%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL371+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 : n015.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 01:07:31 PM UTC 2026
% Result : Theorem 25.43s 3.70s
% Output : CNFRefutation 11.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 28 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 33 ~; 29 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 117 ( 117 !; 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,y),y),implies(implies(y,x),x))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),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(implies(x,y),y),implies(implies(y,x),x))),
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(f19,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)],[f17,f10]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(implies(X0,X2),X3),implies(implies(X1,X2),X3)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f19,f9]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X1,X2),X3))
| ~ is_a_theorem(implies(implies(X0,X2),X3))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f28,f9]) ).
fof(f45,plain,
! [X0] :
( ~ is_a_theorem(implies(implies(X0,y),implies(implies(y,x),x)))
| ~ is_a_theorem(implies(X0,implies(x,y))) ),
inference(resolution,[status(thm)],[f37,f13]) ).
fof(f83,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f11,f14]) ).
fof(f87,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f12,f14]) ).
fof(f88,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f12,f9]) ).
fof(f94,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f88,f14]) ).
fof(f106,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f83,f9]) ).
fof(f110,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f87,f9]) ).
fof(f117,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X0),X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f106,f9]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f110,f94]) ).
fof(f323,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(f407,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)],[f323,f87]) ).
fof(f408,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[f323,f106]) ).
fof(f409,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[f323,f11]) ).
fof(f429,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f409,f14]) ).
fof(f436,plain,
! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f409,f126]) ).
fof(f457,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f436,f11]) ).
fof(f470,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(not(X1),X2)))),
inference(resolution,[status(thm)],[f436,f12]) ).
fof(f705,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(resolution,[status(thm)],[f429,f457]) ).
fof(f711,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,implies(not(X0),X1)),X2),X2)),
inference(resolution,[status(thm)],[f429,f470]) ).
fof(f1418,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f705,f17]) ).
fof(f1513,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(X0,implies(not(X1),X2)))),
inference(resolution,[status(thm)],[f711,f17]) ).
fof(f1588,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f1418,f17]) ).
fof(f1941,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f1588,f110]) ).
fof(f1942,plain,
~ is_a_theorem(implies(not(x),implies(x,y))),
inference(resolution,[status(thm)],[f1588,f45]) ).
fof(f1964,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f1941,f407]) ).
fof(f1988,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f1964,f436]) ).
fof(f2002,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f1988,f117]) ).
fof(f2249,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(not(implies(X1,X0)),X2))),
inference(resolution,[status(thm)],[f2002,f1513]) ).
fof(f2303,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(implies(implies(X2,X0),X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f2249,f408]) ).
fof(f3227,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f2303,f1588]) ).
fof(f3299,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[f3227,f407]) ).
fof(f3307,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1942,f3299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL371+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 00:28:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 25.43/3.70 % Refutation found
% 25.43/3.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 25.43/3.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.67/3.75 % Elapsed time: 3.359208 seconds
% 11.67/3.75 % CPU time: 26.353959 seconds
% 11.67/3.75 % Total memory used: 241.266 MB
% 11.67/3.75 % Net memory used: 210.990 MB
%------------------------------------------------------------------------------