%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO222+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 36.63s 9.94s
% Output : CNFRefutation 36.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 74 ( 26 ~; 39 |; 3 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 4 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X0] : ~ 'distinct$upoints'(X0,X0) ).
fof(apart3,axiom,
! [X0] : ~ 'convergent$ulines'(X0,X0) ).
fof(apart6,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2) ) ) ).
fof(con2,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( ( 'apart$upoint$uand$uline'(X2,X1)
| 'apart$upoint$uand$uline'(X2,X0) )
=> 'distinct$upoints'(X2,'intersection$upoint'(X0,X1)) ) ) ).
fof(ceq3,axiom,
! [X0,X1] :
( 'convergent$ulines'(X0,X1)
=> 'distinct$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$upoint'(X1,X0),X1) ).
fof(ouo1,axiom,
! [X0,X1,X2,X3] :
( 'distinct$ulines'(X1,X2)
=> ( 'unorthogonal$ulines'(X2,X3)
| 'unorthogonal$ulines'(X1,X3)
| 'apart$upoint$uand$uline'(X0,X2)
| 'apart$upoint$uand$uline'(X0,X1) ) ) ).
fof(con,conjecture,
! [X0,X1] : ~ 'convergent$ulines'(X1,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(X1,X0),X0)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : ~ 'convergent$ulines'(X1,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(X1,X0),X0)),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c0,plain,
~ 'distinct$upoints'(X0,X0),
inference(clausification,[status(esa)],[apart1]) ).
cnf(c2,plain,
~ 'convergent$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart3]) ).
cnf(c5,plain,
( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[apart6]) ).
cnf(c8,plain,
( 'distinct$upoints'(X2,'intersection$upoint'(X0,X1))
| ~ 'apart$upoint$uand$uline'(X2,X0)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[con2]) ).
cnf(c9,plain,
( 'distinct$upoints'(X2,'intersection$upoint'(X0,X1))
| ~ 'apart$upoint$uand$uline'(X2,X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[con2]) ).
cnf(c13,plain,
( 'distinct$ulines'(X0,X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ceq3]) ).
cnf(c17,plain,
( 'unorthogonal$ulines'(X0,X1)
| 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[occu1]) ).
cnf(c19,plain,
( 'unorthogonal$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2)
| ~ 'unorthogonal$ulines'(X0,X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[oac1]) ).
cnf(c22,plain,
~ 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(X0,X1),X0),
inference(clausification,[status(esa)],[ooc1]) ).
cnf(c24,plain,
( 'unorthogonal$ulines'(X2,X3)
| 'unorthogonal$ulines'(X1,X3)
| ~ 'distinct$ulines'(X2,X1)
| 'apart$upoint$uand$uline'(X0,X2)
| 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ouo1]) ).
cnf(c25,plain,
'convergent$ulines'(sK51,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK51,sK50),sK50)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'convergent$ulines'(sK51,X0)
| 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK51,sK50),sK50),X0) ),
inference(resolution,[status(thm)],[c5,c25]) ).
cnf(d1,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d2,plain,
'distinct$ulines'(sK51,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK51,sK50),sK50)),
inference(resolution,[status(thm)],[c13,c25]) ).
cnf(d3,plain,
( 'unorthogonal$ulines'(sK51,X1)
| 'unorthogonal$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK51,sK50),sK50),X1)
| 'apart$upoint$uand$uline'(X0,sK51)
| 'apart$upoint$uand$uline'(X0,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK51,sK50),sK50)) ),
inference(resolution,[status(thm)],[c24,d2]) ).
cnf(d4,plain,
( 'unorthogonal$ulines'(sK51,'orthogonal$uthrough$upoint'(sK51,sK50))
| 'apart$upoint$uand$uline'(X0,sK51)
| 'apart$upoint$uand$uline'(X0,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK51,sK50),sK50)) ),
inference(resolution,[status(thm)],[d3,c22]) ).
cnf(d5,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0)
| ~ 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d6,plain,
( 'unorthogonal$ulines'(sK51,'orthogonal$uthrough$upoint'(sK51,sK50))
| 'apart$upoint$uand$uline'('intersection$upoint'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK51,sK50),sK50),X0),sK51)
| ~ 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK51,sK50),sK50),X0) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK51,sK50),sK50),sK51)
| 'unorthogonal$ulines'(sK51,'orthogonal$uthrough$upoint'(sK51,sK50))
| ~ 'convergent$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK51,sK50),sK50),sK51) ),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( 'convergent$ulines'(sK51,sK51)
| 'unorthogonal$ulines'(sK51,'orthogonal$uthrough$upoint'(sK51,sK50)) ),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
'unorthogonal$ulines'(sK51,'orthogonal$uthrough$upoint'(sK51,sK50)),
inference(resolution,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
( 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK51,sK50),X0)
| ~ 'convergent$ulines'(sK51,'orthogonal$uthrough$upoint'(sK51,sK50))
| 'convergent$ulines'(sK51,X0) ),
inference(resolution,[status(thm)],[d9,c19]) ).
cnf(d11,plain,
'convergent$ulines'('orthogonal$uthrough$upoint'(X0,X1),X0),
inference(resolution,[status(thm)],[c17,c22]) ).
cnf(d12,plain,
( 'convergent$ulines'('orthogonal$uthrough$upoint'(X0,X2),X1)
| 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c5,d11]) ).
cnf(d13,plain,
'convergent$ulines'(X0,'orthogonal$uthrough$upoint'(X0,X1)),
inference(resolution,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
( 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK51,sK50),X0)
| 'convergent$ulines'(sK51,X0) ),
inference(resolution,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
'convergent$ulines'(sK51,sK51),
inference(resolution,[status(thm)],[d14,c22]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[c2,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO222+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n001.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Fri Sep 25 13:14:01 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.63/9.94 % SZS status Theorem for theBenchmark.p
% 36.63/9.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------