%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 06:48:06 AM UTC 2026
% Result : Theorem 6.37s 2.52s
% Output : CNFRefutation 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 71 ( 31 ~; 24 |; 8 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 46 ( 6 sgn 15 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(basis_of,axiom,
! [X0,X1] :
( 'basis$uof'(X0,X1)
=> ( 'a$usubset$uof'(X0,'vec$uto$uclass'(X1))
& 'lin$uind$usubset'(X0,X1) ) ) ).
fof(bg_2_2_5,axiom,
! [X0,X1,X2] :
( ( 'basis$uof'(X1,X2)
& 'lin$uind$usubset'(X0,X2) )
=> ? [X3] :
( 'basis$uof'(union(X0,X3),X2)
& 'a$usubset$uof'(X3,X1) ) ) ).
fof(bg_remark_63_a,axiom,
! [X0] :
( 'a$uvector$uspace'(X0)
=> ? [X1] : 'basis$uof'(X1,X0) ) ).
fof(bg_2_4_a,axiom,
! [X0,X1] :
( 'a$uvector$usubspace$uof'(X0,X1)
=> 'a$uvector$uspace'(X0) ) ).
fof(bg_2_4_2,axiom,
! [X0,X1,X2] :
( ( 'a$usubset$uof'(X2,'vec$uto$uclass'(X0))
& 'a$uvector$usubspace$uof'(X0,X1) )
=> ( 'lin$uind$usubset'(X2,X0)
<=> 'lin$uind$usubset'(X2,X1) ) ) ).
fof(bg_2_4_3,conjecture,
! [X0,X1] :
( ( 'a$uvector$uspace'(X1)
& 'a$uvector$usubspace$uof'(X0,X1) )
=> ? [X2,X3] :
( 'basis$uof'(X2,X0)
& 'basis$uof'(union(X2,X3),X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( 'a$uvector$uspace'(X1)
& 'a$uvector$usubspace$uof'(X0,X1) )
=> ? [X2,X3] :
( 'basis$uof'(X2,X0)
& 'basis$uof'(union(X2,X3),X1) ) ),
inference(negate_conjecture,[status(cth)],[bg_2_4_3]) ).
cnf(c0,plain,
( 'lin$uind$usubset'(X0,X1)
| ~ 'basis$uof'(X0,X1) ),
inference(clausification,[status(esa)],[basis_of]) ).
cnf(c1,plain,
( 'a$usubset$uof'(X0,'vec$uto$uclass'(X1))
| ~ 'basis$uof'(X0,X1) ),
inference(clausification,[status(esa)],[basis_of]) ).
cnf(c3,plain,
( 'basis$uof'(union(X0,sK5(X0,X2,X1)),X1)
| ~ 'basis$uof'(X2,X1)
| ~ 'lin$uind$usubset'(X0,X1) ),
inference(clausification,[status(esa)],[bg_2_2_5]) ).
cnf(c4,plain,
( 'basis$uof'(sK7(X0),X0)
| ~ 'a$uvector$uspace'(X0) ),
inference(clausification,[status(esa)],[bg_remark_63_a]) ).
cnf(c5,plain,
( 'a$uvector$uspace'(X0)
| ~ 'a$uvector$usubspace$uof'(X0,X1) ),
inference(clausification,[status(esa)],[bg_2_4_a]) ).
cnf(c6,plain,
( 'lin$uind$usubset'(X2,X1)
| ~ 'lin$uind$usubset'(X2,X0)
| ~ 'a$usubset$uof'(X2,'vec$uto$uclass'(X0))
| ~ 'a$uvector$usubspace$uof'(X0,X1) ),
inference(clausification,[status(esa)],[bg_2_4_2]) ).
cnf(c8,plain,
'a$uvector$usubspace$uof'(sK13,sK14),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c9,plain,
'a$uvector$uspace'(sK14),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10,plain,
( ~ 'basis$uof'(X0,sK13)
| ~ 'basis$uof'(union(X0,X1),sK14) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'basis$uof'(X1,sK13)
| ~ 'lin$uind$usubset'(X1,sK14)
| ~ 'basis$uof'(X0,sK14) ),
inference(resolution,[status(thm)],[c3,c10]) ).
cnf(d1,plain,
( 'lin$uind$usubset'(sK7(X0),X0)
| ~ 'a$uvector$uspace'(X0) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d2,plain,
( ~ 'basis$uof'(X0,X2)
| ~ 'a$uvector$usubspace$uof'(X2,X1)
| ~ 'lin$uind$usubset'(X0,X2)
| 'lin$uind$usubset'(X0,X1) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d3,plain,
( 'lin$uind$usubset'(X0,sK14)
| ~ 'lin$uind$usubset'(X0,sK13)
| ~ 'basis$uof'(X0,sK13) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
( ~ 'a$uvector$uspace'(sK13)
| 'lin$uind$usubset'(sK7(sK13),sK14)
| ~ 'basis$uof'(sK7(sK13),sK13) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
'a$uvector$uspace'(sK13),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(d6,plain,
( 'lin$uind$usubset'(sK7(sK13),sK14)
| ~ 'basis$uof'(sK7(sK13),sK13) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ 'a$uvector$uspace'(sK13)
| 'lin$uind$usubset'(sK7(sK13),sK14) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
'lin$uind$usubset'(sK7(sK13),sK14),
inference(resolution,[status(thm)],[d5,d7]) ).
cnf(d9,plain,
( ~ 'basis$uof'(X0,sK14)
| ~ 'basis$uof'(sK7(sK13),sK13) ),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
( ~ 'a$uvector$uspace'(sK13)
| ~ 'basis$uof'(X0,sK14) ),
inference(resolution,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
~ 'basis$uof'(X0,sK14),
inference(resolution,[status(thm)],[d5,d10]) ).
cnf(d12,plain,
~ 'a$uvector$uspace'(sK14),
inference(resolution,[status(thm)],[d11,c4]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c9,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n008.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 21:27:11 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.37/2.52 % SZS status Theorem for theBenchmark.p
% 6.37/2.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------