%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO223+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 : n009.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 27.37s 7.51s
% Output : CNFRefutation 27.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 75 ( 20 unt; 0 def)
% Number of atoms : 175 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 38 ~; 87 |; 3 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 155 ( 14 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X0] : ~ 'convergent$ulines'(X0,X0) ).
fof(ax6,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2) ) ) ).
fof(ci3,axiom,
! [X0,X1] :
( 'convergent$ulines'(X0,X1)
=> ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0) ) ).
fof(ceq2,axiom,
! [X0,X1,X2] :
( 'apart$upoint$uand$uline'(X0,X1)
=> ( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(ceq3,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(p1,axiom,
! [X0,X1] :
( 'distinct$ulines'(X0,X1)
=> 'convergent$ulines'(X0,X1) ) ).
fof(cp1,axiom,
! [X0,X1] : ~ 'convergent$ulines'('parallel$uthrough$upoint'(X1,X0),X1) ).
fof(cp2,axiom,
! [X0,X1] : ~ 'apart$upoint$uand$uline'(X0,'parallel$uthrough$upoint'(X1,X0)) ).
fof(occu1,axiom,
! [X0,X1] :
( 'unorthogonal$ulines'(X0,X1)
| 'convergent$ulines'(X0,X1) ) ).
fof(oac1,axiom,
! [X0,X1,X2] :
( ( 'unorthogonal$ulines'(X0,X1)
& 'convergent$ulines'(X0,X1) )
=> ( ( 'unorthogonal$ulines'(X1,X2)
& 'convergent$ulines'(X1,X2) )
| ( 'unorthogonal$ulines'(X0,X2)
& 'convergent$ulines'(X0,X2) ) ) ) ).
fof(ooc1,axiom,
! [X0,X1] : ~ 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(X1,X0),X1) ).
fof(ouo1,axiom,
! [X0,X1,X2,X3] :
( 'distinct$ulines'(X1,X2)
=> ( 'unorthogonal$ulines'(X2,X3)
| 'unorthogonal$ulines'(X1,X3)
| 'apart$upoint$uand$uline'(X0,X2)
| 'apart$upoint$uand$uline'(X0,X1) ) ) ).
fof(ax2,axiom,
! [X0,X1] :
( 'equal$ulines'(X0,X1)
<=> ~ 'distinct$ulines'(X0,X1) ) ).
fof(a3,axiom,
! [X0,X1] :
( 'parallel$ulines'(X0,X1)
<=> ~ 'convergent$ulines'(X0,X1) ) ).
fof(a4,axiom,
! [X0,X1] :
( 'incident$upoint$uand$uline'(X0,X1)
<=> ~ 'apart$upoint$uand$uline'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1] : 'equal$ulines'('parallel$uthrough$upoint'(X1,X0),'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(X1,X0),X0)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : 'equal$ulines'('parallel$uthrough$upoint'(X1,X0),'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(X1,X0),X0)),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c2,plain,
~ 'convergent$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart3]) ).
cnf(c5,plain,
( 'convergent$ulines'(X0,X2)
| 'convergent$ulines'(X1,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax6]) ).
cnf(c8,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ci3]) ).
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'(X1,X2)
| 'convergent$ulines'(X0,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ceq3]) ).
cnf(c14,plain,
( 'convergent$ulines'(X0,X1)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c15,plain,
~ 'convergent$ulines'('parallel$uthrough$upoint'(X0,X1),X0),
inference(clausification,[status(esa)],[cp1]) ).
cnf(c16,plain,
~ 'apart$upoint$uand$uline'(X0,'parallel$uthrough$upoint'(X1,X0)),
inference(clausification,[status(esa)],[cp2]) ).
cnf(c18,plain,
( 'unorthogonal$ulines'(X0,X1)
| 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[occu1]) ).
cnf(c21,plain,
( 'convergent$ulines'(X0,X2)
| 'unorthogonal$ulines'(X1,X2)
| ~ 'convergent$ulines'(X0,X1)
| ~ 'unorthogonal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[oac1]) ).
cnf(c23,plain,
~ 'unorthogonal$ulines'('orthogonal$uthrough$upoint'(X0,X1),X0),
inference(clausification,[status(esa)],[ooc1]) ).
cnf(c25,plain,
( 'apart$upoint$uand$uline'(X3,X0)
| 'unorthogonal$ulines'(X1,X2)
| 'apart$upoint$uand$uline'(X3,X1)
| 'unorthogonal$ulines'(X0,X2)
| ~ 'distinct$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ouo1]) ).
cnf(c38,plain,
( ~ 'distinct$ulines'(X0,X1)
| ~ 'equal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax2]) ).
cnf(c39,plain,
( 'distinct$ulines'(X0,X1)
| 'equal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax2]) ).
cnf(c40,plain,
( ~ 'convergent$ulines'(X0,X1)
| ~ 'parallel$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a3]) ).
cnf(c41,plain,
( 'convergent$ulines'(X0,X1)
| 'parallel$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a3]) ).
