%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO203+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:14:43 AM UTC 2026
% Result : Theorem 23.97s 3.37s
% Output : CNFRefutation 23.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 51 ( 19 ~; 21 |; 5 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ci1,axiom,
! [X0,X1] :
( 'distinct$upoints'(X0,X1)
=> ~ 'apart$upoint$uand$uline'(X0,'line$uconnecting'(X0,X1)) ) ).
fof(ci2,axiom,
! [X0,X1] :
( 'distinct$upoints'(X0,X1)
=> ~ 'apart$upoint$uand$uline'(X1,'line$uconnecting'(X0,X1)) ) ).
fof(ci3,axiom,
! [X0,X1] :
( 'convergent$ulines'(X0,X1)
=> ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0) ) ).
fof(cu1,axiom,
! [X0,X1,X2,X3] :
( ( 'distinct$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$uline'(X0,X2) ) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( 'distinct$upoints'('intersection$upoint'(X0,X1),'intersection$upoint'(X0,X2))
& 'convergent$ulines'(X0,X2)
& 'convergent$ulines'(X0,X1) )
=> ~ 'distinct$ulines'('line$uconnecting'('intersection$upoint'(X0,X1),'intersection$upoint'(X0,X2)),X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'distinct$upoints'('intersection$upoint'(X0,X1),'intersection$upoint'(X0,X2))
& 'convergent$ulines'(X0,X2)
& 'convergent$ulines'(X0,X1) )
=> ~ 'distinct$ulines'('line$uconnecting'('intersection$upoint'(X0,X1),'intersection$upoint'(X0,X2)),X0) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c6,plain,
( ~ 'apart$upoint$uand$uline'(X0,'line$uconnecting'(X0,X1))
| ~ 'distinct$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[ci1]) ).
cnf(c7,plain,
( ~ 'apart$upoint$uand$uline'(X1,'line$uconnecting'(X0,X1))
| ~ 'distinct$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[ci2]) ).
cnf(c8,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ci3]) ).
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(c14,plain,
'convergent$ulines'(sK33,sK35),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
'distinct$upoints'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
'convergent$ulines'(sK33,sK34),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
'distinct$ulines'('line$uconnecting'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35)),sK33),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),X0)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),X1)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK35),X0)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK35),X1)
| ~ 'distinct$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c10,c15]) ).
cnf(d1,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),'line$uconnecting'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35)))
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK33)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK35),'line$uconnecting'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35)))
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK35),sK33) ),
inference(resolution,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
~ 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK35),sK33),
inference(resolution,[status(thm)],[c8,c14]) ).
cnf(d3,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK33)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),'line$uconnecting'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35)))
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK35),'line$uconnecting'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35))) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
~ 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK33),
inference(resolution,[status(thm)],[c8,c16]) ).
cnf(d5,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),'line$uconnecting'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35)))
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK35),'line$uconnecting'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35))) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
~ 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),'line$uconnecting'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35))),
inference(resolution,[status(thm)],[c6,c15]) ).
cnf(d7,plain,
'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK35),'line$uconnecting'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35))),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
~ 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK35),'line$uconnecting'('intersection$upoint'(sK33,sK34),'intersection$upoint'(sK33,sK35))),
inference(resolution,[status(thm)],[c7,c15]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO203+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 13:07:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.97/3.37 % SZS status Theorem for theBenchmark.p
% 23.97/3.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------