%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU387+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 : n001.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 08:41:51 AM UTC 2026
% Result : Theorem 15.93s 4.29s
% Output : CNFRefutation 15.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 19 unt; 0 def)
% Number of atoms : 159 ( 5 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 214 ( 93 ~; 77 |; 36 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-1 aty)
% Number of variables : 22 ( 7 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k3_yellow_1,axiom,
! [X0] :
( 'rel$ustr'('boole$uPOSet'(X0))
& 'strict$urel$ustr'('boole$uPOSet'(X0)) ) ).
fof(fc1_waybel_7,axiom,
! [X0] :
( 'complete$urelstr'('boole$uPOSet'(X0))
& 'with$uinfima$urelstr'('boole$uPOSet'(X0))
& 'with$usuprema$urelstr'('boole$uPOSet'(X0))
& 'boolean$urelstr'('boole$uPOSet'(X0))
& 'complemented$urelstr'('boole$uPOSet'(X0))
& 'heyting$urelstr'('boole$uPOSet'(X0))
& 'distributive$urelstr'('boole$uPOSet'(X0))
& ~ 'v1$uyellow$u3'('boole$uPOSet'(X0))
& 'join$ucomplete$urelstr'('boole$uPOSet'(X0))
& 'up$ucomplete$urelstr'('boole$uPOSet'(X0))
& 'bounded$urelstr'('boole$uPOSet'(X0))
& 'upper$ubounded$urelstr'('boole$uPOSet'(X0))
& 'lower$ubounded$urelstr'('boole$uPOSet'(X0))
& 'antisymmetric$urelstr'('boole$uPOSet'(X0))
& 'transitive$urelstr'('boole$uPOSet'(X0))
& 'reflexive$urelstr'('boole$uPOSet'(X0))
& 'strict$urel$ustr'('boole$uPOSet'(X0))
& ~ 'empty$ucarrier'('boole$uPOSet'(X0)) ) ).
fof(t18_yellow_1,axiom,
! [X0] : 'bottom$uof$urelstr'('boole$uPOSet'(X0)) = 'empty$uset' ).
fof(t6_boole,axiom,
! [X0] :
( empty(X0)
=> X0 = 'empty$uset' ) ).
fof(t8_waybel_7,axiom,
! [X0] :
( ( 'rel$ustr'(X0)
& 'lower$ubounded$urelstr'(X0)
& 'antisymmetric$urelstr'(X0)
& 'transitive$urelstr'(X0)
& 'reflexive$urelstr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( ( element(X1,powerset('the$ucarrier'(X0)))
& 'upper$urelstr$usubset'(X1,X0)
& 'filtered$usubset'(X1,X0)
& ~ empty(X1) )
=> ( 'proper$uelement'(X1,powerset('the$ucarrier'(X0)))
<=> ~ in('bottom$uof$urelstr'(X0),X1) ) ) ) ).
fof(t2_yellow19,conjecture,
! [X0] :
( ~ empty(X0)
=> ! [X1] :
( ( element(X1,powerset('the$ucarrier'('boole$uPOSet'(X0))))
& 'proper$uelement'(X1,powerset('the$ucarrier'('boole$uPOSet'(X0))))
& 'upper$urelstr$usubset'(X1,'boole$uPOSet'(X0))
& 'filtered$usubset'(X1,'boole$uPOSet'(X0))
& ~ empty(X1) )
=> ! [X2] :
~ ( empty(X2)
& in(X2,X1) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ! [X1] :
( ( element(X1,powerset('the$ucarrier'('boole$uPOSet'(X0))))
& 'proper$uelement'(X1,powerset('the$ucarrier'('boole$uPOSet'(X0))))
& 'upper$urelstr$usubset'(X1,'boole$uPOSet'(X0))
& 'filtered$usubset'(X1,'boole$uPOSet'(X0))
& ~ empty(X1) )
=> ! [X2] :
~ ( empty(X2)
& in(X2,X1) ) ) ),
inference(negate_conjecture,[status(cth)],[t2_yellow19]) ).
cnf(c61,plain,
'rel$ustr'('boole$uPOSet'(X0)),
inference(clausification,[status(esa)],[dt_k3_yellow_1]) ).
cnf(c76,plain,
~ 'empty$ucarrier'('boole$uPOSet'(X0)),
inference(clausification,[status(esa)],[fc1_waybel_7]) ).
