%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU186+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 08:41:12 AM UTC 2026
% Result : Theorem 17.55s 4.77s
% Output : CNFRefutation 17.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 45 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 17 ~; 13 |; 1 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 4 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_relat_1,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : X1 != 'ordered$upair'(X2,X3)
& in(X1,X0) ) ) ).
fof(d1_xboole_0,axiom,
! [X0] :
( X0 = 'empty$uset'
<=> ! [X1] : ~ in(X1,X0) ) ).
fof(d4_relat_1,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = 'relation$udom'(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in('ordered$upair'(X2,X3),X0) ) ) ) ).
fof(t56_relat_1,conjecture,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in('ordered$upair'(X1,X2),X0)
=> X0 = 'empty$uset' ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in('ordered$upair'(X1,X2),X0)
=> X0 = 'empty$uset' ) ),
inference(negate_conjecture,[status(cth)],[t56_relat_1]) ).
cnf(c9,plain,
( X1 = 'ordered$upair'(sK15(X1),sK16(X1))
| ~ in(X1,X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d1_relat_1]) ).
cnf(c31,plain,
( ~ in(X1,X0)
| X0 != 'empty$uset' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c96,plain,
( in('ordered$upair'(sK83(X0,X1),sK85(X0,X1)),X0)
| in(sK83(X0,X1),X1)
| X1 = 'relation$udom'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d4_relat_1]) ).
cnf(c322,plain,
relation(sK397),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c323,plain,
~ in('ordered$upair'(X0,X1),sK397),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c324,plain,
sK397 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ in(X0,'empty$uset'),
inference(equality_resolution,[status(thm)],[c31]) ).
cnf(d1,plain,
( ~ relation(sK397)
| in(sK83(sK397,X0),X0)
| X0 = 'relation$udom'(sK397) ),
inference(resolution,[status(thm)],[c96,c323]) ).
cnf(d2,plain,
( in(sK83(sK397,X0),X0)
| X0 = 'relation$udom'(sK397) ),
inference(resolution,[status(thm)],[c322,d1]) ).
cnf(d3,plain,
'empty$uset' = 'relation$udom'(sK397),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( in(sK83(sK397,X0),X0)
| X0 = 'empty$uset' ),
inference(demodulation,[status(thm)],[d2,d3]) ).
cnf(d5,plain,
( ~ relation(X0)
| sK83(sK397,X0) = 'ordered$upair'(sK15(sK83(sK397,X0)),sK16(sK83(sK397,X0)))
| X0 = 'empty$uset' ),
inference(resolution,[status(thm)],[d4,c9]) ).
cnf(d6,plain,
( sK83(sK397,sK397) = 'ordered$upair'(sK15(sK83(sK397,sK397)),sK16(sK83(sK397,sK397)))
| sK397 = 'empty$uset' ),
inference(resolution,[status(thm)],[d5,c322]) ).
cnf(d7,plain,
sK83(sK397,sK397) = 'ordered$upair'(sK15(sK83(sK397,sK397)),sK16(sK83(sK397,sK397))),
inference(resolution,[status(thm)],[c324,d6]) ).
cnf(d8,plain,
~ in(sK83(sK397,sK397),sK397),
inference(superposition,[status(thm)],[d7,c323]) ).
cnf(d9,plain,
sK397 = 'empty$uset',
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c324,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU186+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:46:40 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.55/4.77 % SZS status Theorem for theBenchmark.p
% 17.55/4.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------