%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL396-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 01:07:36 PM UTC 2026
% Result : Unsatisfiable 2.46s 1.00s
% Output : CNFRefutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 5
% Syntax : Number of formulae : 65 ( 48 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 157 ( 157 !; 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(implies(implies(not(not(x)),y),implies(x,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(implies(implies(not(not(x)),y),implies(x,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(f16,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(f26,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f16,f9]) ).
fof(f27,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)],[f16,f8]) ).
fof(f28,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f16,f10]) ).
fof(f33,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f28,f7]) ).
fof(f49,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f33,f9]) ).
fof(f57,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X0)),X1)),
inference(resolution,[status(thm)],[f49,f13]) ).
fof(f66,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)],[f27,f7]) ).
fof(f71,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(implies(X2,X2)),X1))),
inference(resolution,[status(thm)],[f57,f16]) ).
fof(f105,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))),
inference(resolution,[status(thm)],[f71,f33]) ).
fof(f115,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(not(implies(X0,X0)),X1),X2),implies(X3,X2))),
inference(resolution,[status(thm)],[f105,f16]) ).
fof(f170,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)],[f115,f7]) ).
fof(f176,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f170,f9]) ).
fof(f190,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1))),
inference(resolution,[status(thm)],[f176,f16]) ).
fof(f234,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f190,f7]) ).
fof(f242,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X2)))),
inference(resolution,[status(thm)],[f234,f190]) ).
fof(f244,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f234,f26]) ).
fof(f259,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,implies(X1,X1)),X2),implies(X3,X2))),
inference(resolution,[status(thm)],[f242,f16]) ).
fof(f283,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),implies(X2,X1))),
inference(resolution,[status(thm)],[f244,f16]) ).
fof(f864,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X2,implies(X0,X1)))),
inference(resolution,[status(thm)],[f66,f283]) ).
fof(f1954,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(not(X0),X1),implies(X2,implies(implies(X1,X0),X0)))),
inference(resolution,[status(thm)],[f864,f66]) ).
fof(f1967,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)],[f864,f7]) ).
fof(f2466,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(implies(X2,X0),X0)))),
inference(resolution,[status(thm)],[f1954,f33]) ).
fof(f2688,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(X0,implies(implies(implies(X1,implies(X2,X2)),X3),X3))),
inference(resolution,[status(thm)],[f1967,f259]) ).
fof(f2731,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(implies(X2,X1),X1)))),
inference(resolution,[status(thm)],[f1967,f2466]) ).
fof(f2747,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f2731,f12]) ).
fof(f2784,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X1,X2))),
inference(resolution,[status(thm)],[f2747,f16]) ).
fof(f3063,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,implies(X1,X1)),X2),X2)),
inference(resolution,[status(thm)],[f2688,f12]) ).
fof(f3103,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X1)),X2)) ),
inference(resolution,[status(thm)],[f3063,f7]) ).
fof(f3229,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X2,implies(X0,X2)))),
inference(resolution,[status(thm)],[f2784,f66]) ).
fof(f3256,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f3229,f3103]) ).
fof(f3291,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(resolution,[status(thm)],[f3256,f16]) ).
fof(f3619,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f3291,f7]) ).
fof(f3712,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(implies(X0,X2),X2)))),
inference(resolution,[status(thm)],[f3619,f1954]) ).
fof(f4119,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(implies(X1,X2),X2)))),
inference(resolution,[status(thm)],[f3712,f1967]) ).
fof(f4315,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f4119,f12]) ).
fof(f4358,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f4315,f16]) ).
fof(f4359,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f4315,f7]) ).
fof(f4442,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(resolution,[status(thm)],[f4359,f9]) ).
fof(f4480,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,implies(not(X0),X1)),X2),X2)),
inference(resolution,[status(thm)],[f4359,f10]) ).
fof(f6298,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f4442,f66]) ).
fof(f6346,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)) ),
inference(resolution,[status(thm)],[f4480,f7]) ).
fof(f7454,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f6298,f66]) ).
fof(f7470,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[f6298,f7]) ).
fof(f7943,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),X0))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f7454,f7]) ).
fof(f10218,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f4358,f66]) ).
fof(f12996,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[f10218,f6346]) ).
fof(f13042,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[f12996,f7470]) ).
fof(f13073,plain,
! [X0] : is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(resolution,[status(thm)],[f13042,f7943]) ).
fof(f13385,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[f13073,f33]) ).
fof(f13446,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(not(X0)),X1),implies(X0,X1))),
inference(resolution,[status(thm)],[f13385,f16]) ).
fof(f18383,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f11,f13446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL396-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:30:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 2.46/1.00 % Refutation found
% 2.46/1.00 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.46/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.46/1.05 % Elapsed time: 0.668844 seconds
% 2.46/1.05 % CPU time: 4.998644 seconds
% 2.46/1.05 % Total memory used: 110.316 MB
% 2.46/1.05 % Net memory used: 102.743 MB
%------------------------------------------------------------------------------