%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET084+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 : n010.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 08:31:57 AM UTC 2026
% Result : Theorem 3.21s 3.32s
% Output : CNFRefutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 25 unt; 0 def)
% Number of atoms : 113 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 31 ~; 36 |; 9 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 64 ( 12 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(extensionality,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ) ).
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(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(element_relation_defn,axiom,
! [X0,X1] :
( member('ordered$upair'(X0,X1),'element$urelation')
<=> ( member(X0,X1)
& member(X1,'universal$uclass') ) ) ).
fof(null_class_defn,axiom,
! [X0] : ~ member(X0,'null$uclass') ).
fof(regularity,axiom,
! [X0] :
( X0 != 'null$uclass'
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,'universal$uclass') ) ) ).
fof(singleton_identified_by_element2,conjecture,
! [X0,X1] :
( ( member(X1,'universal$uclass')
& singleton(X0) = singleton(X1) )
=> X0 = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( member(X1,'universal$uclass')
& singleton(X0) = singleton(X1) )
=> X0 = X1 ),
inference(negate_conjecture,[status(cth)],[singleton_identified_by_element2]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_defn]) ).
cnf(c6,plain,
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[extensionality]) ).
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$upair'(X0,singleton(X1))),
inference(clausification,[status(esa)],[ordered_pair_defn]) ).
cnf(c17,plain,
( first('ordered$upair'(X0,X1)) = X0
| ~ member(X1,'universal$uclass')
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[first_second]) ).
cnf(c20,plain,
( member(X1,'universal$uclass')
| ~ member('ordered$upair'(X0,X1),'element$urelation') ),
inference(clausification,[status(esa)],[element_relation_defn]) ).
cnf(c22,plain,
( ~ member(X0,X1)
| ~ member(X1,'universal$uclass')
| member('ordered$upair'(X0,X1),'element$urelation') ),
inference(clausification,[status(esa)],[element_relation_defn]) ).
cnf(c31,plain,
~ member(X0,'null$uclass'),
inference(clausification,[status(esa)],[null_class_defn]) ).
cnf(c84,plain,
( member(sK85(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity]) ).
cnf(c89,plain,
singleton(sK90) = singleton(sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
member(sK91,'universal$uclass'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c91,plain,
sK90 != sK91,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subclass('null$uclass',X0),
inference(resolution,[status(thm)],[c31,c1]) ).
cnf(d1,plain,
'ordered$upair'(X0,sK90) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(sK91))),
inference(superposition,[status(thm)],[c89,c13]) ).
cnf(d2,plain,
'ordered$upair'(X0,sK90) = 'ordered$upair'(X0,sK91),
inference(demodulation,[status(thm)],[d1,c13]) ).
cnf(d3,plain,
( member(sK90,'universal$uclass')
| ~ member('ordered$upair'(X0,sK91),'element$urelation') ),
inference(superposition,[status(thm)],[d2,c20]) ).
cnf(d4,plain,
( ~ member(X0,sK91)
| ~ member(sK91,'universal$uclass')
| member(sK90,'universal$uclass') ),
inference(resolution,[status(thm)],[d3,c22]) ).
cnf(d5,plain,
( member(sK90,'universal$uclass')
| ~ member(X0,sK91) ),
inference(resolution,[status(thm)],[c90,d4]) ).
cnf(d6,plain,
( subclass(sK91,X0)
| member(sK90,'universal$uclass') ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
( ~ subclass(X0,sK91)
| X0 = sK91
| member(sK90,'universal$uclass') ),
inference(resolution,[status(thm)],[d6,c6]) ).
cnf(d8,plain,
( member(sK90,'universal$uclass')
| 'null$uclass' = sK91 ),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d10,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,d9]) ).
cnf(d11,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d12,plain,
( X0 = sK90
| ~ member(X0,singleton(sK91)) ),
inference(superposition,[status(thm)],[c89,d11]) ).
cnf(d13,plain,
( singleton(sK91) = 'null$uclass'
| sK85(singleton(sK91)) = sK90 ),
inference(resolution,[status(thm)],[d12,c84]) ).
cnf(d14,plain,
( singleton(sK91) = 'null$uclass'
| singleton(sK91) = 'null$uclass'
| member(sK90,singleton(sK91)) ),
inference(superposition,[status(thm)],[d13,c84]) ).
cnf(d15,plain,
( sK90 = sK91
| singleton(sK91) = 'null$uclass' ),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
singleton(sK91) = 'null$uclass',
inference(resolution,[status(thm)],[c91,d15]) ).
cnf(d17,plain,
member(singleton(X0),'universal$uclass'),
inference(superposition,[status(thm)],[c12,c11]) ).
cnf(d18,plain,
( ~ member(X0,'universal$uclass')
| first('ordered$upair'(X0,sK91)) = X0 ),
inference(resolution,[status(thm)],[c17,c90]) ).
cnf(d19,plain,
first('ordered$upair'(singleton(X0),sK91)) = singleton(X0),
inference(resolution,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
first('ordered$upair'(singleton(sK91),sK91)) = singleton(sK90),
inference(superposition,[status(thm)],[c89,d19]) ).
cnf(d21,plain,
singleton(sK91) = singleton(sK90),
inference(demodulation,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
'null$uclass' = singleton(sK90),
inference(demodulation,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
( ~ member(sK90,'universal$uclass')
| member(sK90,'null$uclass') ),
inference(superposition,[status(thm)],[d22,d10]) ).
cnf(d24,plain,
~ member(sK90,'universal$uclass'),
inference(resolution,[status(thm)],[c31,d23]) ).
cnf(d25,plain,
'null$uclass' = sK91,
inference(resolution,[status(thm)],[d24,d8]) ).
cnf(d26,plain,
( ~ member(sK91,'universal$uclass')
| member(sK91,'null$uclass') ),
inference(superposition,[status(thm)],[d16,d10]) ).
cnf(d27,plain,
( member(sK91,'null$uclass')
| ~ member('null$uclass','universal$uclass') ),
inference(demodulation,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
( member('null$uclass','null$uclass')
| ~ member('null$uclass','universal$uclass') ),
inference(demodulation,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
~ member('null$uclass','universal$uclass'),
inference(resolution,[status(thm)],[c31,d28]) ).
cnf(d30,plain,
member('null$uclass','universal$uclass'),
inference(superposition,[status(thm)],[d16,d17]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[d30,d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET084+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
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:04:45 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.21/3.32 % SZS status Theorem for theBenchmark.p
% 3.21/3.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------