%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL365+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 : n020.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 01:07:29 PM UTC 2026
% Result : Theorem 2.85s 0.81s
% Output : CNFRefutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 20 |; 1 &)
% ( 0 <=>; 1 =>; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 62 !; 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(implies(x,implies(implies(y,z),z)),u),implies(implies(not(z),y),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,implies(implies(y,z),z)),u),implies(implies(not(z),y),u))),
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(implies(x,implies(implies(y,z),z)),u),implies(implies(not(z),y),u))),
inference(cnf_transformation,[status(thm)],[f6]) ).
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)],[f10,f9]) ).
fof(f16,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f12,f9]) ).
fof(f17,plain,
~ is_a_theorem(implies(implies(not(z),y),implies(x,implies(implies(y,z),z)))),
inference(resolution,[status(thm)],[f14,f13]) ).
fof(f18,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,f9]) ).
fof(f29,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,implies(x,implies(implies(y,z),z))))
| ~ is_a_theorem(implies(implies(not(z),y),X0)) ),
inference(resolution,[status(thm)],[f18,f17]) ).
fof(f77,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[f18,f11]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X0,implies(implies(X2,X3),implies(X1,X3))))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f18,f10]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(X0,implies(X3,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f18,f14]) ).
fof(f104,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f77,f12]) ).
fof(f107,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X3),implies(implies(X1,X2),X3)))),
inference(resolution,[status(thm)],[f78,f10]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X0,implies(not(X3),X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f79,f16]) ).
fof(f111,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,implies(implies(not(X1),X1),X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f79,f11]) ).
fof(f144,plain,
! [X0] :
( ~ is_a_theorem(implies(x,X0))
| ~ is_a_theorem(implies(implies(not(z),y),implies(X0,implies(implies(y,z),z)))) ),
inference(resolution,[status(thm)],[f29,f14]) ).
fof(f517,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f110,f12]) ).
fof(f546,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))),
inference(resolution,[status(thm)],[f517,f104]) ).
fof(f555,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f546,f77]) ).
fof(f641,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f555,f111]) ).
fof(f795,plain,
~ is_a_theorem(implies(x,implies(implies(not(z),z),z))),
inference(resolution,[status(thm)],[f144,f107]) ).
fof(f1286,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f795,f641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL365+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n020.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 00:25:02 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 2.85/0.81 % Refutation found
% 2.85/0.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.85/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.85/0.82 % Elapsed time: 0.467148 seconds
% 2.85/0.82 % CPU time: 3.408452 seconds
% 2.85/0.82 % Total memory used: 103.401 MB
% 2.85/0.82 % Net memory used: 96.557 MB
%------------------------------------------------------------------------------