cnf(c78,plain,
'reflexive$urelstr'('boole$uPOSet'(X0)),
inference(clausification,[status(esa)],[fc1_waybel_7]) ).
cnf(c79,plain,
'transitive$urelstr'('boole$uPOSet'(X0)),
inference(clausification,[status(esa)],[fc1_waybel_7]) ).
cnf(c80,plain,
'antisymmetric$urelstr'('boole$uPOSet'(X0)),
inference(clausification,[status(esa)],[fc1_waybel_7]) ).
cnf(c81,plain,
'lower$ubounded$urelstr'('boole$uPOSet'(X0)),
inference(clausification,[status(esa)],[fc1_waybel_7]) ).
cnf(c270,plain,
'bottom$uof$urelstr'('boole$uPOSet'(X0)) = 'empty$uset',
inference(clausification,[status(esa)],[t18_yellow_1]) ).
cnf(c277,plain,
( X0 = 'empty$uset'
| ~ empty(X0) ),
inference(clausification,[status(esa)],[t6_boole]) ).
cnf(c280,plain,
( ~ 'proper$uelement'(X0,powerset('the$ucarrier'(X1)))
| ~ 'rel$ustr'(X1)
| ~ element(X0,powerset('the$ucarrier'(X1)))
| ~ in('bottom$uof$urelstr'(X1),X0)
| ~ 'transitive$urelstr'(X1)
| ~ 'filtered$usubset'(X0,X1)
| 'empty$ucarrier'(X1)
| ~ 'lower$ubounded$urelstr'(X1)
| ~ 'antisymmetric$urelstr'(X1)
| ~ 'upper$urelstr$usubset'(X0,X1)
| ~ 'reflexive$urelstr'(X1)
| empty(X0) ),
inference(clausification,[status(esa)],[t8_waybel_7]) ).
cnf(c283,plain,
~ empty(sK120),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c284,plain,
'filtered$usubset'(sK120,'boole$uPOSet'(sK119)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c285,plain,
'upper$urelstr$usubset'(sK120,'boole$uPOSet'(sK119)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c286,plain,
'proper$uelement'(sK120,powerset('the$ucarrier'('boole$uPOSet'(sK119)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c287,plain,
element(sK120,powerset('the$ucarrier'('boole$uPOSet'(sK119)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c288,plain,
in(sK121,sK120),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c289,plain,
empty(sK121),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'upper$urelstr$usubset'(sK120,'boole$uPOSet'(sK119))
| ~ 'filtered$usubset'(sK120,'boole$uPOSet'(sK119))
| ~ element(sK120,powerset('the$ucarrier'('boole$uPOSet'(sK119))))
| empty(sK120)
| ~ 'antisymmetric$urelstr'('boole$uPOSet'(sK119))
| ~ 'transitive$urelstr'('boole$uPOSet'(sK119))
| ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| 'empty$ucarrier'('boole$uPOSet'(sK119))
| ~ 'reflexive$urelstr'('boole$uPOSet'(sK119))
| ~ in('bottom$uof$urelstr'('boole$uPOSet'(sK119)),sK120)
| ~ 'rel$ustr'('boole$uPOSet'(sK119)) ),
inference(resolution,[status(thm)],[c280,c286]) ).
cnf(d1,plain,
( ~ 'upper$urelstr$usubset'(sK120,'boole$uPOSet'(sK119))
| ~ 'filtered$usubset'(sK120,'boole$uPOSet'(sK119))
| ~ element(sK120,powerset('the$ucarrier'('boole$uPOSet'(sK119))))
| empty(sK120)
| ~ 'antisymmetric$urelstr'('boole$uPOSet'(sK119))
| ~ 'transitive$urelstr'('boole$uPOSet'(sK119))
| ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| 'empty$ucarrier'('boole$uPOSet'(sK119))
| ~ 'reflexive$urelstr'('boole$uPOSet'(sK119))
| ~ in('empty$uset',sK120)
| ~ 'rel$ustr'('boole$uPOSet'(sK119)) ),
inference(demodulation,[status(thm)],[d0,c270]) ).
cnf(d2,plain,
( ~ 'upper$urelstr$usubset'(sK120,'boole$uPOSet'(sK119))
| ~ 'filtered$usubset'(sK120,'boole$uPOSet'(sK119))
| ~ element(sK120,powerset('the$ucarrier'('boole$uPOSet'(sK119))))
| ~ 'antisymmetric$urelstr'('boole$uPOSet'(sK119))
| ~ 'transitive$urelstr'('boole$uPOSet'(sK119))
| ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| 'empty$ucarrier'('boole$uPOSet'(sK119))
| ~ 'reflexive$urelstr'('boole$uPOSet'(sK119))
| ~ in('empty$uset',sK120)
| ~ 'rel$ustr'('boole$uPOSet'(sK119)) ),
inference(resolution,[status(thm)],[c283,d1]) ).
