%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO206+3 : TPTP v9.3.1. Bugfixed v4.0.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 07:14:44 AM UTC 2026
% Result : Theorem 12.07s 1.97s
% Output : CNFRefutation 12.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 11 ~; 7 |; 2 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 1 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax6,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2) ) ) ).
fof(p1,axiom,
! [X0,X1] :
( 'distinct$ulines'(X0,X1)
=> 'convergent$ulines'(X0,X1) ) ).
fof(cp1,axiom,
! [X0,X1] : ~ 'convergent$ulines'('parallel$uthrough$upoint'(X1,X0),X1) ).
fof(ax2,axiom,
! [X0,X1] :
( 'equal$ulines'(X0,X1)
<=> ~ 'distinct$ulines'(X0,X1) ) ).
fof(a3,axiom,
! [X0,X1] :
( 'parallel$ulines'(X0,X1)
<=> ~ 'convergent$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( 'parallel$ulines'(X1,X2)
& 'incident$upoint$uand$uline'(X0,X1) )
=> 'equal$ulines'(X1,'parallel$uthrough$upoint'(X2,X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'parallel$ulines'(X1,X2)
& 'incident$upoint$uand$uline'(X0,X1) )
=> 'equal$ulines'(X1,'parallel$uthrough$upoint'(X2,X0)) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c5,plain,
( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax6]) ).
cnf(c14,plain,
( 'convergent$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(c39,plain,
( 'distinct$ulines'(X0,X1)
| 'equal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax2]) ).
cnf(c40,plain,
( ~ 'convergent$ulines'(X0,X1)
| ~ 'parallel$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a3]) ).
cnf(c47,plain,
'parallel$ulines'(sK82,sK83),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
~ 'equal$ulines'(sK82,'parallel$uthrough$upoint'(sK83,sK81)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'distinct$ulines'(sK82,'parallel$uthrough$upoint'(sK83,sK81)),
inference(resolution,[status(thm)],[c39,c48]) ).
cnf(d1,plain,
'convergent$ulines'(sK82,'parallel$uthrough$upoint'(sK83,sK81)),
inference(resolution,[status(thm)],[d0,c14]) ).
cnf(d2,plain,
( 'convergent$ulines'(sK82,X0)
| 'convergent$ulines'('parallel$uthrough$upoint'(sK83,sK81),X0) ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
'convergent$ulines'(sK82,sK83),
inference(resolution,[status(thm)],[d2,c15]) ).
cnf(d4,plain,
~ 'convergent$ulines'(sK82,sK83),
inference(resolution,[status(thm)],[c40,c47]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO206+3 : TPTP v9.3.1. Bugfixed v4.0.1.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n001.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 13:11:41 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.07/1.97 % SZS status Theorem for theBenchmark.p
% 12.07/1.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------