%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU337+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 : 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 08:41:42 AM UTC 2026
% Result : Theorem 65.84s 28.98s
% Output : CNFRefutation 65.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 10 unt; 0 def)
% Number of atoms : 301 ( 15 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 363 ( 156 ~; 174 |; 1 &)
% ( 8 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tops_2,axiom,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset(powerset('the$ucarrier'(X0))))
=> ( 'open$usubsets'(X1,X0)
<=> ! [X2] :
( element(X2,powerset('the$ucarrier'(X0)))
=> ( in(X2,X1)
=> 'open$usubset'(X2,X0) ) ) ) ) ) ).
fof(d2_tops_2,axiom,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset(powerset('the$ucarrier'(X0))))
=> ( 'closed$usubsets'(X1,X0)
<=> ! [X2] :
( element(X2,powerset('the$ucarrier'(X0)))
=> ( in(X2,X1)
=> 'closed$usubset'(X2,X0) ) ) ) ) ) ).
fof(d8_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( X2 = 'complements$uof$usubsets'(X0,X1)
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in('subset$ucomplement'(X0,X3),X1) ) ) ) ) ) ).
fof(dt_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element('subset$ucomplement'(X0,X1),powerset(X0)) ) ).
fof(dt_k7_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element('complements$uof$usubsets'(X0,X1),powerset(powerset(X0))) ) ).
fof(involutiveness_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> 'subset$ucomplement'(X0,'subset$ucomplement'(X0,X1)) = X1 ) ).
fof(involutiveness_k7_setfam_1,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> 'complements$uof$usubsets'(X0,'complements$uof$usubsets'(X0,X1)) = X1 ) ).
fof(t29_tops_1,axiom,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ( 'closed$usubset'(X1,X0)
<=> 'open$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0) ) ) ) ).
fof(t30_tops_1,axiom,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ( 'open$usubset'(X1,X0)
<=> 'closed$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0) ) ) ) ).
fof(t4_subset,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ) ).
fof(t17_tops_2,conjecture,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset(powerset('the$ucarrier'(X0))))
=> ( 'open$usubsets'(X1,X0)
<=> 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(X0),X1),X0) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset(powerset('the$ucarrier'(X0))))
=> ( 'open$usubsets'(X1,X0)
<=> 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(X0),X1),X0) ) ) ),
inference(negate_conjecture,[status(cth)],[t17_tops_2]) ).
cnf(c43,plain,
( 'open$usubset'(X2,X1)
| ~ element(X0,powerset(powerset('the$ucarrier'(X1))))
| ~ element(X2,powerset('the$ucarrier'(X1)))
| ~ 'top$ustr'(X1)
| ~ in(X2,X0)
| ~ 'open$usubsets'(X0,X1) ),
inference(clausification,[status(esa)],[d1_tops_2]) ).
cnf(c45,plain,
( ~ 'open$usubset'(sK33(X0,X1),X0)
| 'open$usubsets'(X1,X0)
| ~ element(X1,powerset(powerset('the$ucarrier'(X0))))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[d1_tops_2]) ).
cnf(c46,plain,
( in(sK33(X0,X1),X1)
| 'open$usubsets'(X1,X0)
| ~ element(X1,powerset(powerset('the$ucarrier'(X0))))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[d1_tops_2]) ).
cnf(c47,plain,
( ~ 'top$ustr'(X1)
| ~ in(X2,X0)
| ~ element(X2,powerset('the$ucarrier'(X1)))
| 'closed$usubset'(X2,X1)
| ~ element(X0,powerset(powerset('the$ucarrier'(X1))))
| ~ 'closed$usubsets'(X0,X1) ),
inference(clausification,[status(esa)],[d2_tops_2]) ).
cnf(c48,plain,
( element(sK37(X0,X1),powerset('the$ucarrier'(X0)))
| 'closed$usubsets'(X1,X0)
| ~ element(X1,powerset(powerset('the$ucarrier'(X0))))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[d2_tops_2]) ).
cnf(c49,plain,
( ~ 'closed$usubset'(sK37(X0,X1),X0)
| 'closed$usubsets'(X1,X0)
| ~ element(X1,powerset(powerset('the$ucarrier'(X0))))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[d2_tops_2]) ).
cnf(c50,plain,
( in(sK37(X0,X1),X1)
| 'closed$usubsets'(X1,X0)
| ~ element(X1,powerset(powerset('the$ucarrier'(X0))))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[d2_tops_2]) ).
cnf(c51,plain,
( ~ in(X0,X3)
| 'complements$uof$usubsets'(X1,X2) != X3
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1)))
| in('subset$ucomplement'(X1,X0),X2)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[d8_setfam_1]) ).
