%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO176+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 : n007.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 07:14:32 AM UTC 2026
% Result : Theorem 13.63s 2.20s
% Output : CNFRefutation 13.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 33 ( 11 ~; 13 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(ceq1,axiom,
! [X0,X1,X2] :
( 'apart$upoint$uand$uline'(X0,X1)
=> ( 'apart$upoint$uand$uline'(X2,X1)
| 'distinct$upoints'(X0,X2) ) ) ).
fof(con,conjecture,
! [X0,X1,X2,X3] :
( ( ( 'apart$upoint$uand$uline'(X0,X3)
| 'apart$upoint$uand$uline'(X0,X2) )
& 'convergent$ulines'(X2,X3)
& 'distinct$upoints'(X0,X1) )
=> 'distinct$upoints'(X0,'intersection$upoint'(X2,X3)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ( 'apart$upoint$uand$uline'(X0,X3)
| 'apart$upoint$uand$uline'(X0,X2) )
& 'convergent$ulines'(X2,X3)
& 'distinct$upoints'(X0,X1) )
=> 'distinct$upoints'(X0,'intersection$upoint'(X2,X3)) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c8,plain,
( ~ 'apart$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$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ci4]) ).
cnf(c11,plain,
( 'apart$upoint$uand$uline'(X2,X1)
| 'distinct$upoints'(X0,X2)
| ~ 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ceq1]) ).
cnf(c47,plain,
'convergent$ulines'(sK83,sK84),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
( 'apart$upoint$uand$uline'(sK81,sK84)
| 'apart$upoint$uand$uline'(sK81,sK83) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c49,plain,
~ 'distinct$upoints'(sK81,'intersection$upoint'(sK83,sK84)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'apart$upoint$uand$uline'(sK81,sK83)
| 'apart$upoint$uand$uline'(X0,sK84)
| 'distinct$upoints'(sK81,X0) ),
inference(resolution,[status(thm)],[c11,c48]) ).
cnf(d1,plain,
( 'apart$upoint$uand$uline'(sK81,sK83)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK83,sK84),sK84) ),
inference(resolution,[status(thm)],[d0,c49]) ).
cnf(d2,plain,
( ~ 'convergent$ulines'(sK83,sK84)
| 'apart$upoint$uand$uline'(sK81,sK83) ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
'apart$upoint$uand$uline'(sK81,sK83),
inference(resolution,[status(thm)],[c47,d2]) ).
cnf(d4,plain,
( 'apart$upoint$uand$uline'(X0,sK83)
| 'distinct$upoints'(sK81,X0) ),
inference(resolution,[status(thm)],[d3,c11]) ).
cnf(d5,plain,
'apart$upoint$uand$uline'('intersection$upoint'(sK83,sK84),sK83),
inference(resolution,[status(thm)],[d4,c49]) ).
cnf(d6,plain,
~ 'convergent$ulines'(sK83,sK84),
inference(resolution,[status(thm)],[d5,c8]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c47,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO176+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 12:59:53 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.63/2.20 % SZS status Theorem for theBenchmark.p
% 13.63/2.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------