%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL120-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(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 : Thu Sep 24 01:06:52 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.55s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 21 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 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 : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Z,Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))),
file('/export/starexec/sandbox/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(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X2,X1))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X2,X1))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X0,X2))) ),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f9,plain,
! [X0,X1] : is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X1,X0)))),
inference(resolution,[status(thm)],[f8,f6]) ).
fof(f10,plain,
! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X0,X1)),X1)),
inference(resolution,[status(thm)],[f9,f8]) ).
fof(f11,plain,
! [X0,X1] :
( is_a_theorem(equivalent(X1,equivalent(X1,X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f9,f5]) ).
fof(f13,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,equivalent(X0,X1))) ),
inference(resolution,[status(thm)],[f10,f5]) ).
fof(f14,plain,
! [X0,X1] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f11,f5]) ).
fof(f19,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X0,X2))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f14,f8]) ).
fof(f24,plain,
! [X0] :
( ~ is_a_theorem(equivalent(X0,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c))))
| ~ is_a_theorem(equivalent(X0,a)) ),
inference(resolution,[status(thm)],[f19,f7]) ).
fof(f25,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2)))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f19,f13]) ).
fof(f27,plain,
! [X0] : ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X0,a)),equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))),
inference(resolution,[status(thm)],[f24,f10]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(equivalent(X2,X1),X3))) ),
inference(resolution,[status(thm)],[f25,f6]) ).
fof(f72,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X1),equivalent(X2,X0)))),
inference(resolution,[status(thm)],[f33,f9]) ).
fof(f380,plain,
$false,
inference(resolution,[status(thm)],[f72,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL120-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 00:06:12 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.14/0.55 % Refutation found
% 0.14/0.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.13/0.58 % Elapsed time: 0.205981 seconds
% 1.13/0.58 % CPU time: 1.385653 seconds
% 1.13/0.58 % Total memory used: 77.342 MB
% 1.13/0.58 % Net memory used: 72.944 MB
%------------------------------------------------------------------------------