cnf(c59,plain,
( element('subset$ucomplement'(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[dt_k3_subset_1]) ).
cnf(c60,plain,
( element('complements$uof$usubsets'(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(clausification,[status(esa)],[dt_k7_setfam_1]) ).
cnf(c72,plain,
( 'subset$ucomplement'(X1,'subset$ucomplement'(X1,X0)) = X0
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[involutiveness_k3_subset_1]) ).
cnf(c73,plain,
( 'complements$uof$usubsets'(X1,'complements$uof$usubsets'(X1,X0)) = X0
| ~ element(X0,powerset(powerset(X1))) ),
inference(clausification,[status(esa)],[involutiveness_k7_setfam_1]) ).
cnf(c87,plain,
( ~ 'open$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0)
| 'closed$usubset'(X1,X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[t29_tops_1]) ).
cnf(c90,plain,
( ~ 'closed$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0)
| 'open$usubset'(X1,X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[t30_tops_1]) ).
cnf(c93,plain,
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t4_subset]) ).
cnf(c98,plain,
'top$ustr'(sK86),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c99,plain,
element(sK87,powerset(powerset('the$ucarrier'(sK86)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c101,plain,
( 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),sK86)
| 'open$usubsets'(sK87,sK86) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c102,plain,
( ~ 'open$usubsets'(sK87,sK86)
| ~ 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),sK86) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ element(X2,powerset(powerset(X1)))
| ~ element('complements$uof$usubsets'(X1,X2),powerset(powerset(X1)))
| ~ element(X0,powerset(X1))
| in('subset$ucomplement'(X1,X0),X2)
| ~ in(X0,'complements$uof$usubsets'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c51]) ).
cnf(d1,plain,
( ~ element(X2,powerset(X1))
| ~ element(X0,powerset(powerset(X1)))
| in('subset$ucomplement'(X1,X2),X0)
| ~ in(X2,'complements$uof$usubsets'(X1,X0))
| ~ element(X0,powerset(powerset(X1))) ),
inference(resolution,[status(thm)],[c60,d0]) ).
cnf(d2,plain,
( ~ element(X0,powerset('the$ucarrier'(sK86)))
| in('subset$ucomplement'('the$ucarrier'(sK86),X0),sK87)
| ~ in(X0,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)) ),
inference(resolution,[status(thm)],[d1,c99]) ).
cnf(d3,plain,
( ~ element(X2,powerset(powerset(X1)))
| element(X0,powerset(X1))
| ~ in(X0,'complements$uof$usubsets'(X1,X2)) ),
inference(resolution,[status(thm)],[c93,c60]) ).
cnf(d4,plain,
( element(X0,powerset('the$ucarrier'(sK86)))
| ~ in(X0,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)) ),
inference(resolution,[status(thm)],[d3,c99]) ).
cnf(d5,plain,
( in('subset$ucomplement'('the$ucarrier'(sK86),X0),sK87)
| ~ in(X0,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))
| ~ in(X0,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
'complements$uof$usubsets'('the$ucarrier'(sK86),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)) = sK87,
inference(resolution,[status(thm)],[c73,c99]) ).
cnf(d7,plain,
( ~ element('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),powerset(powerset('the$ucarrier'(sK86))))
| ~ element(X0,powerset(powerset('the$ucarrier'(sK86))))
| ~ element(X1,powerset('the$ucarrier'(sK86)))
| in('subset$ucomplement'('the$ucarrier'(sK86),X1),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))
| ~ in(X1,X0)
| sK87 != X0 ),
inference(superposition,[status(thm)],[d6,c51]) ).
cnf(d8,plain,
( ~ element('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),powerset(powerset('the$ucarrier'(sK86))))
| ~ element(sK87,powerset(powerset('the$ucarrier'(sK86))))
| ~ element(X0,powerset('the$ucarrier'(sK86)))
| in('subset$ucomplement'('the$ucarrier'(sK86),X0),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))
| ~ in(X0,sK87) ),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( ~ element('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),powerset(powerset('the$ucarrier'(sK86))))
| ~ element(X0,powerset('the$ucarrier'(sK86)))
| in('subset$ucomplement'('the$ucarrier'(sK86),X0),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[c99,d8]) ).
cnf(d10,plain,
( element(X0,powerset('the$ucarrier'(sK86)))
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[c93,c99]) ).
