%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 : Thu Sep 24 01:06:35 PM UTC 2026
% Result : Unsatisfiable 7.36s 1.38s
% Output : CNFRefutation 7.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(X,equivalent(Y,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X0,equivalent(X1,X2)))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
! [X0,X1] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f7,f6]) ).
fof(f12,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(equivalent(X0,X1),X2))),
inference(resolution,[status(thm)],[f8,f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X0,equivalent(X1,X2)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f8,f6]) ).
fof(f14,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,equivalent(X0,equivalent(X1,X2))))),
inference(resolution,[status(thm)],[f13,f8]) ).
fof(f16,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X0,X1),X2)))),
inference(resolution,[status(thm)],[f12,f13]) ).
fof(f20,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,X0))),equivalent(X1,X2))),
inference(resolution,[status(thm)],[f14,f10]) ).
fof(f21,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X2,equivalent(X0,equivalent(X1,X2))))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f14,f6]) ).
fof(f35,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X0),X1)),X2)),
inference(resolution,[status(thm)],[f16,f10]) ).
fof(f46,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X2,X0)))) ),
inference(resolution,[status(thm)],[f20,f6]) ).
fof(f49,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X0,equivalent(X1,X2)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f21,f6]) ).
fof(f111,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(equivalent(X2,X0),X1),X2))),
inference(resolution,[status(thm)],[f35,f13]) ).
fof(f229,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f49,f46]) ).
fof(f2860,plain,
! [X0] :
( ~ is_a_theorem(equivalent(equivalent(b,c),X0))
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(a,b),equivalent(c,a)))) ),
inference(resolution,[status(thm)],[f229,f9]) ).
fof(f4323,plain,
~ is_a_theorem(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),c),a))),
inference(resolution,[status(thm)],[f2860,f8]) ).
fof(f4366,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4323,f111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 00:05:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 7.36/1.38 % Refutation found
% 7.36/1.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.36/1.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.36/1.42 % Elapsed time: 1.046498 seconds
% 7.36/1.42 % CPU time: 7.996336 seconds
% 7.36/1.42 % Total memory used: 144.235 MB
% 7.36/1.42 % Net memory used: 128.217 MB
%------------------------------------------------------------------------------