%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 25 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 64 ( 64 !; 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(X,Y),equivalent(equivalent(X,Z),equivalent(Z,Y)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(a,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(X0,X1),equivalent(equivalent(X0,X2),equivalent(X2,X1)))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(a,c)))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(equivalent(X0,X2),equivalent(X2,X1)))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f9,plain,
! [X0,X1,X2,X3] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X2,equivalent(equivalent(X0,X3),equivalent(X3,X1))))),
inference(resolution,[status(thm)],[f8,f6]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(X2,equivalent(equivalent(X0,X3),equivalent(X3,X1))))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f9,f5]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X1,X2)),equivalent(equivalent(X0,X3),equivalent(X3,X2)))),
inference(resolution,[status(thm)],[f11,f6]) ).
fof(f14,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X1,X2)),equivalent(equivalent(equivalent(X0,X3),X4),equivalent(X4,equivalent(X3,X2))))),
inference(resolution,[status(thm)],[f13,f11]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(equivalent(X0,X3),equivalent(X3,X2)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X1,X2))) ),
inference(resolution,[status(thm)],[f13,f5]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(X3,X2))
| ~ is_a_theorem(equivalent(X0,X3))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X1,X2))) ),
inference(resolution,[status(thm)],[f16,f5]) ).
fof(f20,plain,
! [X0,X1] :
( ~ is_a_theorem(equivalent(X0,equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X1,equivalent(equivalent(c,b),equivalent(a,c))))) ),
inference(resolution,[status(thm)],[f19,f7]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(X0,X3))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X1,X2))) ),
inference(resolution,[status(thm)],[f19,f5]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(X0,X4),equivalent(X4,X1)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X2,X3))) ),
inference(resolution,[status(thm)],[f23,f6]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X0),equivalent(X1,X1)),X2),equivalent(X2,X3))) ),
inference(resolution,[status(thm)],[f26,f13]) ).
fof(f81,plain,
! [X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X1),X0))),
inference(resolution,[status(thm)],[f69,f14]) ).
fof(f82,plain,
! [X0] : is_a_theorem(equivalent(X0,X0)),
inference(resolution,[status(thm)],[f69,f13]) ).
fof(f108,plain,
! [X0,X1] :
( is_a_theorem(equivalent(equivalent(X1,X1),X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f81,f5]) ).
fof(f137,plain,
! [X0] : ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),X0),equivalent(X0,equivalent(equivalent(c,b),equivalent(a,c))))),
inference(resolution,[status(thm)],[f20,f82]) ).
fof(f170,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(X2,X1))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f108,f11]) ).
fof(f580,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))),
inference(resolution,[status(thm)],[f170,f137]) ).
fof(f596,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f580,f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n010.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 : Mon Sep 21 00:00:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.48 % Refutation found
% 0.13/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.51 % Elapsed time: 0.121977 seconds
% 0.13/0.51 % CPU time: 0.748730 seconds
% 0.13/0.51 % Total memory used: 68.309 MB
% 0.13/0.51 % Net memory used: 65.363 MB
%------------------------------------------------------------------------------