cnf(d11,plain,
( ~ element('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),powerset(powerset('the$ucarrier'(sK86))))
| in('subset$ucomplement'('the$ucarrier'(sK86),X0),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))
| ~ in(X0,sK87)
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( ~ element(sK87,powerset(powerset('the$ucarrier'(sK86))))
| in('subset$ucomplement'('the$ucarrier'(sK86),X0),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d11,c60]) ).
cnf(d13,plain,
( in('subset$ucomplement'('the$ucarrier'(sK86),X0),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[c99,d12]) ).
cnf(d14,plain,
( in('subset$ucomplement'('the$ucarrier'(sK86),'subset$ucomplement'('the$ucarrier'(sK86),X0)),sK87)
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
( 'open$usubset'(X0,sK86)
| ~ 'open$usubsets'(sK87,sK86)
| ~ 'top$ustr'(sK86)
| ~ element(X0,powerset('the$ucarrier'(sK86)))
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[c43,c99]) ).
cnf(d16,plain,
( 'open$usubset'(X0,sK86)
| ~ 'open$usubsets'(sK87,sK86)
| ~ element(X0,powerset('the$ucarrier'(sK86)))
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[c98,d15]) ).
cnf(d17,plain,
( 'open$usubset'(X0,sK86)
| ~ 'open$usubsets'(sK87,sK86)
| ~ in(X0,sK87)
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d10,d16]) ).
cnf(d18,plain,
( 'open$usubsets'(sK87,sK86)
| ~ 'top$ustr'(sK86)
| in(sK33(sK86,sK87),sK87) ),
inference(resolution,[status(thm)],[c46,c99]) ).
cnf(d19,plain,
( 'open$usubsets'(sK87,sK86)
| in(sK33(sK86,sK87),sK87) ),
inference(resolution,[status(thm)],[c98,d18]) ).
cnf(d20,plain,
( 'closed$usubset'(X2,X1)
| ~ 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(X1),X0),X1)
| ~ 'top$ustr'(X1)
| ~ element(X2,powerset('the$ucarrier'(X1)))
| ~ in(X2,'complements$uof$usubsets'('the$ucarrier'(X1),X0))
| ~ element(X0,powerset(powerset('the$ucarrier'(X1)))) ),
inference(resolution,[status(thm)],[c60,c47]) ).
cnf(d21,plain,
( 'open$usubsets'(sK87,sK86)
| 'closed$usubset'(X0,sK86)
| ~ 'top$ustr'(sK86)
| ~ element(sK87,powerset(powerset('the$ucarrier'(sK86))))
| ~ element(X0,powerset('the$ucarrier'(sK86)))
| ~ in(X0,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)) ),
inference(resolution,[status(thm)],[d20,c101]) ).
cnf(d22,plain,
( 'closed$usubset'(X0,sK86)
| 'open$usubsets'(sK87,sK86)
| ~ element(sK87,powerset(powerset('the$ucarrier'(sK86))))
| ~ element(X0,powerset('the$ucarrier'(sK86)))
| ~ in(X0,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)) ),
inference(resolution,[status(thm)],[c98,d21]) ).
cnf(d23,plain,
( 'closed$usubset'(X0,sK86)
| 'open$usubsets'(sK87,sK86)
| ~ element(X0,powerset('the$ucarrier'(sK86)))
| ~ in(X0,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)) ),
inference(resolution,[status(thm)],[c99,d22]) ).
cnf(d24,plain,
( 'closed$usubset'(X0,sK86)
| 'open$usubsets'(sK87,sK86)
| ~ in(X0,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))
| ~ in(X0,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)) ),
inference(resolution,[status(thm)],[d4,d23]) ).
cnf(d25,plain,
( 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK86),X0),sK86)
| 'open$usubsets'(sK87,sK86)
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d13,d24]) ).
cnf(d26,plain,
( 'open$usubset'(X0,sK86)
| ~ 'top$ustr'(sK86)
| ~ element(X0,powerset('the$ucarrier'(sK86)))
| 'open$usubsets'(sK87,sK86)
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d25,c90]) ).
cnf(d27,plain,
( 'open$usubset'(X0,sK86)
| 'open$usubsets'(sK87,sK86)
| ~ element(X0,powerset('the$ucarrier'(sK86)))
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[c98,d26]) ).
cnf(d28,plain,
( 'open$usubset'(X0,sK86)
| 'open$usubsets'(sK87,sK86)
| ~ in(X0,sK87)
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d10,d27]) ).
cnf(d29,plain,
( 'open$usubsets'(sK87,sK86)
| 'open$usubset'(sK33(sK86,sK87),sK86)
| 'open$usubsets'(sK87,sK86) ),
inference(resolution,[status(thm)],[d28,d19]) ).
