%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL060-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 01:06:42 PM UTC 2026
% Result : Unsatisfiable 251.49s 32.38s
% Output : CNFRefutation 251.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 30 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 40 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 124 ( 124 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,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,negated_conjecture,
~ is_a_theorem(implies(implies(a,b),implies(implies(not(a),b),b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,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(f9,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(not(a),b),b))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f8,f7]) ).
fof(f25,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)],[f14,f7]) ).
fof(f28,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,implies(implies(not(a),b),b)))
| ~ is_a_theorem(implies(implies(a,b),X0)) ),
inference(resolution,[status(thm)],[f25,f11]) ).
fof(f29,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f25,f7]) ).
fof(f39,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,a))
| ~ is_a_theorem(implies(implies(X0,b),implies(implies(not(a),b),b))) ),
inference(resolution,[status(thm)],[f28,f14]) ).
fof(f65,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f14,f9]) ).
fof(f66,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)],[f14,f8]) ).
fof(f67,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f14,f10]) ).
fof(f125,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[f25,f9]) ).
fof(f134,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f65,f7]) ).
fof(f139,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)],[f67,f25]) ).
fof(f142,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f67,f7]) ).
fof(f245,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)],[f66,f7]) ).
fof(f255,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(implies(not(X1),X2),X3))) ),
inference(resolution,[status(thm)],[f29,f67]) ).
fof(f341,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(implies(X1,X2),implies(not(X0),X2)))),
inference(resolution,[status(thm)],[f142,f8]) ).
fof(f678,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f341,f7]) ).
fof(f843,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f142,f14]) ).
fof(f856,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f125,f14]) ).
fof(f869,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(implies(X2,implies(not(X1),X1)))
| ~ is_a_theorem(implies(X0,X2))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f125,f25]) ).
fof(f901,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X0),X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f134,f7]) ).
fof(f970,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f678,f125]) ).
fof(f982,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f970,f142]) ).
fof(f1039,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f982,f9]) ).
fof(f1528,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(resolution,[status(thm)],[f856,f1039]) ).
fof(f2528,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f1528,f245]) ).
fof(f3746,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f2528,f245]) ).
fof(f5376,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f3746,f142]) ).
fof(f5387,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(not(X0),not(X1))) ),
inference(resolution,[status(thm)],[f3746,f255]) ).
fof(f5534,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f5376,f139]) ).
fof(f5578,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f5534,f982]) ).
fof(f5599,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f5578,f901]) ).
fof(f5600,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),X2)),
inference(resolution,[status(thm)],[f5578,f856]) ).
fof(f6349,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(resolution,[status(thm)],[f5599,f8]) ).
fof(f6438,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X2,X1)))),
inference(resolution,[status(thm)],[f5600,f245]) ).
fof(f7465,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f6349,f7]) ).
fof(f7598,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(implies(X0,X1)),X1),implies(X0,X1))),
inference(resolution,[status(thm)],[f6438,f125]) ).
fof(f7783,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f7465,f3746]) ).
fof(f7874,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[f7783,f139]) ).
fof(f7901,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[f7874,f125]) ).
fof(f7957,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(not(not(X0))),X1))),
inference(resolution,[status(thm)],[f7901,f843]) ).
fof(f10152,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,not(not(X1)))) ),
inference(resolution,[status(thm)],[f7957,f869]) ).
fof(f17366,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X1),X0))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f10152,f5387]) ).
fof(f22350,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(implies(not(X0),X1),X1)),X0)),
inference(resolution,[status(thm)],[f17366,f7783]) ).
fof(f32347,plain,
~ is_a_theorem(implies(not(implies(implies(not(a),b),b)),a)),
inference(resolution,[status(thm)],[f7598,f39]) ).
fof(f32382,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f32347,f22350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL060-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 00:02:27 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 251.49/32.38 % Refutation found
% 251.49/32.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 251.49/32.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 205.57/32.60 % Elapsed time: 32.186897 seconds
% 205.57/32.60 % CPU time: 253.511908 seconds
% 205.57/32.60 % Total memory used: 716.878 MB
% 205.57/32.60 % Net memory used: 627.575 MB
%------------------------------------------------------------------------------