%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO183+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 07:14:35 AM UTC 2026
% Result : Theorem 6.87s 7.67s
% Output : CNFRefutation 6.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 51 ( 19 ~; 20 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X0] : ~ 'distinct$upoints'(X0,X0) ).
fof(con1,axiom,
! [X0,X1,X2] :
( 'distinct$upoints'(X0,X1)
=> ( 'apart$upoint$uand$uline'(X2,'line$uconnecting'(X0,X1))
=> ( 'distinct$upoints'(X2,X1)
& 'distinct$upoints'(X2,X0) ) ) ) ).
fof(ceq2,axiom,
! [X0,X1,X2] :
( 'apart$upoint$uand$uline'(X0,X1)
=> ( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(con,conjecture,
! [X0,X1,X2,X3] :
( ( ~ 'distinct$ulines'(X2,'line$uconnecting'(X0,X1))
& 'convergent$ulines'(X2,X3)
& 'distinct$upoints'(X0,X1) )
=> ( ~ 'apart$upoint$uand$uline'(X1,X2)
& ~ 'apart$upoint$uand$uline'(X0,X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ~ 'distinct$ulines'(X2,'line$uconnecting'(X0,X1))
& 'convergent$ulines'(X2,X3)
& 'distinct$upoints'(X0,X1) )
=> ( ~ 'apart$upoint$uand$uline'(X1,X2)
& ~ 'apart$upoint$uand$uline'(X0,X2) ) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c0,plain,
~ 'distinct$upoints'(X0,X0),
inference(clausification,[status(esa)],[apart1]) ).
cnf(c6,plain,
( 'distinct$upoints'(X2,X0)
| ~ 'apart$upoint$uand$uline'(X2,'line$uconnecting'(X0,X1))
| ~ 'distinct$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[con1]) ).
cnf(c7,plain,
( 'distinct$upoints'(X2,X1)
| ~ 'apart$upoint$uand$uline'(X2,'line$uconnecting'(X0,X1))
| ~ 'distinct$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[con1]) ).
cnf(c12,plain,
( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2)
| ~ 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ceq2]) ).
cnf(c14,plain,
'distinct$upoints'(sK30,sK31),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
~ 'distinct$ulines'(sK32,'line$uconnecting'(sK30,sK31)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
( 'apart$upoint$uand$uline'(sK31,sK32)
| 'apart$upoint$uand$uline'(sK30,sK32) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'apart$upoint$uand$uline'(sK30,sK32)
| 'apart$upoint$uand$uline'(sK31,X0)
| 'distinct$ulines'(sK32,X0) ),
inference(resolution,[status(thm)],[c12,c17]) ).
cnf(d1,plain,
( 'distinct$upoints'(sK31,X1)
| ~ 'distinct$upoints'(X0,X1)
| 'apart$upoint$uand$uline'(sK30,sK32)
| 'distinct$ulines'(sK32,'line$uconnecting'(X0,X1)) ),
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( 'apart$upoint$uand$uline'(sK30,sK32)
| 'distinct$upoints'(sK31,sK31)
| ~ 'distinct$upoints'(sK30,sK31) ),
inference(resolution,[status(thm)],[d1,c16]) ).
cnf(d3,plain,
( 'apart$upoint$uand$uline'(sK30,sK32)
| 'distinct$upoints'(sK31,sK31) ),
inference(resolution,[status(thm)],[c14,d2]) ).
cnf(d4,plain,
'apart$upoint$uand$uline'(sK30,sK32),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
( 'apart$upoint$uand$uline'(sK30,X0)
| 'distinct$ulines'(sK32,X0) ),
inference(resolution,[status(thm)],[d4,c12]) ).
cnf(d6,plain,
( 'distinct$upoints'(sK30,X0)
| ~ 'distinct$upoints'(X0,X1)
| 'distinct$ulines'(sK32,'line$uconnecting'(X0,X1)) ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( 'distinct$upoints'(sK30,sK30)
| ~ 'distinct$upoints'(sK30,sK31) ),
inference(resolution,[status(thm)],[d6,c16]) ).
cnf(d8,plain,
'distinct$upoints'(sK30,sK30),
inference(resolution,[status(thm)],[c14,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c0,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO183+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n012.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Fri Sep 25 13:02:27 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.87/7.67 % SZS status Theorem for theBenchmark.p
% 6.87/7.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------