cnf(d30,plain,
( ~ 'open$usubset'(sK33(sK86,sK87),sK86)
| 'open$usubsets'(sK87,sK86)
| ~ 'top$ustr'(sK86) ),
inference(resolution,[status(thm)],[c45,c99]) ).
cnf(d31,plain,
( ~ 'open$usubset'(sK33(sK86,sK87),sK86)
| 'open$usubsets'(sK87,sK86) ),
inference(resolution,[status(thm)],[c98,d30]) ).
cnf(d32,plain,
( 'open$usubsets'(sK87,sK86)
| 'open$usubsets'(sK87,sK86) ),
inference(resolution,[status(thm)],[d31,d29]) ).
cnf(d33,plain,
( 'open$usubset'(X0,sK86)
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d32,d17]) ).
cnf(d34,plain,
( ~ in(X0,sK87)
| 'open$usubset'('subset$ucomplement'('the$ucarrier'(sK86),'subset$ucomplement'('the$ucarrier'(sK86),X0)),sK86) ),
inference(resolution,[status(thm)],[d33,d14]) ).
cnf(d35,plain,
( 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK86),X0),sK86)
| ~ 'top$ustr'(sK86)
| ~ element('subset$ucomplement'('the$ucarrier'(sK86),X0),powerset('the$ucarrier'(sK86)))
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d34,c87]) ).
cnf(d36,plain,
( 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK86),X0),sK86)
| ~ element('subset$ucomplement'('the$ucarrier'(sK86),X0),powerset('the$ucarrier'(sK86)))
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[c98,d35]) ).
cnf(d37,plain,
( element('subset$ucomplement'('the$ucarrier'(sK86),X0),powerset('the$ucarrier'(sK86)))
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d13,d4]) ).
cnf(d38,plain,
( 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK86),X0),sK86)
| ~ in(X0,sK87)
| ~ in(X0,sK87) ),
inference(resolution,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
( 'closed$usubsets'(X1,X0)
| ~ 'top$ustr'(X0)
| ~ element(X1,powerset(powerset('the$ucarrier'(X0))))
| 'subset$ucomplement'('the$ucarrier'(X0),'subset$ucomplement'('the$ucarrier'(X0),sK37(X0,X1))) = sK37(X0,X1) ),
inference(resolution,[status(thm)],[c72,c48]) ).
cnf(d40,plain,
( ~ element(X1,powerset(powerset('the$ucarrier'(X0))))
| 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(X0),X1),X0)
| ~ 'top$ustr'(X0)
| 'subset$ucomplement'('the$ucarrier'(X0),'subset$ucomplement'('the$ucarrier'(X0),sK37(X0,'complements$uof$usubsets'('the$ucarrier'(X0),X1)))) = sK37(X0,'complements$uof$usubsets'('the$ucarrier'(X0),X1)) ),
inference(resolution,[status(thm)],[d39,c60]) ).
cnf(d41,plain,
( 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),sK86)
| ~ 'top$ustr'(sK86)
| 'subset$ucomplement'('the$ucarrier'(sK86),'subset$ucomplement'('the$ucarrier'(sK86),sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)))) = sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)) ),
inference(resolution,[status(thm)],[d40,c99]) ).
cnf(d42,plain,
( 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),sK86)
| 'subset$ucomplement'('the$ucarrier'(sK86),'subset$ucomplement'('the$ucarrier'(sK86),sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)))) = sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)) ),
inference(resolution,[status(thm)],[c98,d41]) ).
cnf(d43,plain,
~ 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),sK86),
inference(resolution,[status(thm)],[d32,c102]) ).
cnf(d44,plain,
'subset$ucomplement'('the$ucarrier'(sK86),'subset$ucomplement'('the$ucarrier'(sK86),sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)))) = sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),
inference(resolution,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
( ~ in('subset$ucomplement'('the$ucarrier'(sK86),sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))),sK87)
| 'closed$usubset'(sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),sK86) ),
inference(superposition,[status(thm)],[d44,d38]) ).
cnf(d46,plain,
( 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(X1),X0),X1)
| ~ 'top$ustr'(X1)
| in(sK37(X1,'complements$uof$usubsets'('the$ucarrier'(X1),X0)),'complements$uof$usubsets'('the$ucarrier'(X1),X0))
| ~ element(X0,powerset(powerset('the$ucarrier'(X1)))) ),
inference(resolution,[status(thm)],[c60,c50]) ).
cnf(d47,plain,
( 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),sK86)
| ~ 'top$ustr'(sK86)
| ~ element(sK87,powerset(powerset('the$ucarrier'(sK86))))
| in('subset$ucomplement'('the$ucarrier'(sK86),sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))),sK87) ),
inference(resolution,[status(thm)],[d5,d46]) ).