cnf(c42,plain,
( ~ 'apart$upoint$uand$uline'(X0,X1)
| ~ 'incident$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[a4]) ).
cnf(c43,plain,
( 'apart$upoint$uand$uline'(X0,X1)
| 'incident$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[a4]) ).
cnf(c46,plain,
~ 'equal$ulines'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'unorthogonal$ulines'(X0,X1)
| ~ 'parallel$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c40,c18]) ).
cnf(d1,plain,
( 'convergent$ulines'(X0,X2)
| 'convergent$ulines'(X1,X2)
| 'parallel$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c41,c5]) ).
cnf(d2,plain,
( ~ 'parallel$ulines'(X2,X1)
| 'parallel$ulines'(X0,X2)
| 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d1,c40]) ).
cnf(d3,plain,
( 'parallel$ulines'(X0,'parallel$uthrough$upoint'(X1,X2))
| 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d1,c15]) ).
cnf(d4,plain,
'parallel$ulines'(X0,'parallel$uthrough$upoint'(X0,X1)),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( 'convergent$ulines'(X0,X1)
| 'equal$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c39,c14]) ).
cnf(d6,plain,
( ~ 'parallel$ulines'(X0,X1)
| 'equal$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d5,c40]) ).
cnf(d7,plain,
( 'parallel$ulines'(X2,X0)
| 'convergent$ulines'(X2,X1)
| 'distinct$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c13,c41]) ).
cnf(d8,plain,
( ~ 'equal$ulines'(X2,X1)
| 'parallel$ulines'(X0,X2)
| 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d7,c38]) ).
cnf(d9,plain,
( 'parallel$ulines'(X0,X2)
| ~ 'unorthogonal$ulines'(X0,X2)
| 'unorthogonal$ulines'(X2,X1)
| 'convergent$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c21,c41]) ).
cnf(d10,plain,
'equal$ulines'(X0,'parallel$uthrough$upoint'(X0,X1)),
inference(resolution,[status(thm)],[d4,d6]) ).
cnf(d11,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0)
| 'parallel$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c41,c8]) ).
cnf(d12,plain,
( 'incident$upoint$uand$uline'('intersection$upoint'(X0,X1),X0)
| 'parallel$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d11,c43]) ).
cnf(d13,plain,
( 'equal$ulines'(X0,X1)
| 'incident$upoint$uand$uline'('intersection$upoint'(X0,X1),X0) ),
inference(resolution,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
'incident$upoint$uand$uline'('intersection$upoint'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)),'parallel$uthrough$upoint'(sK82,sK81)),
inference(resolution,[status(thm)],[d13,c46]) ).
cnf(d15,plain,
( 'unorthogonal$ulines'(X0,X3)
| 'unorthogonal$ulines'(X1,X3)
| 'apart$upoint$uand$uline'(X2,X0)
| 'apart$upoint$uand$uline'(X2,X1)
| 'equal$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c39,c25]) ).
cnf(d16,plain,
( ~ 'incident$upoint$uand$uline'(X0,X2)
| 'equal$ulines'(X1,X2)
| 'unorthogonal$ulines'(X1,X3)
| 'unorthogonal$ulines'(X2,X3)
| 'apart$upoint$uand$uline'(X0,X1) ),
inference(resolution,[status(thm)],[d15,c42]) ).
cnf(d17,plain,
( 'equal$ulines'(X0,'parallel$uthrough$upoint'(sK82,sK81))
| 'unorthogonal$ulines'(X0,X1)
| 'unorthogonal$ulines'('parallel$uthrough$upoint'(sK82,sK81),X1)
| 'apart$upoint$uand$uline'('intersection$upoint'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)),X0) ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)),X2)
| 'distinct$ulines'(X0,X2)
| 'equal$ulines'(X0,'parallel$uthrough$upoint'(sK82,sK81))
| 'unorthogonal$ulines'('parallel$uthrough$upoint'(sK82,sK81),X1)
| 'unorthogonal$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d17,c12]) ).
cnf(d19,plain,
( ~ 'equal$ulines'(X1,X0)
| 'equal$ulines'(X1,'parallel$uthrough$upoint'(sK82,sK81))
| 'unorthogonal$ulines'('parallel$uthrough$upoint'(sK82,sK81),X2)
| 'unorthogonal$ulines'(X1,X2)
| 'apart$upoint$uand$uline'('intersection$upoint'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)),X0) ),
inference(resolution,[status(thm)],[d18,c38]) ).
cnf(d20,plain,
( 'equal$ulines'(X0,'parallel$uthrough$upoint'(sK82,sK81))
| 'unorthogonal$ulines'('parallel$uthrough$upoint'(sK82,sK81),X2)
| 'unorthogonal$ulines'(X0,X2)
| 'apart$upoint$uand$uline'('intersection$upoint'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,sK81),sK81)),'parallel$uthrough$upoint'(X0,X1)) ),
inference(resolution,[status(thm)],[d19,d10]) ).
