%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL069-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 01:06:43 PM UTC 2026
% Result : Unsatisfiable 0.21s 5.74s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 20 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 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; 2 con; 0-2 aty)
% Number of variables : 80 ( 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Z,Y] : is_a_theorem(implies(implies(not(X),Z),implies(implies(Y,Z),implies(implies(X,Y),Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(a,implies(not(a),b))),
file('/export/starexec/sandbox/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(implies(X0,X1),X2),implies(X1,X2))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X2,X1),implies(implies(X0,X2),X1)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f8,f7]) ).
fof(f13,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(not(X0),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f9,f7]) ).
fof(f15,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f22,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X2,X1),implies(implies(X0,X2),X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f39,plain,
! [X0,X1,X2] : is_a_theorem(implies(not(implies(X0,X1)),implies(X1,X2))),
inference(resolution,[status(thm)],[f13,f8]) ).
fof(f42,plain,
! [X0,X1,X2] : is_a_theorem(implies(not(X0),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f13,f15]) ).
fof(f101,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(implies(X3,X1),X0),implies(X1,X2)))),
inference(resolution,[status(thm)],[f22,f39]) ).
fof(f102,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,implies(X1,implies(X2,X3))),implies(implies(X2,X0),implies(X1,implies(X2,X3))))),
inference(resolution,[status(thm)],[f22,f42]) ).
fof(f240,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(implies(X3,X1),X0),implies(X1,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f101,f7]) ).
fof(f393,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X2,X0),implies(X1,implies(X2,X3))))
| ~ is_a_theorem(implies(X0,implies(X1,implies(X2,X3)))) ),
inference(resolution,[status(thm)],[f102,f7]) ).
fof(f444,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,X1),implies(implies(X2,X1),X3)),implies(X1,X3))),
inference(resolution,[status(thm)],[f240,f8]) ).
fof(f458,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,X1),not(X2)),implies(X1,implies(X2,X3)))),
inference(resolution,[status(thm)],[f240,f42]) ).
fof(f754,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),X3))) ),
inference(resolution,[status(thm)],[f444,f7]) ).
fof(f914,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[f754,f458]) ).
fof(f918,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f754,f8]) ).
fof(f2105,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,not(X1)),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f393,f914]) ).
fof(f2180,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[f2105,f7]) ).
fof(f2189,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(resolution,[status(thm)],[f2180,f918]) ).
fof(f2191,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f11,f2189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL069-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.43 % Computer : n017.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Sun Sep 20 23:58:47 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.45 % Drodi V4.1.1
% 0.21/5.74 % Refutation found
% 0.21/5.74 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/5.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/5.77 % Elapsed time: 0.321598 seconds
% 0.21/5.77 % CPU time: 2.314412 seconds
% 0.21/5.77 % Total memory used: 82.172 MB
% 0.21/5.77 % Net memory used: 76.919 MB
%------------------------------------------------------------------------------