%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU262+1 : 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 : n005.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 08:41:28 AM UTC 2026
% Result : Theorem 10.59s 3.94s
% Output : CNFRefutation 10.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 4 unt; 0 def)
% Number of atoms : 94 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 89 ( 35 ~; 37 |; 3 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 10 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [X0,X1,X2] :
( element(X2,powerset('cartesian$uproduct2'(X0,X1)))
=> relation(X2) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(d4_relat_1,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = 'relation$udom'(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in('ordered$upair'(X2,X3),X0) ) ) ) ).
fof(d5_relat_1,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = 'relation$urng'(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in('ordered$upair'(X3,X2),X0) ) ) ) ).
fof(dt_m2_relset_1,axiom,
! [X0,X1,X2] :
( 'relation$uof2$uas$usubset'(X2,X0,X1)
=> element(X2,powerset('cartesian$uproduct2'(X0,X1))) ) ).
fof(t106_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ) ).
fof(t3_subset,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ) ).
fof(t12_relset_1,conjecture,
! [X0,X1,X2] :
( 'relation$uof2$uas$usubset'(X2,X0,X1)
=> ( subset('relation$urng'(X2),X1)
& subset('relation$udom'(X2),X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( 'relation$uof2$uas$usubset'(X2,X0,X1)
=> ( subset('relation$urng'(X2),X1)
& subset('relation$udom'(X2),X0) ) ),
inference(negate_conjecture,[status(cth)],[t12_relset_1]) ).
cnf(c1,plain,
( relation(X0)
| ~ element(X0,powerset('cartesian$uproduct2'(X1,X2))) ),
inference(clausification,[status(esa)],[cc1_relset_1]) ).
cnf(c3,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c4,plain,
( in(sK10(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c5,plain,
( ~ in(sK10(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c6,plain,
( in('ordered$upair'(X2,sK14(X0,X2)),X0)
| ~ in(X2,X1)
| X1 != 'relation$udom'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d4_relat_1]) ).
cnf(c12,plain,
( in('ordered$upair'(sK22(X0,X2),X2),X0)
| ~ in(X2,X1)
| X1 != 'relation$urng'(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d5_relat_1]) ).
cnf(c19,plain,
( element(X0,powerset('cartesian$uproduct2'(X1,X2)))
| ~ 'relation$uof2$uas$usubset'(X0,X1,X2) ),
inference(clausification,[status(esa)],[dt_m2_relset_1]) ).
cnf(c30,plain,
( in(X0,X2)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[t106_zfmisc_1]) ).
cnf(c31,plain,
( in(X1,X3)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[t106_zfmisc_1]) ).
cnf(c35,plain,
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c42,plain,
'relation$uof2$uas$usubset'(sK72,sK70,sK71),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c43,plain,
( ~ subset('relation$urng'(sK72),sK71)
| ~ subset('relation$udom'(sK72),sK70) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ relation(X1)
| in('ordered$upair'(sK22(X1,X0),X0),X1)
| ~ in(X0,'relation$urng'(X1)) ),
inference(equality_resolution,[status(thm)],[c12]) ).
cnf(d1,plain,
( ~ 'relation$uof2$uas$usubset'(X0,X1,X2)
| subset(X0,'cartesian$uproduct2'(X1,X2)) ),
inference(resolution,[status(thm)],[c35,c19]) ).
cnf(d2,plain,
( ~ in(X3,X0)
| in(X3,'cartesian$uproduct2'(X1,X2))
| ~ 'relation$uof2$uas$usubset'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( in(X0,'cartesian$uproduct2'(sK70,sK71))
| ~ in(X0,sK72) ),
inference(resolution,[status(thm)],[d2,c42]) ).
cnf(d4,plain,
( in(X1,sK71)
| ~ in('ordered$upair'(X0,X1),sK72) ),
inference(resolution,[status(thm)],[d3,c31]) ).
cnf(d5,plain,
( ~ relation(sK72)
| ~ in(X0,'relation$urng'(sK72))
| in(X0,sK71) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( relation(X0)
| ~ 'relation$uof2$uas$usubset'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c19,c1]) ).
cnf(d7,plain,
relation(sK72),
inference(resolution,[status(thm)],[d6,c42]) ).
cnf(d8,plain,
( in(X0,sK71)
| ~ in(X0,'relation$urng'(sK72)) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( subset('relation$urng'(sK72),X0)
| in(sK10('relation$urng'(sK72),X0),sK71) ),
inference(resolution,[status(thm)],[d8,c4]) ).
cnf(d10,plain,
( subset('relation$urng'(sK72),sK71)
| subset('relation$urng'(sK72),sK71) ),
inference(resolution,[status(thm)],[d9,c5]) ).
cnf(d11,plain,
( ~ relation(X1)
| in('ordered$upair'(X0,sK14(X1,X0)),X1)
| ~ in(X0,'relation$udom'(X1)) ),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(d12,plain,
( in(X0,sK70)
| ~ in('ordered$upair'(X0,X1),sK72) ),
inference(resolution,[status(thm)],[d3,c30]) ).
cnf(d13,plain,
( ~ relation(sK72)
| ~ in(X0,'relation$udom'(sK72))
| in(X0,sK70) ),
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( in(X0,sK70)
| ~ in(X0,'relation$udom'(sK72)) ),
inference(resolution,[status(thm)],[d7,d13]) ).
cnf(d15,plain,
( subset('relation$udom'(sK72),X0)
| in(sK10('relation$udom'(sK72),X0),sK70) ),
inference(resolution,[status(thm)],[d14,c4]) ).
cnf(d16,plain,
( subset('relation$udom'(sK72),sK70)
| subset('relation$udom'(sK72),sK70) ),
inference(resolution,[status(thm)],[d15,c5]) ).
cnf(d17,plain,
~ subset('relation$urng'(sK72),sK71),
inference(resolution,[status(thm)],[d16,c43]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU262+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n005.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 09:00:17 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.59/3.94 % SZS status Theorem for theBenchmark.p
% 10.59/3.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------