%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRA010+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 07:18:43 AM UTC 2026
% Result : Theorem 13.96s 2.60s
% Output : CNFRefutation 13.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 63 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 64 ( 23 ~; 24 |; 9 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 19 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sequential_pairs_and_triangles,axiom,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& 'on$upath'(X4,X0)
& 'on$upath'(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> 'number$uof$uin'('sequential$upairs',X0) = 'number$uof$uin'(triangles,X0) ) ).
fof(complete_means_sequential_pairs_and_triangles,conjecture,
( complete
=> ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& 'on$upath'(X4,X0)
& 'on$upath'(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> 'number$uof$uin'('sequential$upairs',X0) = 'number$uof$uin'(triangles,X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& 'on$upath'(X4,X0)
& 'on$upath'(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> 'number$uof$uin'('sequential$upairs',X0) = 'number$uof$uin'(triangles,X0) ) ),
inference(negate_conjecture,[status(cth)],[complete_means_sequential_pairs_and_triangles]) ).
cnf(c11,plain,
( 'number$uof$uin'('sequential$upairs',X2) = 'number$uof$uin'(triangles,X2)
| 'on$upath'(sK13(X2),X2)
| ~ path(X0,X1,X2) ),
inference(clausification,[status(esa)],[sequential_pairs_and_triangles]) ).
cnf(c12,plain,
( 'number$uof$uin'('sequential$upairs',X2) = 'number$uof$uin'(triangles,X2)
| 'on$upath'(sK14(X2),X2)
| ~ path(X0,X1,X2) ),
inference(clausification,[status(esa)],[sequential_pairs_and_triangles]) ).
cnf(c13,plain,
( 'number$uof$uin'('sequential$upairs',X2) = 'number$uof$uin'(triangles,X2)
| sequential(sK13(X2),sK14(X2))
| ~ path(X0,X1,X2) ),
inference(clausification,[status(esa)],[sequential_pairs_and_triangles]) ).
cnf(c14,plain,
( 'number$uof$uin'('sequential$upairs',X2) = 'number$uof$uin'(triangles,X2)
| ~ triangle(sK13(X2),sK14(X2),X3)
| ~ path(X0,X1,X2) ),
inference(clausification,[status(esa)],[sequential_pairs_and_triangles]) ).
cnf(c80,plain,
path(sK82,sK83,sK81),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c81,plain,
( triangle(X0,X1,sK86(X0,X1))
| ~ sequential(X0,X1)
| ~ 'on$upath'(X1,sK81)
| ~ 'on$upath'(X0,sK81) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c82,plain,
'number$uof$uin'('sequential$upairs',sK81) != 'number$uof$uin'(triangles,sK81),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( sequential(sK13(sK81),sK14(sK81))
| 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81) ),
inference(resolution,[status(thm)],[c13,c80]) ).
cnf(d1,plain,
sequential(sK13(sK81),sK14(sK81)),
inference(resolution,[status(thm)],[c82,d0]) ).
cnf(d2,plain,
( ~ 'on$upath'(sK14(X0),sK81)
| ~ 'on$upath'(sK13(X0),sK81)
| ~ sequential(sK13(X0),sK14(X0))
| ~ path(X1,X2,X0)
| 'number$uof$uin'('sequential$upairs',X0) = 'number$uof$uin'(triangles,X0) ),
inference(resolution,[status(thm)],[c14,c81]) ).
cnf(d3,plain,
( ~ 'on$upath'(sK14(sK81),sK81)
| ~ 'on$upath'(sK13(sK81),sK81)
| ~ path(X0,X1,sK81)
| 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ 'on$upath'(sK14(sK81),sK81)
| ~ 'on$upath'(sK13(sK81),sK81)
| ~ path(X0,X1,sK81) ),
inference(resolution,[status(thm)],[c82,d3]) ).
cnf(d5,plain,
( 'on$upath'(sK13(sK81),sK81)
| 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81) ),
inference(resolution,[status(thm)],[c11,c80]) ).
cnf(d6,plain,
'on$upath'(sK13(sK81),sK81),
inference(resolution,[status(thm)],[c82,d5]) ).
cnf(d7,plain,
( ~ 'on$upath'(sK14(sK81),sK81)
| ~ path(X0,X1,sK81) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( 'on$upath'(sK14(sK81),sK81)
| 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81) ),
inference(resolution,[status(thm)],[c12,c80]) ).
cnf(d9,plain,
'on$upath'(sK14(sK81),sK81),
inference(resolution,[status(thm)],[c82,d8]) ).
cnf(d10,plain,
~ path(X0,X1,sK81),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,c80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA010+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 13:50:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.96/2.60 % SZS status Theorem for theBenchmark.p
% 13.96/2.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------