| ? [X1] : singleton(X1) = X0
| X0 = 'null$uclass' ),
inference(negate_conjecture,[status(cth)],[number_of_elements_in_class]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_defn]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_defn]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_defn]) ).
cnf(c3,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c6,plain,
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[extensionality]) ).
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(c26,plain,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection]) ).
cnf(c29,plain,
( member(X0,X1)
| ~ member(X0,'universal$uclass')
| member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement]) ).
cnf(c84,plain,
( member(sK85(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity]) ).
cnf(c89,plain,
sK90 != 'null$uclass',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
singleton(X0) != sK90,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c91,plain,
( ~ member(X1,intersection(complement(singleton(X0)),sK90))
| ~ member(X0,sK90) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X1,sK90)
| ~ member(X0,sK90)
| ~ member(X0,complement(singleton(X1))) ),
inference(resolution,[status(thm)],[c26,c91]) ).
cnf(d1,plain,
( ~ member(X0,sK90)
| ~ member(X1,sK90)
| ~ member(X0,'universal$uclass')
| member(X0,singleton(X1)) ),
inference(resolution,[status(thm)],[c29,d0]) ).
cnf(d2,plain,
( subclass(X1,singleton(X0))
| ~ member(sK3(X1,singleton(X0)),sK90)
| ~ member(sK3(X1,singleton(X0)),'universal$uclass')
| ~ member(X0,sK90) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( subclass(sK90,singleton(X0))
| subclass(sK90,singleton(X0))
| ~ member(sK3(sK90,singleton(X0)),'universal$uclass')
| ~ member(X0,sK90) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d5,plain,
( subclass(X0,X1)
| member(sK3(X0,X1),'universal$uclass') ),
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
( subclass(sK90,singleton(X0))
| ~ member(X0,sK90)
| subclass(sK90,singleton(X0)) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ subclass(singleton(X0),sK90)
| singleton(X0) = sK90
| ~ member(X0,sK90) ),
inference(resolution,[status(thm)],[d6,c6]) ).
cnf(d8,plain,
( ~ subclass(singleton(X0),sK90)
| ~ member(X0,sK90) ),
inference(resolution,[status(thm)],[c90,d7]) ).
cnf(d9,plain,
( subclass('unordered$upair'(X0,X1),X2)
| sK3('unordered$upair'(X0,X1),X2) = X0
| sK3('unordered$upair'(X0,X1),X2) = X1 ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d10,plain,
( sK3('unordered$upair'(X0,X0),X1) = X0
| sK3('unordered$upair'(X0,X0),X1) = X0
| subclass(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c12,d9]) ).
cnf(d11,plain,
( subclass(singleton(X0),X1)
| sK3(singleton(X0),X1) = X0 ),
inference(demodulation,[status(thm)],[d10,c12]) ).
cnf(d12,plain,
( ~ member(X0,sK90)
| sK3(singleton(X0),sK90) = X0 ),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( sK90 = 'null$uclass'
| sK3(singleton(sK85(sK90)),sK90) = sK85(sK90) ),
inference(resolution,[status(thm)],[d12,c84]) ).
cnf(d14,plain,
sK3(singleton(sK85(sK90)),sK90) = sK85(sK90),
inference(resolution,[status(thm)],[c89,d13]) ).
cnf(d15,plain,
( subclass(singleton(sK85(sK90)),sK90)
| ~ member(sK85(sK90),sK90) ),
inference(superposition,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
( ~ member(sK85(sK90),sK90)
| ~ member(sK85(sK90),sK90) ),
inference(resolution,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
sK90 = 'null$uclass',
inference(resolution,[status(thm)],[d16,c84]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[c89,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET097+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 07:12:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.74/6.95 % SZS status Theorem for theBenchmark.p
% 13.74/6.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------