%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO191+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 : n006.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 07:14:38 AM UTC 2026
% Result : Theorem 71.64s 48.79s
% Output : CNFRefutation 71.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 52 ( 15 ~; 27 |; 4 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 6 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X0] : ~ 'convergent$ulines'(X0,X0) ).
fof(ax6,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2) ) ) ).
fof(ceq2,axiom,
! [X0,X1,X2] :
( 'apart$upoint$uand$uline'(X0,X1)
=> ( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(p1,axiom,
! [X0,X1] :
( 'distinct$ulines'(X0,X1)
=> 'convergent$ulines'(X0,X1) ) ).
fof(cp1,axiom,
! [X0,X1] : ~ 'convergent$ulines'('parallel$uthrough$upoint'(X1,X0),X1) ).
fof(cp2,axiom,
! [X0,X1] : ~ 'apart$upoint$uand$uline'(X0,'parallel$uthrough$upoint'(X1,X0)) ).
fof(a3,axiom,
! [X0,X1] :
( 'parallel$ulines'(X0,X1)
<=> ~ 'convergent$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2,X3] :
( ( ( 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X3)
| 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X2) )
& 'convergent$ulines'(X2,X3)
& 'convergent$ulines'(X0,X1) )
=> ( 'apart$upoint$uand$uline'('intersection$upoint'(X2,X3),X1)
| 'apart$upoint$uand$uline'('intersection$upoint'(X2,X3),X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ( 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X3)
| 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X2) )
& 'convergent$ulines'(X2,X3)
& 'convergent$ulines'(X0,X1) )
=> ( 'apart$upoint$uand$uline'('intersection$upoint'(X2,X3),X1)
| 'apart$upoint$uand$uline'('intersection$upoint'(X2,X3),X0) ) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c2,plain,
~ 'convergent$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart3]) ).
cnf(c5,plain,
( 'convergent$ulines'(X0,X2)
| 'convergent$ulines'(X1,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax6]) ).
cnf(c12,plain,
( 'distinct$ulines'(X1,X2)
| 'apart$upoint$uand$uline'(X0,X2)
| ~ 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ceq2]) ).
cnf(c14,plain,
( 'convergent$ulines'(X0,X1)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c15,plain,
~ 'convergent$ulines'('parallel$uthrough$upoint'(X0,X1),X0),
inference(clausification,[status(esa)],[cp1]) ).
cnf(c16,plain,
~ 'apart$upoint$uand$uline'(X0,'parallel$uthrough$upoint'(X1,X0)),
inference(clausification,[status(esa)],[cp2]) ).
cnf(c40,plain,
( ~ 'convergent$ulines'(X0,X1)
| ~ 'parallel$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a3]) ).
cnf(c41,plain,
( 'convergent$ulines'(X0,X1)
| 'parallel$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a3]) ).
cnf(c47,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK84)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK83) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'convergent$ulines'(X0,X2)
| 'convergent$ulines'(X1,X2)
| 'parallel$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c41,c5]) ).
cnf(d1,plain,
( 'parallel$ulines'(X0,'parallel$uthrough$upoint'(X1,X2))
| 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d0,c15]) ).
cnf(d2,plain,
'parallel$ulines'(X0,'parallel$uthrough$upoint'(X0,X1)),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK84)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),X0)
| 'distinct$ulines'(sK83,X0) ),
inference(resolution,[status(thm)],[c12,c47]) ).
cnf(d4,plain,
( 'convergent$ulines'(sK83,X0)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK84)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),X0) ),
inference(resolution,[status(thm)],[d3,c14]) ).
cnf(d5,plain,
( ~ 'parallel$ulines'(sK83,X0)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK84)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),X0) ),
inference(resolution,[status(thm)],[d4,c40]) ).
cnf(d6,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK84)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),'parallel$uthrough$upoint'(sK83,X0)) ),
inference(resolution,[status(thm)],[d2,d5]) ).
cnf(d7,plain,
'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK84),
inference(resolution,[status(thm)],[d6,c16]) ).
cnf(d8,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),X0)
| 'distinct$ulines'(sK84,X0) ),
inference(resolution,[status(thm)],[d7,c12]) ).
cnf(d9,plain,
( 'convergent$ulines'(sK84,X0)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),X0) ),
inference(resolution,[status(thm)],[d8,c14]) ).
cnf(d10,plain,
( ~ 'parallel$ulines'(sK84,X0)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),X0) ),
inference(resolution,[status(thm)],[d9,c40]) ).
cnf(d11,plain,
'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),'parallel$uthrough$upoint'(sK84,X0)),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO191+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/15.37 % Computer : n006.cluster.edu
% 0.09/15.37 % Model : x86_64 x86_64
% 0.09/15.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.37 % Memory : 8046.5625MB
% 0.09/15.37 % 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 13:03:43 UTC 2026
% 0.09/15.38 % CPUTime :
% 0.09/15.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.64/48.79 % SZS status Theorem for theBenchmark.p
% 71.64/48.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------