%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO213+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 : n002.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 07:14:47 AM UTC 2026
% Result : Theorem 12.00s 17.46s
% Output : CNFRefutation 12.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 39 ( 10 ~; 21 |; 3 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 36 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(con,conjecture,
! [X0,X1,X2] :
( 'unorthogonal$ulines'(X0,X1)
=> ( 'unorthogonal$ulines'(X1,X2)
| 'distinct$ulines'(X0,X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( 'unorthogonal$ulines'(X0,X1)
=> ( 'unorthogonal$ulines'(X1,X2)
| 'distinct$ulines'(X0,X2) ) ),
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)],[apart6]) ).
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(c25,plain,
'unorthogonal$ulines'(sK50,sK51),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c26,plain,
~ 'distinct$ulines'(sK50,sK52),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c27,plain,
~ 'unorthogonal$ulines'(sK51,sK52),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'unorthogonal$ulines'(sK51,X0)
| ~ 'convergent$ulines'(sK50,sK51)
| 'convergent$ulines'(sK50,X0) ),
inference(resolution,[status(thm)],[c19,c25]) ).
cnf(d1,plain,
'convergent$ulines'(sK51,sK52),
inference(resolution,[status(thm)],[c17,c27]) ).
cnf(d2,plain,
( 'convergent$ulines'(sK51,X0)
| 'convergent$ulines'(sK52,X0) ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( 'convergent$ulines'(sK52,X1)
| 'convergent$ulines'(X0,X1)
| 'convergent$ulines'(sK51,X0) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( 'convergent$ulines'(sK51,X0)
| 'convergent$ulines'(X0,sK52) ),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( 'distinct$ulines'(X0,sK52)
| 'convergent$ulines'(sK51,X0) ),
inference(resolution,[status(thm)],[d4,c13]) ).
cnf(d6,plain,
'convergent$ulines'(sK51,sK50),
inference(resolution,[status(thm)],[d5,c26]) ).
cnf(d7,plain,
( 'convergent$ulines'(sK51,X0)
| 'convergent$ulines'(sK50,X0) ),
inference(resolution,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
'convergent$ulines'(sK50,sK51),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
( 'unorthogonal$ulines'(sK51,X0)
| 'convergent$ulines'(sK50,X0) ),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
'convergent$ulines'(sK50,sK52),
inference(resolution,[status(thm)],[d9,c27]) ).
cnf(d11,plain,
'distinct$ulines'(sK50,sK52),
inference(resolution,[status(thm)],[d10,c13]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c26,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO213+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/15.38 % Computer : n002.cluster.edu
% 0.09/15.38 % Model : x86_64 x86_64
% 0.09/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.38 % Memory : 8046.5625MB
% 0.09/15.38 % OS : Linux 6.8.0-71-generic
% 0.09/15.38 % CPULimit : 300
% 0.09/15.38 % WCLimit : 300
% 0.09/15.38 % DateTime : Fri Sep 25 13:09:35 UTC 2026
% 0.09/15.38 % CPUTime :
% 0.09/15.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.00/17.46 % SZS status Theorem for theBenchmark.p
% 12.00/17.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------