%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU162+3 : 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 : n007.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 08:41:06 AM UTC 2026
% Result : Theorem 9.60s 1.66s
% Output : CNFRefutation 9.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 39 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 14 ~; 11 |; 1 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l25_zfmisc_1,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ) ).
fof(l28_zfmisc_1,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ) ).
fof(symmetry_r1_xboole_0,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ) ).
fof(t83_xboole_1,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> 'set$udifference'(X0,X1) = X0 ) ).
fof(t65_zfmisc_1,conjecture,
! [X0,X1] :
( 'set$udifference'(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'set$udifference'(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
inference(negate_conjecture,[status(cth)],[t65_zfmisc_1]) ).
cnf(c1,plain,
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(clausification,[status(esa)],[l25_zfmisc_1]) ).
cnf(c2,plain,
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(clausification,[status(esa)],[l28_zfmisc_1]) ).
cnf(c5,plain,
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_r1_xboole_0]) ).
cnf(c6,plain,
( 'set$udifference'(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(clausification,[status(esa)],[t83_xboole_1]) ).
cnf(c7,plain,
( 'set$udifference'(X0,X1) != X0
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[t83_xboole_1]) ).
cnf(c9,plain,
( ~ in(sK13,sK12)
| 'set$udifference'(sK12,singleton(sK13)) = sK12 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10,plain,
( 'set$udifference'(sK12,singleton(sK13)) != sK12
| in(sK13,sK12) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( in(X1,X0)
| disjoint(X0,singleton(X1)) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d1,plain,
( in(X1,X0)
| 'set$udifference'(X0,singleton(X1)) = X0 ),
inference(resolution,[status(thm)],[c6,d0]) ).
cnf(d2,plain,
( 'set$udifference'(sK12,singleton(sK13)) = sK12
| 'set$udifference'(sK12,singleton(sK13)) = sK12 ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( disjoint(sK12,singleton(sK13))
| sK12 != sK12 ),
inference(superposition,[status(thm)],[d2,c7]) ).
cnf(d4,plain,
disjoint(sK12,singleton(sK13)),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
disjoint(singleton(sK13),sK12),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
~ in(sK13,sK12),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
in(sK13,sK12),
inference(resolution,[status(thm)],[d2,c10]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU162+3 : 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 : n007.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 08:40:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.60/1.66 % SZS status Theorem for theBenchmark.p
% 9.60/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------