%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET977+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 08:33:40 AM UTC 2026
% Result : Theorem 15.13s 7.34s
% Output : CNFRefutation 15.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 45 ( 22 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 45 ( 22 ~; 14 |; 4 &)
% ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 4 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X0] :
( X0 = 'empty$uset'
<=> ! [X1] : ~ in(X1,X0) ) ).
fof(t128_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ) ).
fof(t129_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,singleton(X3)))
<=> ( X1 = X3
& in(X0,X2) ) ) ).
fof(t130_zfmisc_1,conjecture,
! [X0,X1] :
( X0 != 'empty$uset'
=> ( 'cartesian$uproduct2'(X0,singleton(X1)) != 'empty$uset'
& 'cartesian$uproduct2'(singleton(X1),X0) != 'empty$uset' ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( X0 != 'empty$uset'
=> ( 'cartesian$uproduct2'(X0,singleton(X1)) != 'empty$uset'
& 'cartesian$uproduct2'(singleton(X1),X0) != 'empty$uset' ) ),
inference(negate_conjecture,[status(cth)],[t130_zfmisc_1]) ).
cnf(c2,plain,
( ~ in(X1,X0)
| X0 != 'empty$uset' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c3,plain,
( in(sK6(X0),X0)
| X0 = 'empty$uset' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c11,plain,
( ~ in(X1,X3)
| X0 != X2
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(singleton(X2),X3)) ),
inference(clausification,[status(esa)],[t128_zfmisc_1]) ).
cnf(c14,plain,
( X1 != X3
| ~ in(X0,X2)
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,singleton(X3))) ),
inference(clausification,[status(esa)],[t129_zfmisc_1]) ).
cnf(c15,plain,
sK21 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
( 'cartesian$uproduct2'(sK21,singleton(sK22)) = 'empty$uset'
| 'cartesian$uproduct2'(singleton(sK22),sK21) = 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( in('ordered$upair'(X0,X2),'cartesian$uproduct2'(X1,singleton(X2)))
| ~ in(X0,X1) ),
inference(equality_resolution,[status(thm)],[c14]) ).
cnf(d1,plain,
( in('ordered$upair'(X2,X0),'cartesian$uproduct2'(singleton(X2),X1))
| ~ in(X0,X1) ),
inference(equality_resolution,[status(thm)],[c11]) ).
cnf(d2,plain,
( 'cartesian$uproduct2'(sK21,singleton(sK22)) = 'empty$uset'
| ~ in(X0,sK21)
| in('ordered$upair'(sK22,X0),'empty$uset') ),
inference(superposition,[status(thm)],[c16,d1]) ).
cnf(d3,plain,
~ in(X0,'empty$uset'),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d4,plain,
( ~ in(X0,sK21)
| 'cartesian$uproduct2'(sK21,singleton(sK22)) = 'empty$uset' ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( sK21 = 'empty$uset'
| 'cartesian$uproduct2'(sK21,singleton(sK22)) = 'empty$uset' ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
'cartesian$uproduct2'(sK21,singleton(sK22)) = 'empty$uset',
inference(resolution,[status(thm)],[c15,d5]) ).
cnf(d7,plain,
( ~ in(X0,sK21)
| in('ordered$upair'(X0,sK22),'empty$uset') ),
inference(superposition,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
~ in(X0,sK21),
inference(resolution,[status(thm)],[d3,d7]) ).
cnf(d9,plain,
sK21 = 'empty$uset',
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c15,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET977+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
% 0.09/5.37 % Computer : n017.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 08:24:25 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.13/7.34 % SZS status Theorem for theBenchmark.p
% 15.13/7.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------