%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO218+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 : n004.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 07:14:49 AM UTC 2026
% Result : Theorem 12.08s 1.94s
% Output : CNFRefutation 12.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 24 ~; 26 |; 3 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 51 ( 0 sgn 24 !; 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(ceq3,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(p1,axiom,
! [X0,X1] :
( 'distinct$ulines'(X0,X1)
=> 'convergent$ulines'(X0,X1) ) ).
fof(occu1,axiom,
! [X0,X1] :
( 'unorthogonal$ulines'(X0,X1)
| 'convergent$ulines'(X0,X1) ) ).
fof(cotno1,axiom,
! [X0,X1,X2] :
( ( ( ~ 'unorthogonal$ulines'(X0,X2)
| ~ 'convergent$ulines'(X0,X2) )
& ( ~ 'unorthogonal$ulines'(X0,X1)
| ~ 'convergent$ulines'(X0,X1) ) )
=> ( ~ 'unorthogonal$ulines'(X1,X2)
| ~ 'convergent$ulines'(X1,X2) ) ) ).
fof(a3,axiom,
! [X0,X1] :
( 'parallel$ulines'(X0,X1)
<=> ~ 'convergent$ulines'(X0,X1) ) ).
fof(a5,axiom,
! [X0,X1] :
( 'orthogonal$ulines'(X0,X1)
<=> ~ 'unorthogonal$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( 'orthogonal$ulines'(X0,X2)
& 'parallel$ulines'(X0,X1) )
=> 'orthogonal$ulines'(X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'orthogonal$ulines'(X0,X2)
& 'parallel$ulines'(X0,X1) )
=> 'orthogonal$ulines'(X1,X2) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c1,plain,
~ 'distinct$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart2]) ).
cnf(c4,plain,
( 'distinct$ulines'(X1,X2)
| 'distinct$ulines'(X0,X2)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[apart5]) ).
cnf(c13,plain,
( 'convergent$ulines'(X0,X2)
| 'distinct$ulines'(X1,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ceq3]) ).
cnf(c14,plain,
( 'convergent$ulines'(X0,X1)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c18,plain,
( 'unorthogonal$ulines'(X0,X1)
| 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[occu1]) ).
cnf(c28,plain,
( ~ 'unorthogonal$ulines'(X1,X2)
| ~ 'convergent$ulines'(X1,X2)
| 'unorthogonal$ulines'(X0,X2)
| 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[cotno1]) ).
cnf(c40,plain,
( ~ 'convergent$ulines'(X0,X1)
| ~ 'parallel$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a3]) ).
cnf(c44,plain,
( ~ 'unorthogonal$ulines'(X0,X1)
| ~ 'orthogonal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a5]) ).
cnf(c45,plain,
( 'unorthogonal$ulines'(X0,X1)
| 'orthogonal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a5]) ).
cnf(c46,plain,
'parallel$ulines'(sK81,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
'orthogonal$ulines'(sK81,sK83),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
~ 'orthogonal$ulines'(sK82,sK83),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'unorthogonal$ulines'(sK81,sK83),
inference(resolution,[status(thm)],[c44,c47]) ).
cnf(d1,plain,
'unorthogonal$ulines'(sK82,sK83),
inference(resolution,[status(thm)],[c45,c48]) ).
cnf(d2,plain,
( 'unorthogonal$ulines'(X0,sK83)
| ~ 'convergent$ulines'(sK82,sK83)
| 'convergent$ulines'(X0,sK82) ),
inference(resolution,[status(thm)],[d1,c28]) ).
cnf(d3,plain,
~ 'convergent$ulines'(sK81,sK82),
inference(resolution,[status(thm)],[c40,c46]) ).
cnf(d4,plain,
'convergent$ulines'(sK81,sK83),
inference(resolution,[status(thm)],[d0,c18]) ).
cnf(d5,plain,
( 'convergent$ulines'(sK81,X0)
| 'distinct$ulines'(sK83,X0) ),
inference(resolution,[status(thm)],[d4,c13]) ).
cnf(d6,plain,
( 'distinct$ulines'(sK83,X1)
| 'distinct$ulines'(X0,X1)
| 'convergent$ulines'(sK81,X0) ),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( 'convergent$ulines'(sK81,X0)
| 'distinct$ulines'(X0,sK83) ),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
( 'convergent$ulines'(X0,sK83)
| 'convergent$ulines'(sK81,X0) ),
inference(resolution,[status(thm)],[d7,c14]) ).
cnf(d9,plain,
'convergent$ulines'(sK82,sK83),
inference(resolution,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
( 'unorthogonal$ulines'(X0,sK83)
| 'convergent$ulines'(X0,sK82) ),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
'convergent$ulines'(sK81,sK82),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d3,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO218+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
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:07:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.08/1.94 % SZS status Theorem for theBenchmark.p
% 12.08/1.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------