cnf(d3,plain,
( ~ 'upper$urelstr$usubset'(sK120,'boole$uPOSet'(sK119))
| ~ element(sK120,powerset('the$ucarrier'('boole$uPOSet'(sK119))))
| ~ 'antisymmetric$urelstr'('boole$uPOSet'(sK119))
| ~ 'transitive$urelstr'('boole$uPOSet'(sK119))
| ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| 'empty$ucarrier'('boole$uPOSet'(sK119))
| ~ 'reflexive$urelstr'('boole$uPOSet'(sK119))
| ~ in('empty$uset',sK120)
| ~ 'rel$ustr'('boole$uPOSet'(sK119)) ),
inference(resolution,[status(thm)],[c284,d2]) ).
cnf(d4,plain,
( ~ element(sK120,powerset('the$ucarrier'('boole$uPOSet'(sK119))))
| ~ 'antisymmetric$urelstr'('boole$uPOSet'(sK119))
| ~ 'transitive$urelstr'('boole$uPOSet'(sK119))
| ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| 'empty$ucarrier'('boole$uPOSet'(sK119))
| ~ 'reflexive$urelstr'('boole$uPOSet'(sK119))
| ~ in('empty$uset',sK120)
| ~ 'rel$ustr'('boole$uPOSet'(sK119)) ),
inference(resolution,[status(thm)],[c285,d3]) ).
cnf(d5,plain,
( ~ 'antisymmetric$urelstr'('boole$uPOSet'(sK119))
| ~ 'transitive$urelstr'('boole$uPOSet'(sK119))
| ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| 'empty$ucarrier'('boole$uPOSet'(sK119))
| ~ 'reflexive$urelstr'('boole$uPOSet'(sK119))
| ~ in('empty$uset',sK120)
| ~ 'rel$ustr'('boole$uPOSet'(sK119)) ),
inference(resolution,[status(thm)],[c287,d4]) ).
cnf(d6,plain,
( ~ 'antisymmetric$urelstr'('boole$uPOSet'(sK119))
| ~ 'transitive$urelstr'('boole$uPOSet'(sK119))
| ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| 'empty$ucarrier'('boole$uPOSet'(sK119))
| ~ 'reflexive$urelstr'('boole$uPOSet'(sK119))
| ~ in('empty$uset',sK120) ),
inference(resolution,[status(thm)],[c61,d5]) ).
cnf(d7,plain,
( ~ 'antisymmetric$urelstr'('boole$uPOSet'(sK119))
| ~ 'transitive$urelstr'('boole$uPOSet'(sK119))
| ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| ~ 'reflexive$urelstr'('boole$uPOSet'(sK119))
| ~ in('empty$uset',sK120) ),
inference(resolution,[status(thm)],[c76,d6]) ).
cnf(d8,plain,
( ~ 'antisymmetric$urelstr'('boole$uPOSet'(sK119))
| ~ 'transitive$urelstr'('boole$uPOSet'(sK119))
| ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| ~ in('empty$uset',sK120) ),
inference(resolution,[status(thm)],[c78,d7]) ).
cnf(d9,plain,
( ~ 'antisymmetric$urelstr'('boole$uPOSet'(sK119))
| ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| ~ in('empty$uset',sK120) ),
inference(resolution,[status(thm)],[c79,d8]) ).
cnf(d10,plain,
( ~ 'lower$ubounded$urelstr'('boole$uPOSet'(sK119))
| ~ in('empty$uset',sK120) ),
inference(resolution,[status(thm)],[c80,d9]) ).
cnf(d11,plain,
~ in('empty$uset',sK120),
inference(resolution,[status(thm)],[c81,d10]) ).
cnf(d12,plain,
sK121 = 'empty$uset',
inference(resolution,[status(thm)],[c277,c289]) ).
cnf(d13,plain,
in('empty$uset',sK120),
inference(demodulation,[status(thm)],[c288,d12]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU387+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n001.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 09:30:13 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.93/4.29 % SZS status Theorem for theBenchmark.p
% 15.93/4.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------