%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL405-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 01:07:38 PM UTC 2026
% Result : Unsatisfiable 10.81s 1.84s
% Output : CNFRefutation 10.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 75 ( 52 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 28 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 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 : 186 ( 186 !; 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(not(implies(implies(x,x),not(implies(y,y))))),
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(not(implies(implies(x,x),not(implies(y,y))))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(resolution,[status(thm)],[f7,f9]) ).
fof(f13,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f7,f10]) ).
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(f53,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f14,f9]) ).
fof(f54,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(f55,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f14,f10]) ).
fof(f59,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)],[f55,f14]) ).
fof(f60,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f55,f7]) ).
fof(f86,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f60,f9]) ).
fof(f94,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X0)),X1)),
inference(resolution,[status(thm)],[f86,f13]) ).
fof(f98,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(implies(X2,X2)),X1))),
inference(resolution,[status(thm)],[f94,f14]) ).
fof(f122,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)],[f54,f7]) ).
fof(f155,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))),
inference(resolution,[status(thm)],[f98,f60]) ).
fof(f165,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(not(implies(X0,X0)),X1),X2),implies(X3,X2))),
inference(resolution,[status(thm)],[f155,f14]) ).
fof(f379,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(implies(not(implies(X0,X0)),X1),X2)) ),
inference(resolution,[status(thm)],[f165,f7]) ).
fof(f407,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f379,f9]) ).
fof(f431,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1))),
inference(resolution,[status(thm)],[f407,f14]) ).
fof(f463,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f431,f7]) ).
fof(f474,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f463,f53]) ).
fof(f535,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),implies(X2,X1))),
inference(resolution,[status(thm)],[f474,f14]) ).
fof(f759,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,not(X1)),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f122,f55]) ).
fof(f765,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X0,X1)))),
inference(resolution,[status(thm)],[f122,f431]) ).
fof(f788,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(resolution,[status(thm)],[f765,f60]) ).
fof(f804,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,implies(not(X1),X2)),X3),implies(X1,X3))),
inference(resolution,[status(thm)],[f788,f14]) ).
fof(f920,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[f759,f7]) ).
fof(f1290,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X2,implies(X0,X1)))),
inference(resolution,[status(thm)],[f535,f122]) ).
fof(f1296,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1)) ),
inference(resolution,[status(thm)],[f535,f7]) ).
fof(f1396,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(implies(X0,implies(not(X1),X2)),X3)) ),
inference(resolution,[status(thm)],[f804,f7]) ).
fof(f1669,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(not(X0),X1),implies(X2,implies(implies(X1,X0),X0)))),
inference(resolution,[status(thm)],[f1290,f122]) ).
fof(f1677,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X2,implies(X0,X1)))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[f1290,f7]) ).
fof(f1687,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(implies(implies(not(not(X1)),X2),X1),X1))),
inference(resolution,[status(thm)],[f1296,f59]) ).
fof(f1754,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(not(not(X0)),X1),X0),X0)),
inference(resolution,[status(thm)],[f1687,f12]) ).
fof(f1774,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(implies(not(not(X0)),X1),X0)) ),
inference(resolution,[status(thm)],[f1754,f7]) ).
fof(f1924,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X0)))),
inference(resolution,[status(thm)],[f1396,f1290]) ).
fof(f1975,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,implies(X1,X2)),X3),implies(X2,X3))),
inference(resolution,[status(thm)],[f1924,f14]) ).
fof(f2338,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f1975,f1296]) ).
fof(f2357,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f2338,f1774]) ).
fof(f2393,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(resolution,[status(thm)],[f2357,f14]) ).
fof(f2626,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f2393,f7]) ).
fof(f5944,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(implies(X0,X2),X2)))),
inference(resolution,[status(thm)],[f1669,f2626]) ).
fof(f5985,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(implies(X0,X2),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f5944,f7]) ).
fof(f6153,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(implies(implies(X1,X1),X2),X2))),
inference(resolution,[status(thm)],[f5985,f86]) ).
fof(f6206,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X0),X1),X1)),
inference(resolution,[status(thm)],[f6153,f1774]) ).
fof(f6260,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(implies(implies(X1,X1),not(X0)),X2))),
inference(resolution,[status(thm)],[f6206,f920]) ).
fof(f6265,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f6206,f7]) ).
fof(f6495,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X0),not(implies(X1,X1))),X2)),
inference(resolution,[status(thm)],[f6260,f6265]) ).
fof(f10885,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(implies(X1,X2),X2)))),
inference(resolution,[status(thm)],[f1677,f5944]) ).
fof(f10954,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f10885,f1774]) ).
fof(f11042,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f10954,f14]) ).
fof(f11043,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f10954,f7]) ).
fof(f11221,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(resolution,[status(thm)],[f11043,f9]) ).
fof(f11328,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,implies(not(X0),X1)),X2),X2)),
inference(resolution,[status(thm)],[f11043,f10]) ).
fof(f11770,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f11221,f122]) ).
fof(f11848,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)) ),
inference(resolution,[status(thm)],[f11328,f7]) ).
fof(f12184,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f11770,f122]) ).
fof(f12208,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[f11770,f7]) ).
fof(f12562,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),X0))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f12184,f7]) ).
fof(f14723,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f11042,f122]) ).
fof(f16380,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[f14723,f11848]) ).
fof(f16435,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[f16380,f12208]) ).
fof(f16473,plain,
! [X0] : is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(resolution,[status(thm)],[f16435,f12562]) ).
fof(f16917,plain,
! [X0] :
( is_a_theorem(not(X0))
| ~ is_a_theorem(implies(X0,not(X0))) ),
inference(resolution,[status(thm)],[f16473,f7]) ).
fof(f17491,plain,
! [X0,X1] : is_a_theorem(not(implies(implies(X0,X0),not(implies(X1,X1))))),
inference(resolution,[status(thm)],[f16917,f6495]) ).
fof(f25194,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f11,f17491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL405-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 00:29:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 10.81/1.84 % Refutation found
% 10.81/1.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.81/1.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.81/1.89 % Elapsed time: 1.505145 seconds
% 10.81/1.89 % CPU time: 11.265946 seconds
% 10.81/1.89 % Total memory used: 138.483 MB
% 10.81/1.89 % Net memory used: 125.278 MB
%------------------------------------------------------------------------------