%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO209+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 07:14:45 AM UTC 2026
% Result : Theorem 12.62s 3.80s
% Output : CNFRefutation 12.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 33 ( 10 ~; 10 |; 8 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 5 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X0] : ~ 'convergent$ulines'(X0,X0) ).
fof(ax6,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2) ) ) ).
fof(ceq2,axiom,
! [X0,X1,X2] :
( 'apart$upoint$uand$uline'(X0,X1)
=> ( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(p1,axiom,
! [X0,X1] :
( 'distinct$ulines'(X0,X1)
=> 'convergent$ulines'(X0,X1) ) ).
fof(cp1,axiom,
! [X0,X1] : ~ 'convergent$ulines'('parallel$uthrough$upoint'(X1,X0),X1) ).
fof(cp2,axiom,
! [X0,X1] : ~ 'apart$upoint$uand$uline'(X0,'parallel$uthrough$upoint'(X1,X0)) ).
fof(con,conjecture,
! [X0,X1,X2,X3] :
( ( 'parallel$ulines'(X3,X1)
& 'parallel$ulines'(X2,X1)
& 'incident$upoint$uand$uline'(X0,X3)
& 'incident$upoint$uand$uline'(X0,X2)
& 'apart$upoint$uand$uline'(X0,X1) )
=> 'equal$ulines'(X2,X3) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( 'parallel$ulines'(X3,X1)
& 'parallel$ulines'(X2,X1)
& 'incident$upoint$uand$uline'(X0,X3)
& 'incident$upoint$uand$uline'(X0,X2)
& 'apart$upoint$uand$uline'(X0,X1) )
=> 'equal$ulines'(X2,X3) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c2,plain,
~ 'convergent$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart3]) ).
cnf(c5,plain,
( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax6]) ).
cnf(c12,plain,
( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2)
| ~ 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ceq2]) ).
cnf(c14,plain,
( 'convergent$ulines'(X0,X1)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c15,plain,
~ 'convergent$ulines'('parallel$uthrough$upoint'(X0,X1),X0),
inference(clausification,[status(esa)],[cp1]) ).
cnf(c16,plain,
~ 'apart$upoint$uand$uline'(X0,'parallel$uthrough$upoint'(X1,X0)),
inference(clausification,[status(esa)],[cp2]) ).
cnf(c46,plain,
'apart$upoint$uand$uline'(sK81,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'apart$upoint$uand$uline'(sK81,X0)
| 'distinct$ulines'(sK82,X0) ),
inference(resolution,[status(thm)],[c12,c46]) ).
cnf(d1,plain,
( 'convergent$ulines'(sK82,X0)
| 'apart$upoint$uand$uline'(sK81,X0) ),
inference(resolution,[status(thm)],[d0,c14]) ).
cnf(d2,plain,
'convergent$ulines'(sK82,'parallel$uthrough$upoint'(X0,sK81)),
inference(resolution,[status(thm)],[d1,c16]) ).
cnf(d3,plain,
( 'convergent$ulines'(sK82,X1)
| 'convergent$ulines'('parallel$uthrough$upoint'(X0,sK81),X1) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
'convergent$ulines'(sK82,X0),
inference(resolution,[status(thm)],[d3,c15]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO209+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.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 13:05:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.62/3.80 % SZS status Theorem for theBenchmark.p
% 12.62/3.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------