%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO262+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 : n002.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 14.00s 2.34s
% Output : CNFRefutation 14.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 45 ( 15 ~; 13 |; 12 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 2 sgn 20 !; 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$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( 'incident$upoint$uand$uline'(X4,X2)
& 'convergent$ulines'(X1,X2)
& 'convergent$ulines'(X0,X2)
& 'incident$upoint$uand$uline'(X4,X1)
& 'convergent$ulines'(X0,X1)
& 'between$uon$uline'(X0,X3,X4,X5) )
=> 'between$uon$uline'(X1,'intersection$upoint'(X1,'parallel$uthrough$upoint'(X2,X3)),X4,'intersection$upoint'(X1,'parallel$uthrough$upoint'(X2,X5))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( 'incident$upoint$uand$uline'(X4,X2)
& 'convergent$ulines'(X1,X2)
& 'convergent$ulines'(X0,X2)
& 'incident$upoint$uand$uline'(X4,X1)
& 'convergent$ulines'(X0,X1)
& 'between$uon$uline'(X0,X3,X4,X5) )
=> 'between$uon$uline'(X1,'intersection$upoint'(X1,'parallel$uthrough$upoint'(X2,X3)),X4,'intersection$upoint'(X1,'parallel$uthrough$upoint'(X2,X5))) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c0,plain,
( 'unequally$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(c76,plain,
'convergent$ulines'(sK85,sK86),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'unequally$udirected$ulines'(sK85,sK86),
inference(resolution,[status(thm)],[c13,c76]) ).
cnf(d1,plain,
( 'left$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$ulines'(sK85,sK86),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
'unequally$udirected$uopposite$ulines'(sK85,sK86),
inference(resolution,[status(thm)],[c14,c76]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO262+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.58 % Computer : n002.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Fri Sep 25 13:14:07 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.00/2.34 % SZS status Theorem for theBenchmark.p
% 14.00/2.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------