%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET016+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 : n026.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 08:31:35 AM UTC 2026
% Result : Theorem 7.44s 6.96s
% Output : CNFRefutation 7.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 56 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 13 ~; 19 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 7 sgn 16 !; 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$upair'(X0,X0) ).
fof(ordered_pair_defn,axiom,
! [X0,X1] : 'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) ).
fof(ordered_pair_determines_components1,conjecture,
! [X0,X1,X2,X3] :
( ( member(X0,'universal$uclass')
& 'ordered$upair'(X0,X1) = 'ordered$upair'(X2,X3) )
=> X0 = X2 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( member(X0,'universal$uclass')
& 'ordered$upair'(X0,X1) = 'ordered$upair'(X2,X3) )
=> X0 = X2 ),
inference(negate_conjecture,[status(cth)],[ordered_pair_determines_components1]) ).
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$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_defn]) ).
cnf(c11,plain,
member('unordered$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(c13,plain,
'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))),
inference(clausification,[status(esa)],[ordered_pair_defn]) ).
cnf(c89,plain,
'ordered$upair'(sK90,sK91) = 'ordered$upair'(sK92,sK93),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
member(sK90,'universal$uclass'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c91,plain,
sK90 != sK92,
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$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,d0]) ).
cnf(d2,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d3,plain,
( X2 = singleton(X0)
| X2 = 'unordered$upair'(X0,singleton(X1))
| ~ member(X2,'ordered$upair'(X0,X1)) ),
inference(superposition,[status(thm)],[c13,c8]) ).
cnf(d4,plain,
( ~ member(singleton(X0),'universal$uclass')
| member(singleton(X0),'ordered$upair'(X0,X1)) ),
inference(superposition,[status(thm)],[c13,d0]) ).
cnf(d5,plain,
member(singleton(X0),'universal$uclass'),
inference(superposition,[status(thm)],[c12,c11]) ).
cnf(d6,plain,
member(singleton(X0),'ordered$upair'(X0,X1)),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
member(singleton(sK92),'ordered$upair'(sK90,sK91)),
inference(superposition,[status(thm)],[c89,d6]) ).
cnf(d8,plain,
( singleton(sK92) = singleton(sK90)
| singleton(sK92) = 'unordered$upair'(sK90,singleton(sK91)) ),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( singleton(sK92) = singleton(sK90)
| ~ member(sK90,'universal$uclass')
| member(sK90,singleton(sK92)) ),
inference(superposition,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
( member(sK90,singleton(sK92))
| singleton(sK92) = singleton(sK90) ),
inference(resolution,[status(thm)],[c90,d9]) ).
cnf(d11,plain,
( sK90 = sK92
| singleton(sK92) = singleton(sK90) ),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
singleton(sK92) = singleton(sK90),
inference(resolution,[status(thm)],[c91,d11]) ).
cnf(d13,plain,
( X0 = sK92
| ~ member(X0,singleton(sK90)) ),
inference(superposition,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
( ~ member(sK90,'universal$uclass')
| sK90 = sK92 ),
inference(resolution,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
sK90 = sK92,
inference(resolution,[status(thm)],[c90,d14]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[c91,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016+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
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 06:53:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.44/6.96 % SZS status Theorem for theBenchmark.p
% 7.44/6.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------