%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:33:38 AM UTC 2026
% Result : Theorem 17.76s 2.76s
% Output : CNFRefutation 17.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 71 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 25 ~; 31 |; 1 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 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 : 45 ( 12 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X0] :
( X0 = 'empty$uset'
<=> ! [X1] : ~ in(X1,X0) ) ).
fof(l55_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ) ).
fof(t2_tarski,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ) ).
fof(t114_zfmisc_1,conjecture,
! [X0,X1] :
( 'cartesian$uproduct2'(X0,X1) = 'cartesian$uproduct2'(X1,X0)
=> ( X0 = X1
| X1 = 'empty$uset'
| X0 = 'empty$uset' ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'cartesian$uproduct2'(X0,X1) = 'cartesian$uproduct2'(X1,X0)
=> ( X0 = X1
| X1 = 'empty$uset'
| X0 = 'empty$uset' ) ),
inference(negate_conjecture,[status(cth)],[t114_zfmisc_1]) ).
cnf(c3,plain,
( in(sK6(X0),X0)
| X0 = 'empty$uset' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c7,plain,
( in(X0,X2)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c8,plain,
( in(X1,X3)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c9,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c13,plain,
( X0 = X1
| in(sK19(X0,X1),X1)
| in(sK19(X0,X1),X0) ),
inference(clausification,[status(esa)],[t2_tarski]) ).
cnf(c14,plain,
( X0 = X1
| ~ in(sK19(X0,X1),X0)
| ~ in(sK19(X0,X1),X1) ),
inference(clausification,[status(esa)],[t2_tarski]) ).
cnf(c16,plain,
'cartesian$uproduct2'(sK20,sK21) = 'cartesian$uproduct2'(sK21,sK20),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
sK20 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
sK21 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
sK20 != sK21,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( in(X0,sK21)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(sK20,sK21)) ),
inference(superposition,[status(thm)],[c16,c7]) ).
cnf(d1,plain,
( in(X0,sK21)
| ~ in(X1,sK21)
| ~ in(X0,sK20) ),
inference(resolution,[status(thm)],[c9,d0]) ).
cnf(d2,plain,
( sK20 = 'empty$uset'
| in(sK6(sK20),sK21)
| ~ in(X0,sK21) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( in(sK6(sK20),sK21)
| ~ in(X0,sK21) ),
inference(resolution,[status(thm)],[c17,d2]) ).
cnf(d4,plain,
( sK21 = 'empty$uset'
| in(sK6(sK20),sK21) ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
in(sK6(sK20),sK21),
inference(resolution,[status(thm)],[c18,d4]) ).
cnf(d6,plain,
( in(X1,sK20)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(sK20,sK21)) ),
inference(superposition,[status(thm)],[c16,c8]) ).
cnf(d7,plain,
( in(X1,sK20)
| ~ in(X1,sK21)
| ~ in(X0,sK20) ),
inference(resolution,[status(thm)],[c9,d6]) ).
cnf(d8,plain,
( sK20 = 'empty$uset'
| ~ in(X0,sK21)
| in(X0,sK20) ),
inference(resolution,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
( ~ in(X0,sK21)
| in(X0,sK20) ),
inference(resolution,[status(thm)],[c17,d8]) ).
cnf(d10,plain,
( in(sK19(X0,sK21),X0)
| X0 = sK21
| in(sK19(X0,sK21),sK20) ),
inference(resolution,[status(thm)],[d9,c13]) ).
cnf(d11,plain,
( in(sK19(sK20,sK21),sK20)
| sK20 = sK21 ),
inference(factoring,[status(thm)],[d10]) ).
cnf(d12,plain,
in(sK19(sK20,sK21),sK20),
inference(resolution,[status(thm)],[c19,d11]) ).
cnf(d13,plain,
( in(sK19(sK20,sK21),sK21)
| ~ in(X0,sK21) ),
inference(resolution,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
( ~ in(sK19(sK20,sK21),sK21)
| sK20 = sK21 ),
inference(resolution,[status(thm)],[d12,c14]) ).
cnf(d15,plain,
~ in(sK19(sK20,sK21),sK21),
inference(resolution,[status(thm)],[c19,d14]) ).
cnf(d16,plain,
~ in(X0,sK21),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[d16,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n018.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 08:29:36 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.76/2.76 % SZS status Theorem for theBenchmark.p
% 17.76/2.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------