%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO188+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 07:14:37 AM UTC 2026
% Result : Theorem 13.58s 3.46s
% Output : CNFRefutation 13.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 37 ( 12 ~; 13 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 3 sgn 21 !; 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(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$upoint'(X1,X0)) ).
fof(a4,axiom,
! [X0,X1] :
( 'incident$upoint$uand$uline'(X0,X1)
<=> ~ 'apart$upoint$uand$uline'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( 'incident$upoint$uand$uline'(X2,'line$uconnecting'(X0,X1))
& 'distinct$upoints'(X1,X2)
& 'distinct$upoints'(X0,X2)
& 'distinct$upoints'(X0,X1) )
=> 'incident$upoint$uand$uline'(X0,'line$uconnecting'(X2,X1)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'incident$upoint$uand$uline'(X2,'line$uconnecting'(X0,X1))
& 'distinct$upoints'(X1,X2)
& 'distinct$upoints'(X0,X2)
& 'distinct$upoints'(X0,X1) )
=> 'incident$upoint$uand$uline'(X0,'line$uconnecting'(X2,X1)) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c1,plain,
~ 'distinct$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart2]) ).
cnf(c4,plain,
( 'distinct$ulines'(X1,X2)
| 'distinct$ulines'(X0,X2)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[apart5]) ).
cnf(c12,plain,
( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2)
| ~ 'apart$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(c43,plain,
( 'apart$upoint$uand$uline'(X0,X1)
| 'incident$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[a4]) ).
cnf(c50,plain,
~ 'incident$upoint$uand$uline'(sK81,'line$uconnecting'(sK83,sK82)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'apart$upoint$uand$uline'(sK81,'line$uconnecting'(sK83,sK82)),
inference(resolution,[status(thm)],[c43,c50]) ).
cnf(d1,plain,
( 'apart$upoint$uand$uline'(sK81,X0)
| 'distinct$ulines'('line$uconnecting'(sK83,sK82),X0) ),
inference(resolution,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
( 'distinct$ulines'('line$uconnecting'(sK83,sK82),X1)
| 'distinct$ulines'(X0,X1)
| 'apart$upoint$uand$uline'(sK81,X0) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( 'apart$upoint$uand$uline'(sK81,X0)
| 'distinct$ulines'(X0,'line$uconnecting'(sK83,sK82)) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
( 'convergent$ulines'(X0,'line$uconnecting'(sK83,sK82))
| 'apart$upoint$uand$uline'(sK81,X0) ),
inference(resolution,[status(thm)],[d3,c14]) ).
cnf(d5,plain,
'apart$upoint$uand$uline'(sK81,'parallel$uthrough$upoint'('line$uconnecting'(sK83,sK82),X0)),
inference(resolution,[status(thm)],[d4,c15]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO188+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n006.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 13:02:56 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.58/3.46 % SZS status Theorem for theBenchmark.p
% 13.58/3.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------