%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO222+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 : 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 07:14:50 AM UTC 2026
% Result : Theorem 14.20s 3.84s
% Output : CNFRefutation 14.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 14 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 78 ( 19 ~; 49 |; 4 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 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 : 79 ( 5 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X0] : ~ 'convergent$ulines'(X0,X0) ).
fof(ax6,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X1,X2)
| 'convergent$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$ulines'(X0,X1) ) ).
fof(oac1,axiom,
! [X0,X1,X2] :
( ( 'unorthogonal$ulines'(X0,X1)
& 'convergent$ulines'(X0,X1) )
=> ( ( 'unorthogonal$ulines'(X1,X2)
& 'convergent$ulines'(X1,X2) )
| ( 'unorthogonal$ulines'(X0,X2)
& 'convergent$ulines'(X0,X2) ) ) ) ).
fof(ooc1,axiom,
! [X0,X1] : ~ 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(X1,X0),X1) ).
fof(couo1,axiom,
! [X0,X1,X2] :
( ( ~ 'unorthogonal$ulines'(X0,X2)
& ~ 'unorthogonal$ulines'(X0,X1) )
=> ~ 'convergent$ulines'(X1,X2) ) ).
fof(a3,axiom,
! [X0,X1] :
( 'parallel$ulines'(X0,X1)
<=> ~ 'convergent$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1] : 'parallel$ulines'(X1,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(X1,X0),X0)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : 'parallel$ulines'(X1,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(X1,X0),X0)),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c2,plain,
~ 'convergent$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart3]) ).
cnf(c5,plain,
( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax6]) ).
cnf(c13,plain,
( 'convergent$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(c20,plain,
( 'unorthogonal$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2)
| ~ 'unorthogonal$ulines'(X0,X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[oac1]) ).
cnf(c23,plain,
~ 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(X0,X1),X0),
inference(clausification,[status(esa)],[ooc1]) ).
cnf(c31,plain,
( ~ 'convergent$ulines'(X1,X2)
| 'unorthogonal$ulines'(X0,X2)
| 'unorthogonal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[couo1]) ).
cnf(c41,plain,
( 'convergent$ulines'(X0,X1)
| 'parallel$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a3]) ).
cnf(c46,plain,
~ 'parallel$ulines'(sK82,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'convergent$ulines'(sK82,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)),
inference(resolution,[status(thm)],[c41,c46]) ).
cnf(d1,plain,
( 'unorthogonal$ulines'(X0,sK82)
| 'unorthogonal$ulines'(X0,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)) ),
inference(resolution,[status(thm)],[c31,d0]) ).
cnf(d2,plain,
( 'unorthogonal$ulines'(X0,sK82)
| 'unorthogonal$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81),X1)
| ~ 'convergent$ulines'(X0,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81))
| 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c20,d1]) ).
cnf(d3,plain,
( 'convergent$ulines'(sK82,X0)
| 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81),X0) ),
inference(resolution,[status(thm)],[c5,d0]) ).
cnf(d4,plain,
'convergent$ulines'('orthogonal$uthrough$upoint'(X0,X1),X0),
inference(resolution,[status(thm)],[c18,c23]) ).
cnf(d5,plain,
( 'unorthogonal$ulines'(X0,'orthogonal$uthrough$upoint'(X1,X2))
| 'unorthogonal$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c31,d4]) ).
cnf(d6,plain,
'unorthogonal$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(X0,X1),X2),X0),
inference(resolution,[status(thm)],[d5,c23]) ).
cnf(d7,plain,
( 'unorthogonal$ulines'(X0,X3)
| ~ 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(X0,X1),X2),X0)
| 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[c20,d6]) ).
cnf(d8,plain,
( 'convergent$ulines'(sK82,sK82)
| 'unorthogonal$ulines'(sK82,X0)
| 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81),X0) ),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( 'unorthogonal$ulines'(sK82,X0)
| 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81),X0) ),
inference(resolution,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
( 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81),X1)
| 'distinct$ulines'(X0,X1)
| 'unorthogonal$ulines'(sK82,X0) ),
inference(resolution,[status(thm)],[d9,c13]) ).
cnf(d11,plain,
( 'unorthogonal$ulines'(sK82,X0)
| 'distinct$ulines'(X0,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)) ),
inference(resolution,[status(thm)],[d10,c2]) ).
cnf(d12,plain,
( 'convergent$ulines'(X0,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81))
| 'unorthogonal$ulines'(sK82,X0) ),
inference(resolution,[status(thm)],[d11,c14]) ).
cnf(d13,plain,
( 'unorthogonal$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81),X1)
| 'unorthogonal$ulines'(X0,sK82)
| 'convergent$ulines'(X0,X1)
| 'unorthogonal$ulines'(sK82,X0) ),
inference(resolution,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
( 'unorthogonal$ulines'(sK82,X0)
| 'unorthogonal$ulines'(X0,sK82)
| 'convergent$ulines'(X0,'orthogonal$uthrough$upoint'(sK82,sK81)) ),
inference(resolution,[status(thm)],[d13,c23]) ).
cnf(d15,plain,
( 'unorthogonal$ulines'(sK82,'orthogonal$uthrough$upoint'(sK82,sK81))
| 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK82,sK81),sK82) ),
inference(resolution,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
'unorthogonal$ulines'(sK82,'orthogonal$uthrough$upoint'(sK82,sK81)),
inference(resolution,[status(thm)],[c23,d15]) ).
cnf(d17,plain,
( 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK82,sK81),X0)
| ~ 'convergent$ulines'(sK82,'orthogonal$uthrough$upoint'(sK82,sK81))
| 'convergent$ulines'(sK82,X0) ),
inference(resolution,[status(thm)],[d16,c20]) ).
cnf(d18,plain,
( 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81),X1)
| 'convergent$ulines'(X0,X1)
| 'convergent$ulines'(sK82,X0) ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d19,plain,
( 'convergent$ulines'(sK82,X0)
| 'convergent$ulines'(X0,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)) ),
inference(resolution,[status(thm)],[d18,c2]) ).
cnf(d20,plain,
( 'convergent$ulines'(sK82,X0)
| 'unorthogonal$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81),X1)
| 'unorthogonal$ulines'(X0,sK82)
| 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d2,d19]) ).
cnf(d21,plain,
( 'unorthogonal$ulines'(X0,sK82)
| 'convergent$ulines'(sK82,X0)
| 'convergent$ulines'(X0,'orthogonal$uthrough$upoint'(sK82,sK81)) ),
inference(resolution,[status(thm)],[d20,c23]) ).
cnf(d22,plain,
( 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK82,sK81),sK82)
| 'convergent$ulines'(sK82,'orthogonal$uthrough$upoint'(sK82,sK81)) ),
inference(resolution,[status(thm)],[d21,c2]) ).
cnf(d23,plain,
'convergent$ulines'(sK82,'orthogonal$uthrough$upoint'(sK82,sK81)),
inference(resolution,[status(thm)],[c23,d22]) ).
cnf(d24,plain,
( 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK82,sK81),X0)
| 'convergent$ulines'(sK82,X0) ),
inference(resolution,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
'convergent$ulines'(sK82,sK82),
inference(resolution,[status(thm)],[d24,c23]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[c2,d25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO222+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
% 0.09/0.34 % Computer : n001.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 13:13:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.20/3.84 % SZS status Theorem for theBenchmark.p
% 14.20/3.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------