%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU252+1 : 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 : n004.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 08:41:27 AM UTC 2026
% Result : Theorem 37.90s 6.84s
% Output : CNFRefutation 37.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 5 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 123 ( 52 ~; 55 |; 3 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k2_wellord1,axiom,
! [X0,X1] :
( relation(X0)
=> relation('relation$urestriction'(X0,X1)) ) ).
fof(l1_wellord1,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,'relation$ufield'(X0))
=> in('ordered$upair'(X1,X1),X0) ) ) ) ).
fof(t106_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ) ).
fof(t16_wellord1,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,'relation$urestriction'(X2,X1))
<=> ( in(X0,'cartesian$uproduct2'(X1,X1))
& in(X0,X2) ) ) ) ).
fof(t19_wellord1,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,'relation$ufield'('relation$urestriction'(X2,X1)))
=> ( in(X0,X1)
& in(X0,'relation$ufield'(X2)) ) ) ) ).
fof(t22_wellord1,conjecture,
! [X0,X1] :
( relation(X1)
=> ( reflexive(X1)
=> reflexive('relation$urestriction'(X1,X0)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( reflexive(X1)
=> reflexive('relation$urestriction'(X1,X0)) ) ),
inference(negate_conjecture,[status(cth)],[t22_wellord1]) ).
cnf(c11,plain,
( relation('relation$urestriction'(X0,X1))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[dt_k2_wellord1]) ).
cnf(c19,plain,
( in('ordered$upair'(X1,X1),X0)
| ~ in(X1,'relation$ufield'(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[l1_wellord1]) ).
cnf(c20,plain,
( in(sK31(X0),'relation$ufield'(X0))
| reflexive(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[l1_wellord1]) ).
cnf(c21,plain,
( ~ in('ordered$upair'(sK31(X0),sK31(X0)),X0)
| reflexive(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[l1_wellord1]) ).
cnf(c34,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[t106_zfmisc_1]) ).
cnf(c37,plain,
( ~ in(X1,'cartesian$uproduct2'(X2,X2))
| ~ in(X1,X0)
| in(X1,'relation$urestriction'(X0,X2))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t16_wellord1]) ).
cnf(c38,plain,
( in(X1,'relation$ufield'(X0))
| ~ in(X1,'relation$ufield'('relation$urestriction'(X0,X2)))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t19_wellord1]) ).
cnf(c39,plain,
( in(X1,X2)
| ~ in(X1,'relation$ufield'('relation$urestriction'(X0,X2)))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t19_wellord1]) ).
cnf(c47,plain,
relation(sK59),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
reflexive(sK59),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c49,plain,
~ reflexive('relation$urestriction'(sK59,sK58)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X0,X3)
| ~ in(X1,X3)
| ~ relation(X2)
| in('ordered$upair'(X0,X1),'relation$urestriction'(X2,X3))
| ~ in('ordered$upair'(X0,X1),X2) ),
inference(resolution,[status(thm)],[c37,c34]) ).
cnf(d1,plain,
( reflexive('relation$urestriction'(X0,X1))
| ~ relation('relation$urestriction'(X0,X1))
| ~ relation(X0)
| ~ in('ordered$upair'(sK31('relation$urestriction'(X0,X1)),sK31('relation$urestriction'(X0,X1))),X0)
| ~ in(sK31('relation$urestriction'(X0,X1)),X1)
| ~ in(sK31('relation$urestriction'(X0,X1)),X1) ),
inference(resolution,[status(thm)],[d0,c21]) ).
cnf(d2,plain,
( reflexive('relation$urestriction'(X0,X1))
| ~ relation(X0)
| ~ in(sK31('relation$urestriction'(X0,X1)),X1)
| ~ in('ordered$upair'(sK31('relation$urestriction'(X0,X1)),sK31('relation$urestriction'(X0,X1))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[c11,d1]) ).
cnf(d3,plain,
( reflexive('relation$urestriction'(X0,X1))
| ~ relation('relation$urestriction'(X0,X1))
| ~ relation(X0)
| in(sK31('relation$urestriction'(X0,X1)),X1) ),
inference(resolution,[status(thm)],[c39,c20]) ).
cnf(d4,plain,
( reflexive('relation$urestriction'(X0,X1))
| ~ relation(X0)
| in(sK31('relation$urestriction'(X0,X1)),X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[c11,d3]) ).
cnf(d5,plain,
( reflexive('relation$urestriction'(X0,X1))
| ~ relation(X0)
| ~ in('ordered$upair'(sK31('relation$urestriction'(X0,X1)),sK31('relation$urestriction'(X0,X1))),X0)
| reflexive('relation$urestriction'(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ reflexive(X0)
| ~ relation(X0)
| ~ in(sK31('relation$urestriction'(X0,X1)),'relation$ufield'(X0))
| reflexive('relation$urestriction'(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[d5,c19]) ).
cnf(d7,plain,
( reflexive('relation$urestriction'(X0,X1))
| ~ relation('relation$urestriction'(X0,X1))
| ~ relation(X0)
| in(sK31('relation$urestriction'(X0,X1)),'relation$ufield'(X0)) ),
inference(resolution,[status(thm)],[c38,c20]) ).
cnf(d8,plain,
( reflexive('relation$urestriction'(X0,X1))
| ~ relation(X0)
| in(sK31('relation$urestriction'(X0,X1)),'relation$ufield'(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[c11,d7]) ).
cnf(d9,plain,
( reflexive('relation$urestriction'(X0,X1))
| ~ reflexive(X0)
| ~ relation(X0)
| reflexive('relation$urestriction'(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( ~ reflexive(sK59)
| ~ relation(sK59) ),
inference(resolution,[status(thm)],[d9,c49]) ).
cnf(d11,plain,
~ reflexive(sK59),
inference(resolution,[status(thm)],[c47,d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c48,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU252+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 08:59:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.90/6.84 % SZS status Theorem for theBenchmark.p
% 37.90/6.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------