cnf(d48,plain,
( 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),sK86)
| ~ element(sK87,powerset(powerset('the$ucarrier'(sK86))))
| in('subset$ucomplement'('the$ucarrier'(sK86),sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))),sK87) ),
inference(resolution,[status(thm)],[c98,d47]) ).
cnf(d49,plain,
( 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),sK86)
| in('subset$ucomplement'('the$ucarrier'(sK86),sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))),sK87) ),
inference(resolution,[status(thm)],[c99,d48]) ).
cnf(d50,plain,
in('subset$ucomplement'('the$ucarrier'(sK86),sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))),sK87),
inference(resolution,[status(thm)],[d43,d49]) ).
cnf(d51,plain,
'closed$usubset'(sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),sK86),
inference(resolution,[status(thm)],[d50,d45]) ).
cnf(d52,plain,
( ~ element(X1,powerset(powerset(X0)))
| 'subset$ucomplement'(powerset(X0),'subset$ucomplement'(powerset(X0),'complements$uof$usubsets'(X0,X1))) = 'complements$uof$usubsets'(X0,X1) ),
inference(resolution,[status(thm)],[c72,c60]) ).
cnf(d53,plain,
'subset$ucomplement'(powerset('the$ucarrier'(sK86)),'subset$ucomplement'(powerset('the$ucarrier'(sK86)),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))) = 'complements$uof$usubsets'('the$ucarrier'(sK86),sK87),
inference(resolution,[status(thm)],[d52,c99]) ).
cnf(d54,plain,
( ~ 'closed$usubset'(sK37(X1,'subset$ucomplement'(powerset('the$ucarrier'(X1)),X0)),X1)
| 'closed$usubsets'('subset$ucomplement'(powerset('the$ucarrier'(X1)),X0),X1)
| ~ 'top$ustr'(X1)
| ~ element(X0,powerset(powerset('the$ucarrier'(X1)))) ),
inference(resolution,[status(thm)],[c59,c49]) ).
cnf(d55,plain,
( 'closed$usubsets'('subset$ucomplement'(powerset('the$ucarrier'(sK86)),'subset$ucomplement'(powerset('the$ucarrier'(sK86)),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87))),sK86)
| ~ 'top$ustr'(sK86)
| ~ element('subset$ucomplement'(powerset('the$ucarrier'(sK86)),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),powerset(powerset('the$ucarrier'(sK86))))
| ~ 'closed$usubset'(sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),sK86) ),
inference(superposition,[status(thm)],[d53,d54]) ).
cnf(d56,plain,
( ~ 'closed$usubset'(sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),sK86)
| 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),sK86)
| ~ 'top$ustr'(sK86)
| ~ element('subset$ucomplement'(powerset('the$ucarrier'(sK86)),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),powerset(powerset('the$ucarrier'(sK86)))) ),
inference(demodulation,[status(thm)],[d55,d53]) ).
cnf(d57,plain,
( ~ 'closed$usubset'(sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),sK86)
| 'closed$usubsets'('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),sK86)
| ~ element('subset$ucomplement'(powerset('the$ucarrier'(sK86)),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),powerset(powerset('the$ucarrier'(sK86)))) ),
inference(resolution,[status(thm)],[c98,d56]) ).
cnf(d58,plain,
( ~ 'closed$usubset'(sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),sK86)
| ~ element('subset$ucomplement'(powerset('the$ucarrier'(sK86)),'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),powerset(powerset('the$ucarrier'(sK86)))) ),
inference(resolution,[status(thm)],[d43,d57]) ).
cnf(d59,plain,
( ~ element('complements$uof$usubsets'('the$ucarrier'(sK86),sK87),powerset(powerset('the$ucarrier'(sK86))))
| ~ 'closed$usubset'(sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),sK86) ),
inference(resolution,[status(thm)],[d58,c59]) ).
cnf(d60,plain,
( ~ element(sK87,powerset(powerset('the$ucarrier'(sK86))))
| ~ 'closed$usubset'(sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),sK86) ),
inference(resolution,[status(thm)],[d59,c60]) ).
cnf(d61,plain,
~ 'closed$usubset'(sK37(sK86,'complements$uof$usubsets'('the$ucarrier'(sK86),sK87)),sK86),
inference(resolution,[status(thm)],[c99,d60]) ).
cnf(d62,plain,
$false,
inference(resolution,[status(thm)],[d61,d51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU337+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 09:15:48 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.84/28.98 % SZS status Theorem for theBenchmark.p
% 65.84/28.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------