%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL368+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 01:07:30 PM UTC 2026
% Result : Theorem 35.00s 4.90s
% Output : CNFRefutation 30.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 25 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 81 ( 42 ~; 37 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 125 ( 125 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
is_a_theorem(implies(implies(implies(x,implies(y,z)),u),implies(implies(y,implies(x,z)),u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,implies(y,z)),u),implies(implies(y,implies(x,z)),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(y,z)),u),implies(implies(y,implies(x,z)),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(f15,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,f10]) ).
fof(f17,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)],[f15,f9]) ).
fof(f18,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X3,X1),implies(X0,implies(X3,X2))))),
inference(resolution,[status(thm)],[f17,f15]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X3,X1),implies(X0,implies(X3,X2))))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f18,f9]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X0,implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f25,f9]) ).
fof(f41,plain,
! [X0] :
( ~ is_a_theorem(implies(implies(y,implies(x,z)),X0))
| ~ is_a_theorem(implies(implies(implies(x,implies(y,z)),u),implies(X0,u))) ),
inference(resolution,[status(thm)],[f34,f13]) ).
fof(f79,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f11,f14]) ).
fof(f80,plain,
! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(resolution,[status(thm)],[f11,f9]) ).
fof(f83,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f12,f14]) ).
fof(f84,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f12,f9]) ).
fof(f89,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f84,f14]) ).
fof(f101,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f79,f9]) ).
fof(f104,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(implies(not(X0),X3),X1),X2))),
inference(resolution,[status(thm)],[f83,f14]) ).
fof(f105,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f83,f9]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(implies(X3,X1),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f89,f14]) ).
fof(f112,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X0),X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f101,f9]) ).
fof(f117,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f105,f11]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f105,f89]) ).
fof(f176,plain,
~ is_a_theorem(implies(implies(y,implies(x,z)),implies(x,implies(y,z)))),
inference(resolution,[status(thm)],[f117,f41]) ).
fof(f189,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))),
inference(resolution,[status(thm)],[f121,f117]) ).
fof(f194,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X0)),X1)),
inference(resolution,[status(thm)],[f189,f80]) ).
fof(f234,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f112,f194]) ).
fof(f255,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(f347,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X0,X3))
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f255,f105]) ).
fof(f351,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f255,f234]) ).
fof(f407,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1)) ),
inference(resolution,[status(thm)],[f351,f79]) ).
fof(f442,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(implies(not(X0),X3),X1),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f104,f9]) ).
fof(f507,plain,
! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f407,f108]) ).
fof(f513,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(not(X1),X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f407,f14]) ).
fof(f530,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f507,f105]) ).
fof(f561,plain,
! [X0,X1,X2,X3] :
( ~ is_a_theorem(implies(X2,implies(X1,X3)))
| is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X0,X3)))) ),
inference(resolution,[status(thm)],[f17,f14]) ).
fof(f585,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f530,f11]) ).
fof(f1385,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f513,f14]) ).
fof(f2217,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(resolution,[status(thm)],[f1385,f585]) ).
fof(f2460,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f2217,f17]) ).
fof(f2872,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f2460,f17]) ).
fof(f3020,plain,
~ is_a_theorem(implies(x,implies(implies(x,z),z))),
inference(resolution,[status(thm)],[f561,f176]) ).
fof(f3853,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(implies(X0,X1),X1),X2)) ),
inference(resolution,[status(thm)],[f2872,f347]) ).
fof(f11579,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(implies(implies(X2,X0),X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f3853,f442]) ).
fof(f12219,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f11579,f2872]) ).
fof(f12296,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f3020,f12219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL368+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n013.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 00:23:52 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 35.00/4.90 % Refutation found
% 35.00/4.90 % SZS status Theorem for theBenchmark: Theorem is valid
% 35.00/4.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 30.32/4.98 % Elapsed time: 4.612868 seconds
% 30.32/4.98 % CPU time: 36.267485 seconds
% 30.32/4.98 % Total memory used: 382.952 MB
% 30.32/4.98 % Net memory used: 333.447 MB
%------------------------------------------------------------------------------