%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO224+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 : n008.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 07:14:51 AM UTC 2026
% Result : Theorem 11.38s 2.14s
% Output : CNFRefutation 11.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 27 ~; 17 |; 7 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 5 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ci4,axiom,
! [X0,X1] :
( 'convergent$ulines'(X0,X1)
=> ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X1) ) ).
fof(occu1,axiom,
! [X0,X1] :
( 'unorthogonal$ulines'(X0,X1)
| 'convergent$ulines'(X0,X1) ) ).
fof(ooc1,axiom,
! [X0,X1] : ~ 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(X1,X0),X1) ).
fof(int1,axiom,
! [X0,X1] :
( ( 'convergent$ulines'(X0,X1)
& line(X1)
& line(X0) )
=> point('intersection$upoint'(X0,X1)) ) ).
fof(orth1,axiom,
! [X0,X1] :
( ( point(X1)
& line(X0) )
=> line('orthogonal$uthrough$upoint'(X0,X1)) ) ).
fof(a4,axiom,
! [X0,X1] :
( 'incident$upoint$uand$uline'(X0,X1)
<=> ~ 'apart$upoint$uand$uline'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1] :
( ( line(X1)
& point(X0) )
=> ? [X2] :
( 'incident$upoint$uand$uline'(X2,X1)
& point(X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( line(X1)
& point(X0) )
=> ? [X2] :
( 'incident$upoint$uand$uline'(X2,X1)
& point(X2) ) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c9,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ci4]) ).
cnf(c18,plain,
( 'unorthogonal$ulines'(X0,X1)
| 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[occu1]) ).
cnf(c23,plain,
~ 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(X0,X1),X0),
inference(clausification,[status(esa)],[ooc1]) ).
cnf(c33,plain,
( point('intersection$upoint'(X0,X1))
| ~ 'convergent$ulines'(X0,X1)
| ~ line(X1)
| ~ line(X0) ),
inference(clausification,[status(esa)],[int1]) ).
cnf(c35,plain,
( line('orthogonal$uthrough$upoint'(X0,X1))
| ~ point(X1)
| ~ line(X0) ),
inference(clausification,[status(esa)],[orth1]) ).
cnf(c43,plain,
( 'apart$upoint$uand$uline'(X0,X1)
| 'incident$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[a4]) ).
cnf(c46,plain,
point(sK81),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
line(sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
( ~ 'incident$upoint$uand$uline'(X0,sK82)
| ~ point(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'convergent$ulines'('orthogonal$uthrough$upoint'(X0,X1),X0),
inference(resolution,[status(thm)],[c18,c23]) ).
cnf(d1,plain,
( ~ point(X0)
| 'apart$upoint$uand$uline'(X0,sK82) ),
inference(resolution,[status(thm)],[c43,c48]) ).
cnf(d2,plain,
( ~ 'convergent$ulines'(X0,sK82)
| ~ point('intersection$upoint'(X0,sK82)) ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( ~ 'convergent$ulines'(X0,sK82)
| ~ line(sK82)
| ~ line(X0)
| ~ 'convergent$ulines'(X0,sK82) ),
inference(resolution,[status(thm)],[c33,d2]) ).
cnf(d4,plain,
( ~ line(X0)
| ~ 'convergent$ulines'(X0,sK82) ),
inference(resolution,[status(thm)],[c47,d3]) ).
cnf(d5,plain,
~ line('orthogonal$uthrough$upoint'(sK82,X0)),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ line(sK82)
| ~ point(X0) ),
inference(resolution,[status(thm)],[d5,c35]) ).
cnf(d7,plain,
~ point(X0),
inference(resolution,[status(thm)],[c47,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,c46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO224+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
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:09:09 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.38/2.14 % SZS status Theorem for theBenchmark.p
% 11.38/2.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------