%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO210+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 : n026.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 07:14:46 AM UTC 2026
% Result : Theorem 21.59s 5.16s
% Output : CNFRefutation 21.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 17 ~; 24 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 2 sgn 18 !; 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(ooc1,axiom,
! [X0,X1] : ~ 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(X1,X0),X1) ).
fof(ooc2,axiom,
! [X0,X1] : ~ 'apart$upoint$uand$uline'(X0,'orthogonal$uthrough$upoint'(X1,X0)) ).
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$uline'(X0,X1) ) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( ~ 'unorthogonal$ulines'(X1,X2)
& ~ 'apart$upoint$uand$uline'(X0,X1) )
=> ~ 'distinct$ulines'(X1,'orthogonal$uthrough$upoint'(X2,X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ 'unorthogonal$ulines'(X1,X2)
& ~ 'apart$upoint$uand$uline'(X0,X1) )
=> ~ 'distinct$ulines'(X1,'orthogonal$uthrough$upoint'(X2,X0)) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c1,plain,
~ 'distinct$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart2]) ).
cnf(c4,plain,
( 'distinct$ulines'(X1,X2)
| 'distinct$ulines'(X0,X2)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[apart5]) ).
cnf(c22,plain,
~ 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(X0,X1),X0),
inference(clausification,[status(esa)],[ooc1]) ).
cnf(c23,plain,
~ 'apart$upoint$uand$uline'(X0,'orthogonal$uthrough$upoint'(X1,X0)),
inference(clausification,[status(esa)],[ooc2]) ).
cnf(c24,plain,
( 'unorthogonal$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,
~ 'apart$upoint$uand$uline'(sK50,sK51),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c26,plain,
~ 'unorthogonal$ulines'(sK51,sK52),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c27,plain,
'distinct$ulines'(sK51,'orthogonal$uthrough$upoint'(sK52,sK50)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'distinct$ulines'(sK51,X0)
| 'distinct$ulines'('orthogonal$uthrough$upoint'(sK52,sK50),X0) ),
inference(resolution,[status(thm)],[c4,c27]) ).
cnf(d1,plain,
( 'distinct$ulines'('orthogonal$uthrough$upoint'(sK52,sK50),X1)
| 'distinct$ulines'(X0,X1)
| 'distinct$ulines'(sK51,X0) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( 'distinct$ulines'(sK51,X0)
| 'distinct$ulines'(X0,'orthogonal$uthrough$upoint'(sK52,sK50)) ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( 'distinct$ulines'(sK51,X1)
| 'unorthogonal$ulines'(X1,X2)
| 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK52,sK50),X2)
| 'apart$upoint$uand$uline'(X0,X1)
| 'apart$upoint$uand$uline'(X0,'orthogonal$uthrough$upoint'(sK52,sK50)) ),
inference(resolution,[status(thm)],[c24,d2]) ).
cnf(d4,plain,
( 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK52,sK50),X0)
| 'unorthogonal$ulines'(sK51,X0)
| 'apart$upoint$uand$uline'(sK50,'orthogonal$uthrough$upoint'(sK52,sK50))
| 'distinct$ulines'(sK51,sK51) ),
inference(resolution,[status(thm)],[d3,c25]) ).
cnf(d5,plain,
( 'unorthogonal$ulines'(sK51,X0)
| 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK52,sK50),X0)
| 'apart$upoint$uand$uline'(sK50,'orthogonal$uthrough$upoint'(sK52,sK50)) ),
inference(resolution,[status(thm)],[c1,d4]) ).
cnf(d6,plain,
( 'unorthogonal$ulines'(sK51,X0)
| 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK52,sK50),X0) ),
inference(resolution,[status(thm)],[c23,d5]) ).
cnf(d7,plain,
'unorthogonal$ulines'(sK51,sK52),
inference(resolution,[status(thm)],[d6,c22]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c26,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO210+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n026.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 13:08:55 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.59/5.16 % SZS status Theorem for theBenchmark.p
% 21.59/5.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------