%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO192+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 : n009.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 07:14:39 AM UTC 2026
% Result : Theorem 12.08s 1.98s
% Output : CNFRefutation 12.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 16 ~; 14 |; 2 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 31 ( 0 sgn 17 !; 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(ci3,axiom,
! [X0,X1] :
( 'convergent$ulines'(X0,X1)
=> ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0) ) ).
fof(ci4,axiom,
! [X0,X1] :
( 'convergent$ulines'(X0,X1)
=> ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X1) ) ).
fof(ceq2,axiom,
! [X0,X1,X2] :
( 'apart$upoint$uand$uline'(X0,X1)
=> ( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X2)
=> ( 'distinct$ulines'(X1,X2)
& 'distinct$ulines'(X0,X2) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X2)
=> ( 'distinct$ulines'(X1,X2)
& 'distinct$ulines'(X0,X2) ) ) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c1,plain,
~ 'distinct$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart2]) ).
cnf(c4,plain,
( 'distinct$ulines'(X1,X2)
| 'distinct$ulines'(X0,X2)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[apart5]) ).
cnf(c8,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ci3]) ).
cnf(c9,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ci4]) ).
cnf(c12,plain,
( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2)
| ~ 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ceq2]) ).
cnf(c46,plain,
'convergent$ulines'(sK81,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK83),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
( ~ 'distinct$ulines'(sK82,sK83)
| ~ 'distinct$ulines'(sK81,sK83) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),X0)
| 'distinct$ulines'(sK83,X0) ),
inference(resolution,[status(thm)],[c12,c47]) ).
cnf(d1,plain,
( ~ 'convergent$ulines'(sK81,sK82)
| 'distinct$ulines'(sK83,sK81) ),
inference(resolution,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
'distinct$ulines'(sK83,sK81),
inference(resolution,[status(thm)],[c46,d1]) ).
cnf(d3,plain,
( 'distinct$ulines'(sK83,X0)
| 'distinct$ulines'(sK81,X0) ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
'distinct$ulines'(sK81,sK83),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
( ~ 'convergent$ulines'(sK81,sK82)
| 'distinct$ulines'(sK83,sK82) ),
inference(resolution,[status(thm)],[d0,c9]) ).
cnf(d6,plain,
'distinct$ulines'(sK83,sK82),
inference(resolution,[status(thm)],[c46,d5]) ).
cnf(d7,plain,
( 'distinct$ulines'(sK83,X0)
| 'distinct$ulines'(sK82,X0) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
'distinct$ulines'(sK82,sK83),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
~ 'distinct$ulines'(sK81,sK83),
inference(resolution,[status(thm)],[d8,c48]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO192+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
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:04:31 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.08/1.98 % SZS status Theorem for theBenchmark.p
% 12.08/1.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------