%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO196+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 07:14:40 AM UTC 2026
% Result : Theorem 39.51s 5.45s
% Output : CNFRefutation 39.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 13 unt; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 113 ( 29 ~; 68 |; 9 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X0] : ~ 'convergent$ulines'(X0,X0) ).
fof(ci3,axiom,
! [X0,X1] :
( 'convergent$ulines'(X0,X1)
=> ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0) ) ).
fof(ci4,axiom,
! [X0,X1] :
( 'convergent$ulines'(X0,X1)
=> ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X1) ) ).
fof(cu1,axiom,
! [X0,X1,X2,X3] :
( ( 'distinct$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(ceq3,axiom,
! [X0,X1,X2] :
( 'convergent$ulines'(X0,X1)
=> ( 'convergent$ulines'(X0,X2)
| 'distinct$ulines'(X1,X2) ) ) ).
fof(con,conjecture,
! [X0,X1,X2,X3] :
( ( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X3)
& ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X2)
& 'convergent$ulines'(X2,X3)
& 'convergent$ulines'(X0,X1) )
=> ( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X2,X3),X1)
& ~ 'apart$upoint$uand$uline'('intersection$upoint'(X2,X3),X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X3)
& ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X2)
& 'convergent$ulines'(X2,X3)
& 'convergent$ulines'(X0,X1) )
=> ( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X2,X3),X1)
& ~ 'apart$upoint$uand$uline'('intersection$upoint'(X2,X3),X0) ) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c2,plain,
~ 'convergent$ulines'(X0,X0),
inference(clausification,[status(esa)],[apart3]) ).
cnf(c8,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X0)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ci3]) ).
cnf(c9,plain,
( ~ 'apart$upoint$uand$uline'('intersection$upoint'(X0,X1),X1)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ci4]) ).
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,
( 'distinct$upoints'(X0,X2)
| 'apart$upoint$uand$uline'(X2,X1)
| ~ 'apart$upoint$uand$uline'(X0,X1) ),
inference(clausification,[status(esa)],[ceq1]) ).
cnf(c13,plain,
( 'distinct$ulines'(X1,X2)
| 'convergent$ulines'(X0,X2)
| ~ 'convergent$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ceq3]) ).
cnf(c14,plain,
'convergent$ulines'(sK35,sK36),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
~ 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK36),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
~ 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK35),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
'convergent$ulines'(sK33,sK34),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK34)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK33) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'convergent$ulines'(sK35,X0)
| 'distinct$ulines'(sK36,X0) ),
inference(resolution,[status(thm)],[c13,c14]) ).
cnf(d1,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK34)
| 'apart$upoint$uand$uline'(X0,sK33)
| 'distinct$upoints'('intersection$upoint'(sK35,sK36),X0) ),
inference(resolution,[status(thm)],[c11,c18]) ).
cnf(d2,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),X1)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),X2)
| 'apart$upoint$uand$uline'(X0,X1)
| 'apart$upoint$uand$uline'(X0,X2)
| ~ 'distinct$ulines'(X1,X2)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK34)
| 'apart$upoint$uand$uline'(X0,sK33) ),
inference(resolution,[status(thm)],[d1,c10]) ).
cnf(d3,plain,
( 'convergent$ulines'(sK35,X1)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK34)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK36)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),X1)
| 'apart$upoint$uand$uline'(X0,sK33)
| 'apart$upoint$uand$uline'(X0,sK36)
| 'apart$upoint$uand$uline'(X0,X1) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
~ 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK36),
inference(resolution,[status(thm)],[c9,c14]) ).
cnf(d5,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK34)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),X0)
| 'apart$upoint$uand$uline'(X1,sK33)
| 'apart$upoint$uand$uline'(X1,sK36)
| 'apart$upoint$uand$uline'(X1,X0)
| 'convergent$ulines'(sK35,X0) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK34)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK35)
| 'apart$upoint$uand$uline'(X0,sK33)
| 'apart$upoint$uand$uline'(X0,sK36)
| 'apart$upoint$uand$uline'(X0,sK35) ),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
~ 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK35),
inference(resolution,[status(thm)],[c8,c14]) ).
cnf(d8,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK34)
| 'apart$upoint$uand$uline'(X0,sK33)
| 'apart$upoint$uand$uline'(X0,sK36)
| 'apart$upoint$uand$uline'(X0,sK35) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK34)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK33)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK36) ),
inference(resolution,[status(thm)],[d8,c16]) ).
cnf(d10,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK33)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK34) ),
inference(resolution,[status(thm)],[c15,d9]) ).
cnf(d11,plain,
~ 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK33),
inference(resolution,[status(thm)],[c8,c17]) ).
cnf(d12,plain,
'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK34),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( 'apart$upoint$uand$uline'(X0,sK34)
| 'distinct$upoints'('intersection$upoint'(sK35,sK36),X0) ),
inference(resolution,[status(thm)],[d12,c11]) ).
cnf(d14,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),X1)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),X2)
| 'apart$upoint$uand$uline'(X0,X1)
| 'apart$upoint$uand$uline'(X0,X2)
| ~ 'distinct$ulines'(X1,X2)
| 'apart$upoint$uand$uline'(X0,sK34) ),
inference(resolution,[status(thm)],[d13,c10]) ).
cnf(d15,plain,
( 'convergent$ulines'(sK35,X1)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK36)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),X1)
| 'apart$upoint$uand$uline'(X0,sK34)
| 'apart$upoint$uand$uline'(X0,sK36)
| 'apart$upoint$uand$uline'(X0,X1) ),
inference(resolution,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),X0)
| 'apart$upoint$uand$uline'(X1,sK34)
| 'apart$upoint$uand$uline'(X1,sK36)
| 'apart$upoint$uand$uline'(X1,X0)
| 'convergent$ulines'(sK35,X0) ),
inference(resolution,[status(thm)],[d4,d15]) ).
cnf(d17,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK35,sK36),sK35)
| 'apart$upoint$uand$uline'(X0,sK34)
| 'apart$upoint$uand$uline'(X0,sK36)
| 'apart$upoint$uand$uline'(X0,sK35) ),
inference(resolution,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
( 'apart$upoint$uand$uline'(X0,sK34)
| 'apart$upoint$uand$uline'(X0,sK36)
| 'apart$upoint$uand$uline'(X0,sK35) ),
inference(resolution,[status(thm)],[d7,d17]) ).
cnf(d19,plain,
( 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK34)
| 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK36) ),
inference(resolution,[status(thm)],[d18,c16]) ).
cnf(d20,plain,
'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK34),
inference(resolution,[status(thm)],[c15,d19]) ).
cnf(d21,plain,
~ 'apart$upoint$uand$uline'('intersection$upoint'(sK33,sK34),sK34),
inference(resolution,[status(thm)],[c9,c17]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO196+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n011.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Fri Sep 25 13:04:29 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.53 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.51/5.45 % SZS status Theorem for theBenchmark.p
% 39.51/5.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------