%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO189+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 : 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 07:14:38 AM UTC 2026
% Result : Theorem 8.37s 2.45s
% Output : CNFRefutation 8.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 37 ( 12 ~; 13 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 3 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X0] : ~ 'distinct$ulines'(X0,X0) ).
fof(apart5,axiom,
! [X0,X1,X2] :
( 'distinct$ulines'(X0,X1)
=> ( 'distinct$ulines'(X1,X2)
| 'distinct$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$upoint'(X1,X0)) ).
fof(a4,axiom,
! [X0,X1] :
( 'incident$upoint$uand$uline'(X0,X1)
<=> ~ 'apart$upoint$uand$uline'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( 'incident$upoint$uand$uline'(X2,'line$uconnecting'(X0,X1))
& 'distinct$upoints'(X1,X2)
& 'distinct$upoints'(X0,X2)
& 'distinct$upoints'(X0,X1) )
=> 'incident$upoint$uand$uline'(X1,'line$uconnecting'(X0,X2)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'incident$upoint$uand$uline'(X2,'line$uconnecting'(X0,X1))
& 'distinct$upoints'(X1,X2)
& 'distinct$upoints'(X0,X2)
& 'distinct$upoints'(X0,X1) )
=> 'incident$upoint$uand$uline'(X1,'line$uconnecting'(X0,X2)) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c1,plain,
~ 'distinct$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart2]) ).
cnf(c4,plain,
( 'distinct$ulines'(X1,X2)
| 'distinct$ulines'(X0,X2)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[apart5]) ).
cnf(c12,plain,
( 'apart$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(c43,plain,
( 'apart$upoint$uand$uline'(X0,X1)
| 'incident$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[a4]) ).
cnf(c50,plain,
~ 'incident$upoint$uand$uline'(sK82,'line$uconnecting'(sK81,sK83)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'apart$upoint$uand$uline'(sK82,'line$uconnecting'(sK81,sK83)),
inference(resolution,[status(thm)],[c43,c50]) ).
cnf(d1,plain,
( 'apart$upoint$uand$uline'(sK82,X0)
| 'distinct$ulines'('line$uconnecting'(sK81,sK83),X0) ),
inference(resolution,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
( 'distinct$ulines'('line$uconnecting'(sK81,sK83),X1)
| 'distinct$ulines'(X0,X1)
| 'apart$upoint$uand$uline'(sK82,X0) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( 'apart$upoint$uand$uline'(sK82,X0)
| 'distinct$ulines'(X0,'line$uconnecting'(sK81,sK83)) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
( 'convergent$ulines'(X0,'line$uconnecting'(sK81,sK83))
| 'apart$upoint$uand$uline'(sK82,X0) ),
inference(resolution,[status(thm)],[d3,c14]) ).
cnf(d5,plain,
'apart$upoint$uand$uline'(sK82,'parallel$uthrough$upoint'('line$uconnecting'(sK81,sK83),X0)),
inference(resolution,[status(thm)],[d4,c15]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO189+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 13:05:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.37/2.45 % SZS status Theorem for theBenchmark.p
% 8.37/2.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------