%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL382+1 : TPTP v9.3.1. Released v9.1.0.
% 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 01:07:33 PM UTC 2026
% Result : Theorem 20.68s 3.71s
% Output : CNFRefutation 20.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 26 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 29 ~; 24 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 96 ( 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
is_a_theorem(implies(implies(x,y),implies(implies(y,not(x)),not(x)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(implies(y,not(x)),not(x)))),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
~ is_a_theorem(implies(implies(x,y),implies(implies(y,not(x)),not(x)))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f10,f9]) ).
fof(f26,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f25,f9]) ).
fof(f28,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,implies(implies(y,not(x)),not(x))))
| ~ is_a_theorem(implies(implies(x,y),X0)) ),
inference(resolution,[status(thm)],[f26,f13]) ).
fof(f116,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f25,f11]) ).
fof(f117,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3))),
inference(resolution,[status(thm)],[f25,f10]) ).
fof(f118,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f25,f12]) ).
fof(f122,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f116,f9]) ).
fof(f129,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f118,f9]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X0,implies(X1,X3)))
| ~ is_a_theorem(implies(X0,implies(implies(not(X1),X2),X3))) ),
inference(resolution,[status(thm)],[f26,f118]) ).
fof(f151,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[f26,f11]) ).
fof(f161,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(implies(X1,X2),implies(not(X0),X2)))),
inference(resolution,[status(thm)],[f129,f10]) ).
fof(f313,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f161,f9]) ).
fof(f322,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X2,X0),X3))
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)) ),
inference(resolution,[status(thm)],[f117,f9]) ).
fof(f444,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,x))
| ~ is_a_theorem(implies(implies(X0,y),implies(implies(y,not(x)),not(x)))) ),
inference(resolution,[status(thm)],[f28,f25]) ).
fof(f595,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f129,f313]) ).
fof(f625,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f151,f25]) ).
fof(f635,plain,
! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f151,f595]) ).
fof(f640,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f635,f11]) ).
fof(f880,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X0),X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f122,f9]) ).
fof(f984,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(resolution,[status(thm)],[f625,f640]) ).
fof(f2883,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f322,f984]) ).
fof(f3979,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f2883,f322]) ).
fof(f5403,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f3979,f129]) ).
fof(f5404,plain,
~ is_a_theorem(implies(not(not(x)),x)),
inference(resolution,[status(thm)],[f3979,f444]) ).
fof(f5435,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f5403,f149]) ).
fof(f5468,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f5435,f635]) ).
fof(f5558,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f5468,f880]) ).
fof(f6904,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(resolution,[status(thm)],[f5558,f10]) ).
fof(f7279,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f6904,f9]) ).
fof(f7365,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f7279,f3979]) ).
fof(f7448,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[f7365,f149]) ).
fof(f7467,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[f7448,f151]) ).
fof(f7475,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f5404,f7467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL382+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:31:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 20.68/3.71 % Refutation found
% 20.68/3.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 20.68/3.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 20.68/3.76 % Elapsed time: 3.380057 seconds
% 20.68/3.76 % CPU time: 26.245375 seconds
% 20.68/3.76 % Total memory used: 219.533 MB
% 20.68/3.76 % Net memory used: 193.205 MB
%------------------------------------------------------------------------------