%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:41:07 AM UTC 2026
% Result : Theorem 20.07s 2.94s
% Output : CNFRefutation 20.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 3 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 32 ( 14 ~; 12 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l55_zfmisc_1,lemma,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ) ).
fof(t106_zfmisc_1,conjecture,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
inference(negate_conjecture,[status(cth)],[t106_zfmisc_1]) ).
cnf(c120,plain,
( in(X0,X2)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c121,plain,
( in(X1,X3)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c122,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c187,plain,
( in(sK215,sK217)
| in('ordered$upair'(sK215,sK216),'cartesian$uproduct2'(sK217,sK218)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c188,plain,
( in(sK216,sK218)
| in('ordered$upair'(sK215,sK216),'cartesian$uproduct2'(sK217,sK218)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c189,plain,
( ~ in('ordered$upair'(sK215,sK216),'cartesian$uproduct2'(sK217,sK218))
| ~ in(sK216,sK218)
| ~ in(sK215,sK217) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( in(sK215,sK217)
| in(sK215,sK217) ),
inference(resolution,[status(thm)],[c120,c187]) ).
cnf(d1,plain,
( ~ in(sK216,sK218)
| ~ in('ordered$upair'(sK215,sK216),'cartesian$uproduct2'(sK217,sK218)) ),
inference(resolution,[status(thm)],[d0,c189]) ).
cnf(d2,plain,
( in(sK216,sK218)
| in(sK216,sK218) ),
inference(resolution,[status(thm)],[c121,c188]) ).
cnf(d3,plain,
~ in('ordered$upair'(sK215,sK216),'cartesian$uproduct2'(sK217,sK218)),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ in(sK215,sK217)
| ~ in(sK216,sK218) ),
inference(resolution,[status(thm)],[d3,c122]) ).
cnf(d5,plain,
~ in(sK216,sK218),
inference(resolution,[status(thm)],[d0,d4]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d2,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n020.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 08:44:03 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.07/2.94 % SZS status Theorem for theBenchmark.p
% 20.07/2.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------