%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO205+2 : 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 : n020.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 07:14:44 AM UTC 2026
% Result : Theorem 12.16s 4.46s
% Output : CNFRefutation 12.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 23 ~; 46 |; 5 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X0] : ~ 'distinct$upoints'(X0,X0) ).
fof(apart6,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2) ) ) ).
fof(con2,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( ( 'apart$upoint$uand$uline'(X2,X1)
| 'apart$upoint$uand$uline'(X2,X0) )
=> 'distinct$upoints'(X2,'intersection$upoint'(X0,X1)) ) ) ).
fof(cu1,axiom,
! [X0,X1,X2,X3] :
( ( 'distinct$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] :
( 'convergent$ulines'(X0,X1)
=> 'distinct$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( ~ 'distinct$ulines'(X1,X2)
& 'convergent$ulines'(X0,X1) )
=> ( ~ 'distinct$upoints'('intersection$upoint'(X0,X1),'intersection$upoint'(X0,X2))
& 'convergent$ulines'(X0,X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ 'distinct$ulines'(X1,X2)
& 'convergent$ulines'(X0,X1) )
=> ( ~ 'distinct$upoints'('intersection$upoint'(X0,X1),'intersection$upoint'(X0,X2))
& 'convergent$ulines'(X0,X2) ) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c0,plain,
~ 'distinct$upoints'(X0,X0),
inference(clausification,[status(esa)],[apart1]) ).
cnf(c5,plain,
( 'convergent$ulines'(X0,X2)
| 'convergent$ulines'(X1,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[apart6]) ).
cnf(c8,plain,
( ~ 'apart$upoint$uand$uline'(X2,X0)
| 'distinct$upoints'(X2,'intersection$upoint'(X0,X1))
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[con2]) ).
cnf(c9,plain,
( ~ 'apart$upoint$uand$uline'(X2,X1)
| 'distinct$upoints'(X2,'intersection$upoint'(X0,X1))
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[con2]) ).
cnf(c10,plain,
( ~ 'distinct$upoints'(X0,X3)
| 'apart$upoint$uand$uline'(X3,X1)
| 'apart$upoint$uand$uline'(X3,X2)
| ~ 'distinct$ulines'(X1,X2)
| 'apart$upoint$uand$uline'(X0,X2)
| 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[cu1]) ).
cnf(c12,plain,
( 'distinct$ulines'(X1,X2)
| 'apart$upoint$uand$uline'(X0,X2)
| ~ 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ceq2]) ).
cnf(c13,plain,
( 'distinct$ulines'(X0,X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ceq3]) ).
cnf(c14,plain,
~ 'distinct$ulines'(sK31,sK32),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
'convergent$ulines'(sK30,sK31),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
( 'distinct$upoints'('intersection$upoint'(sK30,sK31),'intersection$upoint'(sK30,sK32))
| ~ 'convergent$ulines'(sK30,sK32) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'convergent$ulines'(sK30,X0)
| 'convergent$ulines'(sK31,X0) ),
inference(resolution,[status(thm)],[c5,c15]) ).
cnf(d1,plain,
( 'distinct$ulines'(sK31,X0)
| 'convergent$ulines'(sK30,X0) ),
inference(resolution,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
'convergent$ulines'(sK30,sK32),
inference(resolution,[status(thm)],[d1,c14]) ).
cnf(d3,plain,
( ~ 'apart$upoint$uand$uline'(X0,sK30)
| 'distinct$upoints'(X0,'intersection$upoint'(sK30,sK32)) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
( ~ 'apart$upoint$uand$uline'(X0,sK32)
| 'distinct$upoints'(X0,'intersection$upoint'(sK30,sK32)) ),
inference(resolution,[status(thm)],[d2,c9]) ).
cnf(d5,plain,
( ~ 'apart$upoint$uand$uline'(X0,sK30)
| 'distinct$upoints'(X0,'intersection$upoint'(sK30,sK31)) ),
inference(resolution,[status(thm)],[c8,c15]) ).
cnf(d6,plain,
( ~ 'apart$upoint$uand$uline'(X0,sK31)
| 'distinct$upoints'(X0,'intersection$upoint'(sK30,sK31)) ),
inference(resolution,[status(thm)],[c9,c15]) ).
cnf(d7,plain,
'distinct$ulines'(sK30,sK31),
inference(resolution,[status(thm)],[c13,c15]) ).
cnf(d8,plain,
'distinct$upoints'('intersection$upoint'(sK30,sK31),'intersection$upoint'(sK30,sK32)),
inference(resolution,[status(thm)],[d2,c16]) ).
cnf(d9,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK31),X0)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK31),X1)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),X0)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),X1)
| ~ 'distinct$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d8,c10]) ).
cnf(d10,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK30)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK31)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK31),sK30)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK31),sK31) ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( 'distinct$upoints'('intersection$upoint'(sK30,sK31),'intersection$upoint'(sK30,sK31))
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK30)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK31)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK31),sK30) ),
inference(resolution,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK30)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK31)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK31),sK30) ),
inference(resolution,[status(thm)],[c0,d11]) ).
cnf(d13,plain,
( 'distinct$upoints'('intersection$upoint'(sK30,sK31),'intersection$upoint'(sK30,sK31))
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK30)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK31) ),
inference(resolution,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK30)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK31) ),
inference(resolution,[status(thm)],[c0,d13]) ).
cnf(d15,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),X0)
| 'distinct$ulines'(sK31,X0)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK30) ),
inference(resolution,[status(thm)],[d14,c12]) ).
cnf(d16,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK30)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK32) ),
inference(resolution,[status(thm)],[d15,c14]) ).
cnf(d17,plain,
( 'distinct$upoints'('intersection$upoint'(sK30,sK32),'intersection$upoint'(sK30,sK32))
| 'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK30) ),
inference(resolution,[status(thm)],[d16,d4]) ).
cnf(d18,plain,
'apart$upoint$uand$uline'('intersection$upoint'(sK30,sK32),sK30),
inference(resolution,[status(thm)],[c0,d17]) ).
cnf(d19,plain,
'distinct$upoints'('intersection$upoint'(sK30,sK32),'intersection$upoint'(sK30,sK32)),
inference(resolution,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[c0,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO205+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 13:06:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.16/4.46 % SZS status Theorem for theBenchmark.p
% 12.16/4.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------