%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET879+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 : n017.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 16.77s 2.65s
% Output : CNFRefutation 16.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 40 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 18 ~; 14 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ) ).
fof(l34_zfmisc_1,axiom,
! [X0,X1] :
( 'set$udifference'(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ) ).
fof(t20_zfmisc_1,conjecture,
! [X0,X1] :
( 'set$udifference'(singleton(X0),singleton(X1)) = singleton(X0)
<=> X0 != X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'set$udifference'(singleton(X0),singleton(X1)) = singleton(X0)
<=> X0 != X1 ),
inference(negate_conjecture,[status(cth)],[t20_zfmisc_1]) ).
cnf(c1,plain,
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c2,plain,
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c7,plain,
( ~ in(X0,X1)
| 'set$udifference'(singleton(X0),X1) != singleton(X0) ),
inference(clausification,[status(esa)],[l34_zfmisc_1]) ).
cnf(c8,plain,
( in(X0,X1)
| 'set$udifference'(singleton(X0),X1) = singleton(X0) ),
inference(clausification,[status(esa)],[l34_zfmisc_1]) ).
cnf(c12,plain,
( sK10 != sK11
| 'set$udifference'(singleton(sK10),singleton(sK11)) = singleton(sK10) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c13,plain,
( 'set$udifference'(singleton(sK10),singleton(sK11)) != singleton(sK10)
| sK10 = sK11 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(d1,plain,
( X0 = X1
| 'set$udifference'(singleton(X0),singleton(X1)) = singleton(X0) ),
inference(resolution,[status(thm)],[c8,d0]) ).
cnf(d2,plain,
( sK10 = sK11
| sK10 = sK11
| singleton(sK10) != singleton(sK10) ),
inference(superposition,[status(thm)],[d1,c13]) ).
cnf(d3,plain,
sK10 = sK11,
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
'set$udifference'(singleton(sK10),singleton(sK11)) = singleton(sK10),
inference(resolution,[status(thm)],[d3,c12]) ).
cnf(d5,plain,
'set$udifference'(singleton(sK10),singleton(sK10)) = singleton(sK10),
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ in(sK10,singleton(sK10))
| singleton(sK10) != singleton(sK10) ),
inference(superposition,[status(thm)],[d5,c7]) ).
cnf(d7,plain,
( in(X0,singleton(X1))
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d8,plain,
in(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
singleton(sK10) != singleton(sK10),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
$false,
inference(equality_resolution,[status(thm)],[d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET879+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45 % Computer : n017.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.45 % WCLimit : 300
% 0.21/0.45 % DateTime : Sat Sep 26 08:19:33 UTC 2026
% 0.21/0.45 % CPUTime :
% 0.21/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.77/2.65 % SZS status Theorem for theBenchmark.p
% 16.77/2.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------