%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO219+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 : n016.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 10.80s 1.97s
% Output : CNFRefutation 10.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 49 ( 24 ~; 17 |; 4 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 29 ( 0 sgn 15 !; 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(coipo1,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(con,conjecture,
! [X0,X1,X2] :
( ( ~ 'convergent$ulines'(X0,X2)
& ~ 'unorthogonal$ulines'(X0,X1) )
=> ~ 'unorthogonal$ulines'(X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ 'convergent$ulines'(X0,X2)
& ~ 'unorthogonal$ulines'(X0,X1) )
=> ~ 'unorthogonal$ulines'(X1,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(c14,plain,
( 'unorthogonal$ulines'(X0,X1)
| 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[coipo1]) ).
cnf(c17,plain,
( ~ 'unorthogonal$ulines'(X1,X2)
| ~ 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2)
| 'unorthogonal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[cotno1]) ).
cnf(c20,plain,
~ 'unorthogonal$ulines'(sK38,sK39),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c21,plain,
~ 'convergent$ulines'(sK38,sK40),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c22,plain,
'unorthogonal$ulines'(sK39,sK40),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'unorthogonal$ulines'(X0,sK39)
| ~ 'convergent$ulines'(sK39,sK40)
| 'convergent$ulines'(X0,sK40) ),
inference(resolution,[status(thm)],[c17,c22]) ).
cnf(d1,plain,
'convergent$ulines'(sK38,sK39),
inference(resolution,[status(thm)],[c14,c20]) ).
cnf(d2,plain,
( 'convergent$ulines'(sK38,X0)
| 'convergent$ulines'(sK39,X0) ),
inference(resolution,[status(thm)],[c5,d1]) ).
cnf(d3,plain,
( 'convergent$ulines'(sK39,X1)
| 'convergent$ulines'(X0,X1)
| 'convergent$ulines'(sK38,X0) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( 'convergent$ulines'(sK39,sK40)
| 'convergent$ulines'(sK38,sK38) ),
inference(resolution,[status(thm)],[d3,c21]) ).
cnf(d5,plain,
'convergent$ulines'(sK39,sK40),
inference(resolution,[status(thm)],[c2,d4]) ).
cnf(d6,plain,
( 'unorthogonal$ulines'(X0,sK39)
| 'convergent$ulines'(X0,sK40) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
'convergent$ulines'(sK38,sK40),
inference(resolution,[status(thm)],[d6,c20]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c21,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO219+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
% 0.07/0.35 % Computer : n016.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 13:12:43 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.80/1.97 % SZS status Theorem for theBenchmark.p
% 10.80/1.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------