%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET103+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 : 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 08:32:03 AM UTC 2026
% Result : Theorem 28.61s 4.08s
% Output : CNFRefutation 28.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 37 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 7 ~; 12 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 11 !; 1 ?)
% 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$upair'(X0,X0) ).
fof(ordered_pair_defn,axiom,
! [X0,X1] : 'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) ).
fof(regularity,axiom,
! [X0] :
( X0 != 'null$uclass'
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,'universal$uclass') ) ) ).
fof(property_1_of_ordered_pair,conjecture,
! [X0,X1] :
( member(X1,'universal$uclass')
| 'unordered$upair'(singleton(X0),'unordered$upair'(X0,'null$uclass')) = 'ordered$upair'(X0,X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( member(X1,'universal$uclass')
| 'unordered$upair'(singleton(X0),'unordered$upair'(X0,'null$uclass')) = 'ordered$upair'(X0,X1) ),
inference(negate_conjecture,[status(cth)],[property_1_of_ordered_pair]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ 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(c13,plain,
'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))),
inference(clausification,[status(esa)],[ordered_pair_defn]) ).
cnf(c83,plain,
( member(sK85(X0),'universal$uclass')
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity]) ).
cnf(c84,plain,
( member(sK85(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity]) ).
cnf(c89,plain,
'unordered$upair'(singleton(sK90),'unordered$upair'(sK90,'null$uclass')) != 'ordered$upair'(sK90,sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
~ member(sK91,'universal$uclass'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c8]) ).
cnf(d1,plain,
( singleton(X0) = 'null$uclass'
| sK85(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[d0,c84]) ).
cnf(d2,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(superposition,[status(thm)],[d1,c83]) ).
cnf(d3,plain,
singleton(sK91) = 'null$uclass',
inference(resolution,[status(thm)],[d2,c90]) ).
cnf(d4,plain,
'ordered$upair'(X0,sK91) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,'null$uclass')),
inference(superposition,[status(thm)],[d3,c13]) ).
cnf(d5,plain,
'ordered$upair'(sK90,sK91) != 'ordered$upair'(sK90,sK91),
inference(demodulation,[status(thm)],[c89,d4]) ).
cnf(d6,plain,
$false,
inference(equality_resolution,[status(thm)],[d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET103+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
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:12:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.61/4.08 % SZS status Theorem for theBenchmark.p
% 28.61/4.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------