%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 07:14:42 AM UTC 2026
% Result : Theorem 35.89s 35.46s
% Output : CNFRefutation 35.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 15 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 29 ~; 53 |; 1 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 5 sgn 30 !; 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(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(ceq2,axiom,
! [X0,X1,X2] :
( 'apart$upoint$uand$uline'(X0,X1)
=> ( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(ceq3,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X0,X2)
| 'distinct$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(ax1,axiom,
! [X0,X1] :
( 'equal$upoints'(X0,X1)
<=> ~ 'distinct$upoints'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1] :
( 'convergent$ulines'(X0,X1)
=> 'equal$upoints'('intersection$upoint'(X0,X1),'intersection$upoint'(X1,X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'convergent$ulines'(X0,X1)
=> 'equal$upoints'('intersection$upoint'(X0,X1),'intersection$upoint'(X1,X0)) ),
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)],[ax6]) ).
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(c12,plain,
( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2)
| ~ 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ceq2]) ).
cnf(c13,plain,
( 'convergent$ulines'(X0,X2)
| 'distinct$ulines'(X1,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ceq3]) ).
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(c37,plain,
( 'distinct$upoints'(X0,X1)
| 'equal$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[ax1]) ).
cnf(c46,plain,
'convergent$ulines'(sK81,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
~ 'equal$upoints'('intersection$upoint'(sK81,sK82),'intersection$upoint'(sK82,sK81)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'distinct$upoints'('intersection$upoint'(sK81,sK82),'intersection$upoint'(sK82,sK81)),
inference(resolution,[status(thm)],[c37,c47]) ).
cnf(d1,plain,
( 'convergent$ulines'(sK81,X0)
| 'convergent$ulines'(sK82,X0) ),
inference(resolution,[status(thm)],[c5,c46]) ).
cnf(d2,plain,
( 'convergent$ulines'(sK82,X1)
| 'convergent$ulines'(X0,X1)
| 'convergent$ulines'(sK81,X0) ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( 'convergent$ulines'(sK81,X0)
| 'convergent$ulines'(X0,sK82) ),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
( 'convergent$ulines'(sK81,X1)
| 'convergent$ulines'(X0,X1)
| 'convergent$ulines'(X0,sK82) ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
( 'convergent$ulines'(X0,sK82)
| 'convergent$ulines'(X0,sK81) ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
'convergent$ulines'('parallel$uthrough$upoint'(sK82,X0),sK81),
inference(resolution,[status(thm)],[d5,c15]) ).
cnf(d7,plain,
( 'convergent$ulines'('parallel$uthrough$upoint'(sK82,X1),X0)
| 'distinct$ulines'(sK81,X0) ),
inference(resolution,[status(thm)],[c13,d6]) ).
cnf(d8,plain,
'distinct$ulines'(sK81,'parallel$uthrough$upoint'(sK82,X0)),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
( 'apart$upoint$uand$uline'(X0,sK81)
| 'apart$upoint$uand$uline'(X0,'parallel$uthrough$upoint'(sK82,X2))
| 'apart$upoint$uand$uline'(X1,sK81)
| 'apart$upoint$uand$uline'(X1,'parallel$uthrough$upoint'(sK82,X2))
| ~ 'distinct$upoints'(X0,X1) ),
inference(resolution,[status(thm)],[d8,c10]) ).
cnf(d10,plain,
( 'apart$upoint$uand$uline'(X0,sK81)
| 'apart$upoint$uand$uline'(X1,sK81)
| 'apart$upoint$uand$uline'(X1,'parallel$uthrough$upoint'(sK82,X0))
| ~ 'distinct$upoints'(X0,X1) ),
inference(resolution,[status(thm)],[d9,c16]) ).
cnf(d11,plain,
( 'apart$upoint$uand$uline'(X1,X2)
| 'distinct$ulines'('parallel$uthrough$upoint'(sK82,X0),X2)
| 'apart$upoint$uand$uline'(X0,sK81)
| 'apart$upoint$uand$uline'(X1,sK81)
| ~ 'distinct$upoints'(X0,X1) ),
inference(resolution,[status(thm)],[d10,c12]) ).
cnf(d12,plain,
( 'convergent$ulines'('parallel$uthrough$upoint'(sK82,X0),X2)
| 'apart$upoint$uand$uline'(X0,sK81)
| 'apart$upoint$uand$uline'(X1,sK81)
| 'apart$upoint$uand$uline'(X1,X2)
| ~ 'distinct$upoints'(X0,X1) ),
inference(resolution,[status(thm)],[d11,c14]) ).
cnf(d13,plain,
( 'apart$upoint$uand$uline'(X0,sK81)
| 'apart$upoint$uand$uline'(X1,sK81)
| 'apart$upoint$uand$uline'(X1,sK82)
| ~ 'distinct$upoints'(X0,X1) ),
inference(resolution,[status(thm)],[d12,c15]) ).
cnf(d14,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK81)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK82,sK81),sK82)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK82,sK81),sK81) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
( ~ 'convergent$ulines'(sK82,sK81)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK82,sK81),sK81)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK81) ),
inference(resolution,[status(thm)],[d14,c8]) ).
cnf(d16,plain,
'convergent$ulines'(sK82,sK81),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d17,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK82,sK81),sK81)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK81) ),
inference(resolution,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
( ~ 'convergent$ulines'(sK82,sK81)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK81) ),
inference(resolution,[status(thm)],[d17,c9]) ).
cnf(d19,plain,
'apart$upoint$uand$uline'('intersection$upoint'(sK81,sK82),sK81),
inference(resolution,[status(thm)],[d16,d18]) ).
cnf(d20,plain,
~ 'convergent$ulines'(sK81,sK82),
inference(resolution,[status(thm)],[d19,c8]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[c46,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n006.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Fri Sep 25 13:04:52 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.89/35.46 % SZS status Theorem for theBenchmark.p
% 35.89/35.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------