%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO209+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 15.40s 2.63s
% Output : CNFRefutation 15.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 41 ( 17 ~; 12 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart6,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2) ) ) ).
fof(cup1,axiom,
! [X0,X1,X2] :
( 'distinct$ulines'(X1,X2)
=> ( 'convergent$ulines'(X1,X2)
| 'apart$upoint$uand$uline'(X0,X2)
| 'apart$upoint$uand$uline'(X0,X1) ) ) ).
fof(con,conjecture,
! [X0,X1,X2,X3] :
( ( ~ 'convergent$ulines'(X3,X1)
& ~ 'convergent$ulines'(X2,X1)
& ~ 'apart$upoint$uand$uline'(X0,X3)
& ~ 'apart$upoint$uand$uline'(X0,X2)
& 'apart$upoint$uand$uline'(X0,X1) )
=> ~ 'distinct$ulines'(X2,X3) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ~ 'convergent$ulines'(X3,X1)
& ~ 'convergent$ulines'(X2,X1)
& ~ 'apart$upoint$uand$uline'(X0,X3)
& ~ 'apart$upoint$uand$uline'(X0,X2)
& 'apart$upoint$uand$uline'(X0,X1) )
=> ~ 'distinct$ulines'(X2,X3) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c5,plain,
( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[apart6]) ).
cnf(c16,plain,
( 'convergent$ulines'(X0,X1)
| 'apart$upoint$uand$uline'(X2,X1)
| 'apart$upoint$uand$uline'(X2,X0)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[cup1]) ).
cnf(c18,plain,
~ 'apart$upoint$uand$uline'(sK37,sK39),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
~ 'apart$upoint$uand$uline'(sK37,sK40),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c20,plain,
~ 'convergent$ulines'(sK39,sK38),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c21,plain,
~ 'convergent$ulines'(sK40,sK38),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c22,plain,
'distinct$ulines'(sK39,sK40),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'apart$upoint$uand$uline'(X0,sK39)
| 'apart$upoint$uand$uline'(X0,sK40)
| 'convergent$ulines'(sK39,sK40) ),
inference(resolution,[status(thm)],[c16,c22]) ).
cnf(d1,plain,
( 'apart$upoint$uand$uline'(sK37,sK39)
| 'convergent$ulines'(sK39,sK40) ),
inference(resolution,[status(thm)],[d0,c19]) ).
cnf(d2,plain,
'convergent$ulines'(sK39,sK40),
inference(resolution,[status(thm)],[c18,d1]) ).
cnf(d3,plain,
( 'convergent$ulines'(sK39,X0)
| 'convergent$ulines'(sK40,X0) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
'convergent$ulines'(sK39,sK38),
inference(resolution,[status(thm)],[d3,c21]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c20,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO209+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 13:08:35 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.40/2.63 % SZS status Theorem for theBenchmark.p
% 15.40/2.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------