%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET067+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 : n002.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 08:31:52 AM UTC 2026
% Result : Theorem 18.37s 2.76s
% Output : CNFRefutation 18.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 48 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 15 ~; 17 |; 1 &)
% ( 2 <=>; 1 =>; 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 : 37 ( 4 sgn 12 !; 0 ?)
% 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$uclass') ).
fof(unordered_pair_defn,axiom,
! [X0,X1,X2] :
( member(X0,'unordered$upair'(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,'universal$uclass') ) ) ).
fof(singleton_set_defn,axiom,
! [X0] : singleton(X0) = 'unordered$upair'(X0,X0) ).
fof(pair_contains_other,conjecture,
! [X0,X1] : subclass('unordered$upair'(X0,X0),'unordered$upair'(X0,X1)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : subclass('unordered$upair'(X0,X0),'unordered$upair'(X0,X1)),
inference(negate_conjecture,[status(cth)],[pair_contains_other]) ).
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$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_defn]) ).
cnf(c9,plain,
( X0 != X1
| ~ member(X0,'universal$uclass')
| member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_defn]) ).
cnf(c12,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set_defn]) ).
cnf(c89,plain,
~ subclass('unordered$upair'(sK90,sK90),'unordered$upair'(sK90,sK91)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d1,plain,
~ subclass(singleton(sK90),'unordered$upair'(sK90,sK91)),
inference(demodulation,[status(thm)],[c89,c12]) ).
cnf(d2,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d3,plain,
( subclass(singleton(X0),X1)
| sK3(singleton(X0),X1) = X0 ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
sK3(singleton(sK90),'unordered$upair'(sK90,sK91)) = sK90,
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( subclass(singleton(sK90),'unordered$upair'(sK90,sK91))
| ~ member(sK90,'unordered$upair'(sK90,sK91)) ),
inference(superposition,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
~ member(sK90,'unordered$upair'(sK90,sK91)),
inference(resolution,[status(thm)],[d1,d5]) ).
cnf(d7,plain,
~ member(sK90,'universal$uclass'),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d9,plain,
( subclass(X0,X1)
| member(sK3(X0,X1),'universal$uclass') ),
inference(resolution,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
( subclass(singleton(sK90),'unordered$upair'(sK90,sK91))
| member(sK90,'universal$uclass') ),
inference(superposition,[status(thm)],[d4,d9]) ).
cnf(d11,plain,
member(sK90,'universal$uclass'),
inference(resolution,[status(thm)],[d1,d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET067+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
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 07:04:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.37/2.76 % SZS status Theorem for theBenchmark.p
% 18.37/2.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------