%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO261+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 : n005.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 07:15:00 AM UTC 2026
% Result : Theorem 20.23s 3.08s
% Output : CNFRefutation 20.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 39 ( 15 ~; 13 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 34 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X0,X1] :
( 'unequally$udirected$uopposite$ulines'(X0,X1)
<=> 'unequally$udirected$ulines'(X0,'reverse$uline'(X1)) ) ).
fof(a7_defns,axiom,
! [X0,X1] :
( 'convergent$ulines'(X0,X1)
<=> ( 'unequally$udirected$uopposite$ulines'(X0,X1)
& 'unequally$udirected$ulines'(X0,X1) ) ) ).
fof(ax9_basics,axiom,
! [X0,X1] :
( ( 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
& 'unequally$udirected$ulines'(X0,X1) )
=> ( 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| 'left$uconvergent$ulines'(X0,X1) ) ) ).
fof(ax11_basics,axiom,
! [X0,X1] :
~ ( 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| 'left$uconvergent$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2,X3,X4] :
( ( 'incident$upoint$uand$uline'(X3,X1)
& 'convergent$ulines'(X0,X1)
& 'between$uon$uline'(X0,X2,X3,X4) )
=> 'divides$upoints'(X1,X2,X4) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( 'incident$upoint$uand$uline'(X3,X1)
& 'convergent$ulines'(X0,X1)
& 'between$uon$uline'(X0,X2,X3,X4) )
=> 'divides$upoints'(X1,X2,X4) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c0,plain,
( 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$uopposite$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a1_defns]) ).
cnf(c13,plain,
( 'unequally$udirected$ulines'(X0,X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a7_defns]) ).
cnf(c14,plain,
( 'unequally$udirected$uopposite$ulines'(X0,X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a7_defns]) ).
cnf(c50,plain,
( 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| 'left$uconvergent$ulines'(X0,X1)
| ~ 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax9_basics]) ).
cnf(c53,plain,
~ 'left$uconvergent$ulines'(X0,X1),
inference(clausification,[status(esa)],[ax11_basics]) ).
cnf(c73,plain,
'convergent$ulines'(sK84,sK85),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'unequally$udirected$ulines'(sK84,sK85),
inference(resolution,[status(thm)],[c13,c73]) ).
cnf(d1,plain,
( 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c53,c50]) ).
cnf(d2,plain,
( ~ 'unequally$udirected$uopposite$ulines'(X0,X1)
| 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
( ~ 'unequally$udirected$ulines'(X0,X1)
| ~ 'unequally$udirected$uopposite$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c53,d2]) ).
cnf(d4,plain,
~ 'unequally$udirected$uopposite$ulines'(sK84,sK85),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
'unequally$udirected$uopposite$ulines'(sK84,sK85),
inference(resolution,[status(thm)],[c14,c73]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO261+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n005.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 13:10:47 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.23/3.08 % SZS status Theorem for theBenchmark.p
% 20.23/3.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------