%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET083+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 : n019.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 18.64s 3.03s
% Output : CNFRefutation 18.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 7 unt; 0 def)
% Number of atoms : 34 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 27 ( 10 ~; 11 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 2 sgn 8 !; 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(singleton_set_defn,axiom,
! [X0] : singleton(X0) = 'unordered$upair'(X0,X0) ).
fof(singleton_identified_by_element1,conjecture,
! [X0,X1] :
( ( member(X0,'universal$uclass')
& singleton(X0) = singleton(X1) )
=> X0 = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( member(X0,'universal$uclass')
& singleton(X0) = singleton(X1) )
=> X0 = X1 ),
inference(negate_conjecture,[status(cth)],[singleton_identified_by_element1]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$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$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set_defn]) ).
cnf(c89,plain,
singleton(sK90) = singleton(sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
member(sK90,'universal$uclass'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c91,plain,
sK90 != sK91,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d1,plain,
( X0 = sK91
| ~ member(X0,singleton(sK90)) ),
inference(superposition,[status(thm)],[c89,d0]) ).
cnf(d2,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d3,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,d2]) ).
cnf(d4,plain,
( sK90 = sK91
| ~ member(sK90,'universal$uclass') ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
sK90 = sK91,
inference(resolution,[status(thm)],[c90,d4]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c91,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET083+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 : n019.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 07:04:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.64/3.03 % SZS status Theorem for theBenchmark.p
% 18.64/3.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------