%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET095+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 : n013.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 08:32:00 AM UTC 2026
% Result : Theorem 19.80s 2.98s
% Output : CNFRefutation 19.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 35 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 5 ~; 11 |; 1 &)
% ( 2 <=>; 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 : 26 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,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$upair'(X0,X0) ).
fof(property_of_singletons2,conjecture,
! [X0,X1] :
( member(X0,X1)
=> subclass(singleton(X0),X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( member(X0,X1)
=> subclass(singleton(X0),X1) ),
inference(negate_conjecture,[status(cth)],[property_of_singletons2]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_defn]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_defn]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_defn]) ).
cnf(c12,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set_defn]) ).
cnf(c89,plain,
member(sK90,sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
~ subclass(singleton(sK90),sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subclass('unordered$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(d1,plain,
( sK3('unordered$upair'(X0,X0),X1) = X0
| sK3('unordered$upair'(X0,X0),X1) = X0
| subclass(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c12,d0]) ).
cnf(d2,plain,
( subclass(singleton(X0),X1)
| sK3(singleton(X0),X1) = X0 ),
inference(demodulation,[status(thm)],[d1,c12]) ).
cnf(d3,plain,
sK3(singleton(sK90),sK91) = sK90,
inference(resolution,[status(thm)],[d2,c90]) ).
cnf(d4,plain,
( subclass(singleton(sK90),sK91)
| ~ member(sK90,sK91) ),
inference(superposition,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
subclass(singleton(sK90),sK91),
inference(resolution,[status(thm)],[c89,d4]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c90,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET095+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
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 07:05:53 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.80/2.98 % SZS status Theorem for theBenchmark.p
% 19.80/2.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------