%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO172+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 : 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 07:14:31 AM UTC 2026
% Result : Theorem 13.08s 16.43s
% Output : CNFRefutation 13.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 22 ~; 27 |; 5 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X0] : ~ 'convergent$ulines'(X0,X0) ).
fof(ci3,axiom,
! [X0,X1] :
( 'convergent$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$upoint'(X0,X1),X1) ) ).
fof(cu1,axiom,
! [X0,X1,X2,X3] :
( ( 'distinct$ulines'(X2,X3)
& 'distinct$upoints'(X0,X1) )
=> ( 'apart$upoint$uand$uline'(X1,X3)
| 'apart$upoint$uand$uline'(X1,X2)
| 'apart$upoint$uand$uline'(X0,X3)
| 'apart$upoint$uand$uline'(X0,X2) ) ) ).
fof(ceq3,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(ax1,axiom,
! [X0,X1] :
( 'equal$upoints'(X0,X1)
<=> ~ 'distinct$upoints'(X0,X1) ) ).
fof(a4,axiom,
! [X0,X1] :
( 'incident$upoint$uand$uline'(X0,X1)
<=> ~ 'apart$upoint$uand$uline'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( 'incident$upoint$uand$uline'(X2,X1)
& 'incident$upoint$uand$uline'(X2,X0)
& 'convergent$ulines'(X0,X1) )
=> 'equal$upoints'(X2,'intersection$upoint'(X0,X1)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'incident$upoint$uand$uline'(X2,X1)
& 'incident$upoint$uand$uline'(X2,X0)
& 'convergent$ulines'(X0,X1) )
=> 'equal$upoints'(X2,'intersection$upoint'(X0,X1)) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c2,plain,
~ 'convergent$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart3]) ).
cnf(c8,plain,
( ~ 'apart$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$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ci4]) ).
cnf(c10,plain,
( 'apart$upoint$uand$uline'(X3,X2)
| 'apart$upoint$uand$uline'(X3,X1)
| ~ 'distinct$ulines'(X2,X1)
| ~ 'distinct$upoints'(X0,X3)
| 'apart$upoint$uand$uline'(X0,X2)
| 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[cu1]) ).
cnf(c13,plain,
( 'convergent$ulines'(X0,X2)
| 'distinct$ulines'(X1,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ceq3]) ).
cnf(c37,plain,
( 'distinct$upoints'(X0,X1)
| 'equal$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[ax1]) ).
cnf(c42,plain,
( ~ 'apart$upoint$uand$uline'(X0,X1)
| ~ 'incident$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[a4]) ).
cnf(c46,plain,
'convergent$ulines'(sK81,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
'incident$upoint$uand$uline'(sK83,sK81),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
'incident$upoint$uand$uline'(sK83,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c49,plain,
~ 'equal$upoints'(sK83,'intersection$upoint'(sK81,sK82)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'distinct$upoints'(sK83,'intersection$upoint'(sK81,sK82)),
inference(resolution,[status(thm)],[c37,c49]) ).
cnf(d1,plain,
( 'convergent$ulines'(sK81,X0)
| 'distinct$ulines'(sK82,X0) ),
inference(resolution,[status(thm)],[c13,c46]) ).
cnf(d2,plain,
'distinct$ulines'(sK82,sK81),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( 'apart$upoint$uand$uline'(X0,sK82)
| 'apart$upoint$uand$uline'(X0,sK81)
| 'apart$upoint$uand$uline'(X1,sK82)
| 'apart$upoint$uand$uline'(X1,sK81)
| ~ 'distinct$upoints'(X0,X1) ),
inference(resolution,[status(thm)],[d2,c10]) ).
cnf(d4,plain,
( 'apart$upoint$uand$uline'(sK83,sK82)
| 'apart$upoint$uand$uline'(sK83,sK81)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK82)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK81) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
~ 'apart$upoint$uand$uline'(sK83,sK81),
inference(resolution,[status(thm)],[c42,c47]) ).
cnf(d6,plain,
( 'apart$upoint$uand$uline'(sK83,sK82)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK82)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK81) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
~ 'apart$upoint$uand$uline'(sK83,sK82),
inference(resolution,[status(thm)],[c42,c48]) ).
cnf(d8,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK82)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK81) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ 'convergent$ulines'(sK81,sK82)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK81) ),
inference(resolution,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK81),
inference(resolution,[status(thm)],[c46,d9]) ).
cnf(d11,plain,
~ 'convergent$ulines'(sK81,sK82),
inference(resolution,[status(thm)],[d10,c8]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c46,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO172+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.43 % Computer : n016.cluster.edu
% 0.16/10.43 % Model : x86_64 x86_64
% 0.16/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.43 % Memory : 8046.5625MB
% 0.16/10.43 % OS : Linux 6.8.0-71-generic
% 0.16/10.43 % CPULimit : 300
% 0.16/10.43 % WCLimit : 300
% 0.16/10.43 % DateTime : Fri Sep 25 13:05:54 UTC 2026
% 0.16/10.43 % CPUTime :
% 0.16/10.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.08/16.43 % SZS status Theorem for theBenchmark.p
% 13.08/16.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------