%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO204+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 07:14:44 AM UTC 2026
% Result : Theorem 69.49s 10.72s
% Output : CNFRefutation 69.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 86 ( 31 ~; 41 |; 5 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X0] : ~ 'distinct$upoints'(X0,X0) ).
fof(apart4,axiom,
! [X0,X1,X2] :
( 'distinct$upoints'(X0,X1)
=> ( 'distinct$upoints'(X1,X2)
| 'distinct$upoints'(X0,X2) ) ) ).
fof(ci1,axiom,
! [X0,X1] :
( 'distinct$upoints'(X0,X1)
=> ~ 'apart$upoint$uand$uline'(X0,'line$uconnecting'(X0,X1)) ) ).
fof(ci2,axiom,
! [X0,X1] :
( 'distinct$upoints'(X0,X1)
=> ~ 'apart$upoint$uand$uline'(X1,'line$uconnecting'(X0,X1)) ) ).
fof(cu1,axiom,
! [X0,X1,X2,X3] :
( ( 'distinct$ulines'(X2,X3)
& 'distinct$upoints'(X0,X1) )
=> ( 'apart$upoint$uand$uline'(X1,X3)
| 'apart$upoint$uand$uline'(X1,X2)
| 'apart$upoint$uand$uline'(X0,X3)
| 'apart$upoint$uand$uline'(X0,X2) ) ) ).
fof(ceq1,axiom,
! [X0,X1,X2] :
( 'apart$upoint$uand$uline'(X0,X1)
=> ( 'apart$upoint$uand$uline'(X2,X1)
| 'distinct$upoints'(X0,X2) ) ) ).
fof(ax1,axiom,
! [X0,X1] :
( 'equal$upoints'(X0,X1)
<=> ~ 'distinct$upoints'(X0,X1) ) ).
fof(ax2,axiom,
! [X0,X1] :
( 'equal$ulines'(X0,X1)
<=> ~ 'distinct$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( 'equal$upoints'(X1,X2)
& 'distinct$upoints'(X0,X1) )
=> ( 'equal$ulines'('line$uconnecting'(X0,X1),'line$uconnecting'(X0,X2))
& 'distinct$upoints'(X0,X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'equal$upoints'(X1,X2)
& 'distinct$upoints'(X0,X1) )
=> ( 'equal$ulines'('line$uconnecting'(X0,X1),'line$uconnecting'(X0,X2))
& 'distinct$upoints'(X0,X2) ) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c0,plain,
~ 'distinct$upoints'(X0,X0),
inference(clausification,[status(esa)],[apart1]) ).
cnf(c3,plain,
( 'distinct$upoints'(X1,X2)
| 'distinct$upoints'(X0,X2)
| ~ 'distinct$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[apart4]) ).
cnf(c6,plain,
( ~ 'apart$upoint$uand$uline'(X0,'line$uconnecting'(X0,X1))
| ~ 'distinct$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[ci1]) ).
cnf(c7,plain,
( ~ 'apart$upoint$uand$uline'(X1,'line$uconnecting'(X0,X1))
| ~ 'distinct$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[ci2]) ).
cnf(c10,plain,
( 'apart$upoint$uand$uline'(X3,X2)
| 'apart$upoint$uand$uline'(X3,X1)
| ~ 'distinct$ulines'(X2,X1)
| ~ 'distinct$upoints'(X0,X3)
| 'apart$upoint$uand$uline'(X0,X2)
| 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[cu1]) ).
cnf(c11,plain,
( 'apart$upoint$uand$uline'(X2,X1)
| 'distinct$upoints'(X0,X2)
| ~ 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ceq1]) ).
cnf(c36,plain,
( ~ 'distinct$upoints'(X0,X1)
| ~ 'equal$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[ax1]) ).
cnf(c39,plain,
( 'distinct$ulines'(X0,X1)
| 'equal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax2]) ).
cnf(c46,plain,
'distinct$upoints'(sK81,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
'equal$upoints'(sK82,sK83),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
( ~ 'equal$ulines'('line$uconnecting'(sK81,sK82),'line$uconnecting'(sK81,sK83))
| ~ 'distinct$upoints'(sK81,sK83) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'distinct$upoints'(sK82,sK83),
inference(resolution,[status(thm)],[c36,c47]) ).
cnf(d1,plain,
( 'distinct$upoints'(sK81,X0)
| 'distinct$upoints'(sK82,X0) ),
inference(resolution,[status(thm)],[c3,c46]) ).
cnf(d2,plain,
'distinct$upoints'(sK81,sK83),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
~ 'equal$ulines'('line$uconnecting'(sK81,sK82),'line$uconnecting'(sK81,sK83)),
inference(resolution,[status(thm)],[d2,c48]) ).
cnf(d4,plain,
'distinct$ulines'('line$uconnecting'(sK81,sK82),'line$uconnecting'(sK81,sK83)),
inference(resolution,[status(thm)],[c39,d3]) ).
cnf(d5,plain,
( 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK83))
| 'apart$upoint$uand$uline'(X1,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(X1,'line$uconnecting'(sK81,sK83))
| ~ 'distinct$upoints'(X0,X1) ),
inference(resolution,[status(thm)],[d4,c10]) ).
cnf(d6,plain,
( ~ 'distinct$upoints'(sK81,sK83)
| 'apart$upoint$uand$uline'(sK81,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK83))
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK82))
| ~ 'distinct$upoints'(sK81,X0) ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( 'apart$upoint$uand$uline'(sK81,'line$uconnecting'(sK81,sK82))
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK83))
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK82))
| ~ 'distinct$upoints'(sK81,X0) ),
inference(resolution,[status(thm)],[d2,d6]) ).
cnf(d8,plain,
( ~ 'distinct$upoints'(sK81,sK82)
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK83))
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK82))
| ~ 'distinct$upoints'(sK81,X0) ),
inference(resolution,[status(thm)],[d7,c6]) ).
cnf(d9,plain,
( 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK83))
| 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK82))
| ~ 'distinct$upoints'(sK81,X0) ),
inference(resolution,[status(thm)],[c46,d8]) ).
cnf(d10,plain,
( ~ 'distinct$upoints'(sK81,sK83)
| 'apart$upoint$uand$uline'(sK83,'line$uconnecting'(sK81,sK82))
| ~ 'distinct$upoints'(sK81,sK83) ),
inference(resolution,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
'apart$upoint$uand$uline'(sK83,'line$uconnecting'(sK81,sK82)),
inference(resolution,[status(thm)],[d2,d10]) ).
cnf(d12,plain,
( 'apart$upoint$uand$uline'(X0,'line$uconnecting'(sK81,sK82))
| 'distinct$upoints'(sK83,X0) ),
inference(resolution,[status(thm)],[d11,c11]) ).
cnf(d13,plain,
( ~ 'distinct$upoints'(sK81,sK82)
| 'distinct$upoints'(sK83,sK82) ),
inference(resolution,[status(thm)],[d12,c7]) ).
cnf(d14,plain,
'distinct$upoints'(sK83,sK82),
inference(resolution,[status(thm)],[c46,d13]) ).
cnf(d15,plain,
( 'distinct$upoints'(sK83,X0)
| 'distinct$upoints'(sK82,X0) ),
inference(resolution,[status(thm)],[d14,c3]) ).
cnf(d16,plain,
'distinct$upoints'(sK82,sK83),
inference(resolution,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[d0,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO204+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
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 13:05:32 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 69.49/10.72 % SZS status Theorem for theBenchmark.p
% 69.49/10.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------