%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 : Thu Sep 24 01:06:35 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 16 ~; 11 |; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 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,Z] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X1),equivalent(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(equivalent(X2,X1),equivalent(X0,X2)))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f9,plain,
! [X0,X1,X2,X3] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(X3,X1))),equivalent(equivalent(X3,X2),X0))),
inference(resolution,[status(thm)],[f8,f6]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(equivalent(X3,X2),X0))
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(X3,X1)))) ),
inference(resolution,[status(thm)],[f9,f5]) ).
fof(f13,plain,
! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X0,X1))),
inference(resolution,[status(thm)],[f11,f6]) ).
fof(f15,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(equivalent(X1,X2),X0))),
inference(resolution,[status(thm)],[f13,f8]) ).
fof(f17,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(X2,X1)))),
inference(resolution,[status(thm)],[f15,f11]) ).
fof(f19,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(equivalent(X1,X2),X0))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(resolution,[status(thm)],[f15,f5]) ).
fof(f20,plain,
! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,X0),equivalent(X1,X1))),
inference(resolution,[status(thm)],[f17,f11]) ).
fof(f22,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(equivalent(X0,X2),equivalent(X2,X1)))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f17,f5]) ).
fof(f25,plain,
! [X0,X1] :
( is_a_theorem(equivalent(X1,X1))
| ~ is_a_theorem(equivalent(X0,X0)) ),
inference(resolution,[status(thm)],[f20,f5]) ).
fof(f29,plain,
~ is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b))),
inference(resolution,[status(thm)],[f19,f7]) ).
fof(f40,plain,
~ is_a_theorem(equivalent(b,b)),
inference(resolution,[status(thm)],[f22,f29]) ).
fof(f45,plain,
! [X0] : ~ is_a_theorem(equivalent(X0,X0)),
inference(resolution,[status(thm)],[f40,f25]) ).
fof(f47,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f13,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 00:01:59 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.41 % Elapsed time: 0.030647 seconds
% 0.11/0.41 % CPU time: 0.072651 seconds
% 0.11/0.41 % Total memory used: 7.107 MB
% 0.11/0.41 % Net memory used: 7.073 MB
%------------------------------------------------------------------------------