%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO226+2 : 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 : n015.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 07:14:52 AM UTC 2026
% Result : Theorem 12.56s 2.28s
% Output : CNFRefutation 12.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 48 ( 21 ~; 14 |; 6 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X0] : ~ 'distinct$upoints'(X0,X0) ).
fof(apart3,axiom,
! [X0] : ~ 'convergent$ulines'(X0,X0) ).
fof(apart6,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2) ) ) ).
fof(con2,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( ( 'apart$upoint$uand$uline'(X2,X1)
| 'apart$upoint$uand$uline'(X2,X0) )
=> 'distinct$upoints'(X2,'intersection$upoint'(X0,X1)) ) ) ).
fof(con,conjecture,
! [X0,X1] :
( ( 'convergent$ulines'(X0,X1)
& line(X1)
& line(X0) )
=> ? [X2] :
( point(X2)
=> ( ~ 'apart$upoint$uand$uline'(X2,X1)
& ~ 'apart$upoint$uand$uline'(X2,X0) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( 'convergent$ulines'(X0,X1)
& line(X1)
& line(X0) )
=> ? [X2] :
( point(X2)
=> ( ~ 'apart$upoint$uand$uline'(X2,X1)
& ~ 'apart$upoint$uand$uline'(X2,X0) ) ) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c0,plain,
~ 'distinct$upoints'(X0,X0),
inference(clausification,[status(esa)],[apart1]) ).
cnf(c2,plain,
~ 'convergent$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart3]) ).
cnf(c5,plain,
( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[apart6]) ).
cnf(c8,plain,
( 'distinct$upoints'(X2,'intersection$upoint'(X0,X1))
| ~ 'apart$upoint$uand$uline'(X2,X0)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[con2]) ).
cnf(c9,plain,
( 'distinct$upoints'(X2,'intersection$upoint'(X0,X1))
| ~ 'apart$upoint$uand$uline'(X2,X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[con2]) ).
cnf(c20,plain,
'convergent$ulines'(sK38,sK39),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c22,plain,
( 'apart$upoint$uand$uline'(X0,sK39)
| 'apart$upoint$uand$uline'(X0,sK38) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'convergent$ulines'(sK38,X0)
| 'convergent$ulines'(sK39,X0) ),
inference(resolution,[status(thm)],[c5,c20]) ).
cnf(d1,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d2,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0)
| ~ 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d3,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK39,X0),sK38)
| ~ 'convergent$ulines'(sK39,X0) ),
inference(resolution,[status(thm)],[d2,c22]) ).
cnf(d4,plain,
( ~ 'convergent$ulines'(sK39,sK38)
| ~ 'convergent$ulines'(sK39,sK38) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
'convergent$ulines'(sK38,sK38),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c2,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO226+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 13:11:57 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.56/2.28 % SZS status Theorem for theBenchmark.p
% 12.56/2.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------