%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET096+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 : n007.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 17.48s 12.69s
% Output : CNFRefutation 17.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 69 ( 30 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 53 ( 17 ~; 25 |; 4 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
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$upair'(X0,X0) ).
fof(regularity,axiom,
! [X0] :
( X0 != 'null$uclass'
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,'universal$uclass') ) ) ).
fof(two_subsets_of_singleton,conjecture,
! [X0,X1] :
( subclass(X0,singleton(X1))
=> ( singleton(X1) = X0
| X0 = 'null$uclass' ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( subclass(X0,singleton(X1))
=> ( singleton(X1) = X0
| X0 = 'null$uclass' ) ),
inference(negate_conjecture,[status(cth)],[two_subsets_of_singleton]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_defn]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_defn]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_defn]) ).
cnf(c6,plain,
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[extensionality]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_defn]) ).
cnf(c12,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set_defn]) ).
cnf(c84,plain,
( member(sK85(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity]) ).
cnf(c89,plain,
subclass(sK90,singleton(sK91)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
sK90 != 'null$uclass',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c91,plain,
singleton(sK91) != sK90,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ subclass(singleton(sK91),sK90)
| singleton(sK91) = sK90 ),
inference(resolution,[status(thm)],[c6,c89]) ).
cnf(d1,plain,
~ subclass(singleton(sK91),sK90),
inference(resolution,[status(thm)],[c91,d0]) ).
cnf(d2,plain,
( subclass('unordered$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(d3,plain,
( sK3('unordered$upair'(X0,X0),X1) = X0
| sK3('unordered$upair'(X0,X0),X1) = X0
| subclass(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c12,d2]) ).
cnf(d4,plain,
( subclass(singleton(X0),X1)
| sK3(singleton(X0),X1) = X0 ),
inference(demodulation,[status(thm)],[d3,c12]) ).
cnf(d5,plain,
sK3(singleton(sK91),sK90) = sK91,
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( subclass(singleton(sK91),sK90)
| ~ member(sK91,sK90) ),
inference(superposition,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
~ member(sK91,sK90),
inference(resolution,[status(thm)],[d1,d6]) ).
cnf(d8,plain,
( ~ member(X0,sK90)
| member(X0,singleton(sK91)) ),
inference(resolution,[status(thm)],[c89,c0]) ).
cnf(d9,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d10,plain,
( ~ member(X0,sK90)
| X0 = sK91 ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( sK90 = 'null$uclass'
| sK85(sK90) = sK91 ),
inference(resolution,[status(thm)],[d10,c84]) ).
cnf(d12,plain,
sK85(sK90) = sK91,
inference(resolution,[status(thm)],[c90,d11]) ).
cnf(d13,plain,
( sK90 = 'null$uclass'
| member(sK91,sK90) ),
inference(superposition,[status(thm)],[d12,c84]) ).
cnf(d14,plain,
member(sK91,sK90),
inference(resolution,[status(thm)],[c90,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET096+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n007.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Sat Sep 26 07:04:19 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.48/12.69 % SZS status Theorem for theBenchmark.p
% 17.48/12.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------