%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL372+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 01:07:31 PM UTC 2026
% Result : Theorem 150.89s 19.65s
% Output : CNFRefutation 150.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 23 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 72 ( 38 ~; 32 |; 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 : 112 ( 112 !; 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(implies(x,y),y),z),implies(implies(implies(y,u),x),z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))),
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(implies(x,y),y),z),implies(implies(implies(y,u),x),z))),
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(f29,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f11,f14]) ).
fof(f32,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f12,f14]) ).
fof(f33,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f12,f9]) ).
fof(f35,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f33,f14]) ).
fof(f46,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f29,f9]) ).
fof(f48,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)],[f32,f14]) ).
fof(f49,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f32,f9]) ).
fof(f51,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)],[f35,f14]) ).
fof(f57,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X0),X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f46,f9]) ).
fof(f62,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)],[f48,f9]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X3,X1),X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f51,f9]) ).
fof(f115,plain,
~ is_a_theorem(implies(implies(implies(y,u),x),implies(implies(x,y),y))),
inference(resolution,[status(thm)],[f14,f13]) ).
fof(f116,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(f137,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(f150,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)],[f116,f49]) ).
fof(f151,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,implies(implies(x,y),y)))
| ~ is_a_theorem(implies(implies(implies(y,u),x),X0)) ),
inference(resolution,[status(thm)],[f116,f115]) ).
fof(f819,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X1,not(X0)),X3))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X2)),X3)) ),
inference(resolution,[status(thm)],[f62,f137]) ).
fof(f936,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f94,f11]) ).
fof(f1004,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f936,f49]) ).
fof(f1115,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f1004,f11]) ).
fof(f1347,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1)) ),
inference(resolution,[status(thm)],[f1115,f57]) ).
fof(f5776,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),X0))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f28,f1347]) ).
fof(f5919,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(resolution,[status(thm)],[f5776,f1115]) ).
fof(f6999,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f5919,f137]) ).
fof(f8261,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f6999,f137]) ).
fof(f18511,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(resolution,[status(thm)],[f819,f6999]) ).
fof(f19466,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f18511,f150]) ).
fof(f20270,plain,
! [X0] :
( ~ is_a_theorem(implies(implies(X0,x),implies(implies(x,y),y)))
| ~ is_a_theorem(implies(X0,implies(y,u))) ),
inference(resolution,[status(thm)],[f14,f151]) ).
fof(f21721,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[f19466,f18511]) ).
fof(f22311,plain,
~ is_a_theorem(implies(not(y),implies(y,u))),
inference(resolution,[status(thm)],[f20270,f8261]) ).
fof(f25876,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f22311,f21721]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL372+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 : n013.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 00:24:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 150.89/19.65 % Refutation found
% 150.89/19.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 150.89/19.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 138.77/19.79 % Elapsed time: 19.390323 seconds
% 138.77/19.79 % CPU time: 153.181113 seconds
% 138.77/19.79 % Total memory used: 624.932 MB
% 138.77/19.79 % Net memory used: 541.518 MB
%------------------------------------------------------------------------------