%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET094+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 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 08:32:00 AM UTC 2026
% Result : Theorem 15.30s 3.06s
% Output : CNFRefutation 15.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 43 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 9 ~; 9 |; 5 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 3 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [X0,X1,X2] :
( member(X0,'unordered$upair'(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,'universal$uclass') ) ) ).
fof(unordered_pair,axiom,
! [X0,X1] : member('unordered$upair'(X0,X1),'universal$uclass') ).
fof(singleton_set_defn,axiom,
! [X0] : singleton(X0) = 'unordered$upair'(X0,X0) ).
fof(first_second,axiom,
! [X0,X1] :
( ( member(X1,'universal$uclass')
& member(X0,'universal$uclass') )
=> ( second('ordered$upair'(X0,X1)) = X1
& first('ordered$upair'(X0,X1)) = X0 ) ) ).
fof(property_of_singletons1_1,conjecture,
! [X0,X1] :
( ( member(X1,X0)
& singleton('member$uof'(X0)) = X0 )
=> 'member$uof'(X0) = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( member(X1,X0)
& singleton('member$uof'(X0)) = X0 )
=> 'member$uof'(X0) = X1 ),
inference(negate_conjecture,[status(cth)],[property_of_singletons1_1]) ).
cnf(c12,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_defn]) ).
cnf(c15,plain,
member('unordered$upair'(X0,X1),'universal$uclass'),
inference(clausification,[status(esa)],[unordered_pair]) ).
cnf(c16,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set_defn]) ).
cnf(c21,plain,
( first('ordered$upair'(X0,X1)) = X0
| ~ member(X1,'universal$uclass')
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[first_second]) ).
cnf(c93,plain,
singleton('member$uof'(sK94)) = sK94,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c94,plain,
member(sK95,sK94),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c95,plain,
'member$uof'(sK94) != sK95,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c16,c12]) ).
cnf(d1,plain,
member(singleton(X0),'universal$uclass'),
inference(superposition,[status(thm)],[c16,c15]) ).
cnf(d2,plain,
member(sK94,'universal$uclass'),
inference(superposition,[status(thm)],[c93,d1]) ).
cnf(d3,plain,
( ~ member(X0,'universal$uclass')
| first('ordered$upair'(X0,sK94)) = X0 ),
inference(resolution,[status(thm)],[c21,d2]) ).
cnf(d4,plain,
first('ordered$upair'(sK94,sK94)) = sK94,
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
first('ordered$upair'(singleton(X0),sK94)) = singleton(X0),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d6,plain,
first('ordered$upair'(sK94,sK94)) = singleton('member$uof'(sK94)),
inference(superposition,[status(thm)],[c93,d5]) ).
cnf(d7,plain,
sK94 = singleton('member$uof'(sK94)),
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( X0 = 'member$uof'(sK94)
| ~ member(X0,sK94) ),
inference(superposition,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
sK95 = 'member$uof'(sK94),
inference(resolution,[status(thm)],[d8,c94]) ).
cnf(d10,plain,
sK95 != sK95,
inference(demodulation,[status(thm)],[c95,d9]) ).
cnf(d11,plain,
$false,
inference(equality_resolution,[status(thm)],[d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET094+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.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 07:08:21 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.30/3.06 % SZS status Theorem for theBenchmark.p
% 15.30/3.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------