%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET079+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:31:56 AM UTC 2026
% Result : Theorem 19.28s 2.79s
% Output : CNFRefutation 19.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 16 unt; 0 def)
% Number of atoms : 42 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 9 |; 3 &)
% ( 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 6 sgn 11 !; 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$upair'(X0,X1)) = X0 ) ) ).
fof(null_class_defn,axiom,
! [X0] : ~ member(X0,'null$uclass') ).
fof(corollary_to_set_in_its_singleton,conjecture,
! [X0] :
( member(X0,'universal$uclass')
=> singleton(X0) != 'null$uclass' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( member(X0,'universal$uclass')
=> singleton(X0) != 'null$uclass' ),
inference(negate_conjecture,[status(cth)],[corollary_to_set_in_its_singleton]) ).
cnf(c9,plain,
( X0 != X1
| ~ member(X0,'universal$uclass')
| member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_defn]) ).
cnf(c11,plain,
member('unordered$upair'(X0,X1),'universal$uclass'),
inference(clausification,[status(esa)],[unordered_pair]) ).
cnf(c12,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set_defn]) ).
cnf(c17,plain,
( first('ordered$upair'(X0,X1)) = X0
| ~ member(X1,'universal$uclass')
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[first_second]) ).
cnf(c31,plain,
~ member(X0,'null$uclass'),
inference(clausification,[status(esa)],[null_class_defn]) ).
cnf(c89,plain,
member(sK90,'universal$uclass'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
singleton(sK90) = 'null$uclass',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d1,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,d0]) ).
cnf(d2,plain,
member(singleton(X0),'universal$uclass'),
inference(superposition,[status(thm)],[c12,c11]) ).
cnf(d3,plain,
member('null$uclass','universal$uclass'),
inference(superposition,[status(thm)],[c90,d2]) ).
cnf(d4,plain,
( ~ member(X0,'universal$uclass')
| first('ordered$upair'(X0,sK90)) = X0 ),
inference(resolution,[status(thm)],[c17,c89]) ).
cnf(d5,plain,
first('ordered$upair'('null$uclass',sK90)) = 'null$uclass',
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
first('ordered$upair'(singleton(X0),sK90)) = singleton(X0),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d7,plain,
first('ordered$upair'('null$uclass',sK90)) = singleton(sK90),
inference(superposition,[status(thm)],[c90,d6]) ).
cnf(d8,plain,
'null$uclass' = singleton(sK90),
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ member(sK90,'universal$uclass')
| member(sK90,'null$uclass') ),
inference(superposition,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
member(sK90,'null$uclass'),
inference(resolution,[status(thm)],[c89,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c31,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET079+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 07:08:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.28/2.79 % SZS status Theorem for theBenchmark.p
% 19.28/2.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------