%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO200+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 07:14:42 AM UTC 2026
% Result : Theorem 41.56s 5.94s
% Output : CNFRefutation 41.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 20 ~; 42 |; 1 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X0] : ~ 'distinct$upoints'(X0,X0) ).
fof(apart4,axiom,
! [X0,X1,X2] :
( 'distinct$upoints'(X0,X1)
=> ( 'distinct$upoints'(X1,X2)
| 'distinct$upoints'(X0,X2) ) ) ).
fof(ci1,axiom,
! [X0,X1] :
( 'distinct$upoints'(X0,X1)
=> ~ 'apart$upoint$uand$uline'(X0,'line$uconnecting'(X0,X1)) ) ).
fof(ci2,axiom,
! [X0,X1] :
( 'distinct$upoints'(X0,X1)
=> ~ 'apart$upoint$uand$uline'(X1,'line$uconnecting'(X0,X1)) ) ).
fof(cu1,axiom,
! [X0,X1,X2,X3] :
( ( 'distinct$ulines'(X2,X3)
& 'distinct$upoints'(X0,X1) )
=> ( 'apart$upoint$uand$uline'(X1,X3)
| 'apart$upoint$uand$uline'(X1,X2)
| 'apart$upoint$uand$uline'(X0,X3)
| 'apart$upoint$uand$uline'(X0,X2) ) ) ).
fof(ax2,axiom,
! [X0,X1] :
( 'equal$ulines'(X0,X1)
<=> ~ 'distinct$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1] :
( 'distinct$upoints'(X0,X1)
=> 'equal$ulines'('line$uconnecting'(X0,X1),'line$uconnecting'(X1,X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'distinct$upoints'(X0,X1)
=> 'equal$ulines'('line$uconnecting'(X0,X1),'line$uconnecting'(X1,X0)) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c0,plain,
~ 'distinct$upoints'(X0,X0),
inference(clausification,[status(esa)],[apart1]) ).
cnf(c3,plain,
( 'distinct$upoints'(X1,X2)
| 'distinct$upoints'(X0,X2)
| ~ 'distinct$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[apart4]) ).
cnf(c6,plain,
( ~ 'apart$upoint$uand$uline'(X0,'line$uconnecting'(X0,X1))
| ~ 'distinct$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[ci1]) ).
cnf(c7,plain,
( ~ 'apart$upoint$uand$uline'(X1,'line$uconnecting'(X0,X1))
| ~ 'distinct$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[ci2]) ).
cnf(c10,plain,
( 'apart$upoint$uand$uline'(X3,X2)
| 'apart$upoint$uand$uline'(X3,X1)
| ~ 'distinct$ulines'(X2,X1)
| ~ 'distinct$upoints'(X0,X3)
| 'apart$upoint$uand$uline'(X0,X2)
| 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[cu1]) ).
cnf(c39,plain,
( 'distinct$ulines'(X0,X1)
| 'equal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax2]) ).
cnf(c46,plain,
'distinct$upoints'(sK81,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
~ 'equal$ulines'('line$uconnecting'(sK81,sK82),'line$uconnecting'(sK82,sK81)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'distinct$upoints'(sK81,X0)
| 'distinct$upoints'(sK82,X0) ),
inference(resolution,[status(thm)],[c3,c46]) ).
cnf(d1,plain,
( 'distinct$upoints'(sK82,X1)
| 'distinct$upoints'(X0,X1)
| 'distinct$upoints'(sK81,X0) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( 'distinct$upoints'(sK81,X0)
| 'distinct$upoints'(X0,sK82) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
'distinct$ulines'('line$uconnecting'(sK81,sK82),'line$uconnecting'(sK82,sK81)),
inference(resolution,[status(thm)],[c39,c47]) ).
cnf(d4,plain,
( 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK82,sK81))
| 'apart$upoint$uand$uline'(X1,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(X1,'line$uconnecting'(sK82,sK81))
| ~ 'distinct$upoints'(X0,X1) ),
inference(resolution,[status(thm)],[d3,c10]) ).
cnf(d5,plain,
( 'distinct$upoints'(sK81,X0)
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK82,sK81))
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK82,sK81))
| 'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK81,sK82)) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ 'distinct$upoints'(sK82,sK81)
| 'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK82,sK81))
| 'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(sK81,'line$uconnecting'(sK81,sK82))
| 'distinct$upoints'(sK81,sK81) ),
inference(resolution,[status(thm)],[d5,c7]) ).
cnf(d7,plain,
( 'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK82,sK81))
| 'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(sK81,'line$uconnecting'(sK81,sK82))
| ~ 'distinct$upoints'(sK82,sK81) ),
inference(resolution,[status(thm)],[c0,d6]) ).
cnf(d8,plain,
( 'distinct$upoints'(sK81,X1)
| 'distinct$upoints'(X0,X1)
| 'distinct$upoints'(X0,sK82) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d9,plain,
( 'distinct$upoints'(X0,sK82)
| 'distinct$upoints'(X0,sK81) ),
inference(resolution,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
'distinct$upoints'(sK82,sK81),
inference(resolution,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
( 'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK82,sK81))
| 'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(sK81,'line$uconnecting'(sK81,sK82)) ),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( ~ 'distinct$upoints'(sK82,sK81)
| 'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(sK81,'line$uconnecting'(sK81,sK82)) ),
inference(resolution,[status(thm)],[d11,c6]) ).
cnf(d13,plain,
( 'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(sK81,'line$uconnecting'(sK81,sK82)) ),
inference(resolution,[status(thm)],[d10,d12]) ).
cnf(d14,plain,
( ~ 'distinct$upoints'(sK81,sK82)
| 'apart$upoint$uand$uline'(sK81,'line$uconnecting'(sK81,sK82)) ),
inference(resolution,[status(thm)],[d13,c7]) ).
cnf(d15,plain,
'apart$upoint$uand$uline'(sK81,'line$uconnecting'(sK81,sK82)),
inference(resolution,[status(thm)],[c46,d14]) ).
cnf(d16,plain,
~ 'distinct$upoints'(sK81,sK82),
inference(resolution,[status(thm)],[d15,c6]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[c46,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO200+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.62 % Computer : n014.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Fri Sep 25 13:05:04 UTC 2026
% 0.15/0.63 % CPUTime :
% 0.15/0.63 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.56/5.94 % SZS status Theorem for theBenchmark.p
% 41.56/5.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------