cnf(d21,plain,
( 'equal$ulines'(X0,'parallel$uthrough$upoint'(sK82,sK81))
| 'unorthogonal$ulines'('parallel$uthrough$upoint'(sK82,sK81),X1)
| 'unorthogonal$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d20,c16]) ).
cnf(d22,plain,
( 'equal$ulines'('orthogonal$uthrough$upoint'(X0,X1),'parallel$uthrough$upoint'(sK82,sK81))
| 'unorthogonal$ulines'('parallel$uthrough$upoint'(sK82,sK81),X0) ),
inference(resolution,[status(thm)],[d21,c23]) ).
cnf(d23,plain,
( 'parallel$ulines'('parallel$uthrough$upoint'(sK82,sK81),X0)
| 'unorthogonal$ulines'(X0,X2)
| 'convergent$ulines'('parallel$uthrough$upoint'(sK82,sK81),X2)
| 'equal$ulines'('orthogonal$uthrough$upoint'(X0,X1),'parallel$uthrough$upoint'(sK82,sK81)) ),
inference(resolution,[status(thm)],[d22,d9]) ).
cnf(d24,plain,
( 'parallel$ulines'('parallel$uthrough$upoint'(sK82,sK81),X0)
| 'equal$ulines'('orthogonal$uthrough$upoint'(X0,X1),'parallel$uthrough$upoint'(sK82,sK81))
| 'unorthogonal$ulines'(X0,sK82) ),
inference(resolution,[status(thm)],[d23,c15]) ).
cnf(d25,plain,
( 'parallel$ulines'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'(sK82,X0))
| 'equal$ulines'('orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,X0),X1),'parallel$uthrough$upoint'(sK82,sK81)) ),
inference(resolution,[status(thm)],[d24,c23]) ).
cnf(d26,plain,
( 'parallel$ulines'(X1,'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,X0),X2))
| 'convergent$ulines'(X1,'parallel$uthrough$upoint'(sK82,sK81))
| 'parallel$ulines'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'(sK82,X0)) ),
inference(resolution,[status(thm)],[d25,d8]) ).
cnf(d27,plain,
( 'parallel$ulines'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'(sK82,X0))
| 'parallel$ulines'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,X0),X1)) ),
inference(resolution,[status(thm)],[d26,c2]) ).
cnf(d28,plain,
( 'equal$ulines'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'('orthogonal$uthrough$upoint'(sK82,X0),X1))
| 'parallel$ulines'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'(sK82,X0)) ),
inference(resolution,[status(thm)],[d27,d6]) ).
cnf(d29,plain,
'parallel$ulines'('parallel$uthrough$upoint'(sK82,sK81),'orthogonal$uthrough$upoint'(sK82,sK81)),
inference(resolution,[status(thm)],[d28,c46]) ).
cnf(d30,plain,
( 'parallel$ulines'(X0,'parallel$uthrough$upoint'(sK82,sK81))
| 'convergent$ulines'(X0,'orthogonal$uthrough$upoint'(sK82,sK81)) ),
inference(resolution,[status(thm)],[d29,d2]) ).
cnf(d31,plain,
'parallel$ulines'('orthogonal$uthrough$upoint'(sK82,sK81),'parallel$uthrough$upoint'(sK82,sK81)),
inference(resolution,[status(thm)],[d30,c2]) ).
cnf(d32,plain,
( 'parallel$ulines'(X0,'orthogonal$uthrough$upoint'(sK82,sK81))
| 'convergent$ulines'(X0,'parallel$uthrough$upoint'(sK82,sK81)) ),
inference(resolution,[status(thm)],[d31,d2]) ).
cnf(d33,plain,
( ~ 'parallel$ulines'(X0,'parallel$uthrough$upoint'(sK82,sK81))
| 'parallel$ulines'(X0,'orthogonal$uthrough$upoint'(sK82,sK81)) ),
inference(resolution,[status(thm)],[d32,c40]) ).
cnf(d34,plain,
'parallel$ulines'(sK82,'orthogonal$uthrough$upoint'(sK82,sK81)),
inference(resolution,[status(thm)],[d33,d4]) ).
cnf(d35,plain,
( 'parallel$ulines'(X0,sK82)
| 'convergent$ulines'(X0,'orthogonal$uthrough$upoint'(sK82,sK81)) ),
inference(resolution,[status(thm)],[d34,d2]) ).
cnf(d36,plain,
'parallel$ulines'('orthogonal$uthrough$upoint'(sK82,sK81),sK82),
inference(resolution,[status(thm)],[d35,c2]) ).
cnf(d37,plain,
'unorthogonal$ulines'('orthogonal$uthrough$upoint'(sK82,sK81),sK82),
inference(resolution,[status(thm)],[d36,d0]) ).
cnf(d38,plain,
$false,
inference(resolution,[status(thm)],[c23,d37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO223+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n009.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 13:07:59 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.37/7.51 % SZS status Theorem for theBenchmark.p
% 27.37/7.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------