%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO174+1 : 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 : 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 07:14:31 AM UTC 2026
% Result : Theorem 11.23s 1.88s
% Output : CNFRefutation 11.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 33 ( 11 ~; 13 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 24 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(ceq2,axiom,
! [X0,X1,X2] :
( 'apart$upoint$uand$uline'(X0,X1)
=> ( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(con,conjecture,
! [X0,X1,X2,X3] :
( ( ( 'apart$upoint$uand$uline'(X1,X2)
| 'apart$upoint$uand$uline'(X0,X2) )
& 'convergent$ulines'(X2,X3)
& 'distinct$upoints'(X0,X1) )
=> 'distinct$ulines'(X2,'line$uconnecting'(X0,X1)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ( 'apart$upoint$uand$uline'(X1,X2)
| 'apart$upoint$uand$uline'(X0,X2) )
& 'convergent$ulines'(X2,X3)
& 'distinct$upoints'(X0,X1) )
=> 'distinct$ulines'(X2,'line$uconnecting'(X0,X1)) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c6,plain,
( ~ 'apart$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$upoints'(X0,X1) ),
inference(clausification,[status(esa)],[ci2]) ).
cnf(c12,plain,
( 'apart$upoint$uand$uline'(X0,X2)
| 'distinct$ulines'(X1,X2)
| ~ 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ceq2]) ).
cnf(c14,plain,
'distinct$upoints'(sK33,sK34),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
( 'apart$upoint$uand$uline'(sK34,sK35)
| 'apart$upoint$uand$uline'(sK33,sK35) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
~ 'distinct$ulines'(sK35,'line$uconnecting'(sK33,sK34)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'apart$upoint$uand$uline'(sK33,sK35)
| 'apart$upoint$uand$uline'(sK34,X0)
| 'distinct$ulines'(sK35,X0) ),
inference(resolution,[status(thm)],[c12,c16]) ).
cnf(d1,plain,
( 'apart$upoint$uand$uline'(sK34,'line$uconnecting'(sK33,sK34))
| 'apart$upoint$uand$uline'(sK33,sK35) ),
inference(resolution,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( ~ 'distinct$upoints'(sK33,sK34)
| 'apart$upoint$uand$uline'(sK33,sK35) ),
inference(resolution,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
'apart$upoint$uand$uline'(sK33,sK35),
inference(resolution,[status(thm)],[c14,d2]) ).
cnf(d4,plain,
( 'apart$upoint$uand$uline'(sK33,X0)
| 'distinct$ulines'(sK35,X0) ),
inference(resolution,[status(thm)],[d3,c12]) ).
cnf(d5,plain,
'apart$upoint$uand$uline'(sK33,'line$uconnecting'(sK33,sK34)),
inference(resolution,[status(thm)],[d4,c17]) ).
cnf(d6,plain,
~ 'distinct$upoints'(sK33,sK34),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c14,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO174+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 13:01:29 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.23/1.88 % SZS status Theorem for theBenchmark.p
% 11.23/1.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------