%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:33:29 AM UTC 2026
% Result : Theorem 10.37s 1.77s
% Output : CNFRefutation 10.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 def)
% Number of atoms : 35 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 33 ( 15 ~; 12 |; 1 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ) ).
fof(l39_zfmisc_1,axiom,
! [X0,X1,X2] :
( 'set$udifference'('unordered$upair'(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ) ).
fof(t23_zfmisc_1,conjecture,
! [X0,X1] :
( X0 != X1
=> 'set$udifference'('unordered$upair'(X0,X1),singleton(X1)) = singleton(X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( X0 != X1
=> 'set$udifference'('unordered$upair'(X0,X1),singleton(X1)) = singleton(X0) ),
inference(negate_conjecture,[status(cth)],[t23_zfmisc_1]) ).
cnf(c2,plain,
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c3,plain,
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c10,plain,
( ~ in(X1,X2)
| in(X0,X2)
| 'set$udifference'('unordered$upair'(X0,X1),X2) = singleton(X0) ),
inference(clausification,[status(esa)],[l39_zfmisc_1]) ).
cnf(c14,plain,
sK13 != sK14,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
'set$udifference'('unordered$upair'(sK13,sK14),singleton(sK14)) != singleton(sK13),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d1,plain,
( in(X0,singleton(X1))
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(d2,plain,
in(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
( in(X0,singleton(X1))
| 'set$udifference'('unordered$upair'(X0,X1),singleton(X1)) = singleton(X0) ),
inference(resolution,[status(thm)],[c10,d2]) ).
cnf(d4,plain,
( X0 = X1
| 'set$udifference'('unordered$upair'(X0,X1),singleton(X1)) = singleton(X0) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( sK13 = sK14
| singleton(sK13) != singleton(sK13) ),
inference(superposition,[status(thm)],[d4,c15]) ).
cnf(d6,plain,
singleton(sK13) != singleton(sK13),
inference(resolution,[status(thm)],[c14,d5]) ).
cnf(d7,plain,
$false,
inference(equality_resolution,[status(thm)],[d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.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 08:24:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.37/1.77 % SZS status Theorem for theBenchmark.p
% 10.37/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------