%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL368-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 : Unsatisfiable 36.42s 5.07s
% Output : CNFRefutation 36.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 24 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 79 ( 42 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 123 ( 123 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,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,negated_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,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(implies(x,implies(y,z)),u),implies(implies(y,implies(x,z)),u))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,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(f13,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)],[f12,f8]) ).
fof(f15,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)],[f13,f7]) ).
fof(f16,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)],[f15,f13]) ).
fof(f23,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)],[f16,f7]) ).
fof(f32,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)],[f23,f7]) ).
fof(f39,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)],[f32,f11]) ).
fof(f77,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f9,f12]) ).
fof(f78,plain,
! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(resolution,[status(thm)],[f9,f7]) ).
fof(f81,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f10,f12]) ).
fof(f82,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f87,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f82,f12]) ).
fof(f99,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f77,f7]) ).
fof(f102,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)],[f81,f12]) ).
fof(f103,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f81,f7]) ).
fof(f106,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)],[f87,f12]) ).
fof(f110,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X0),X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f99,f7]) ).
fof(f115,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f103,f9]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f103,f87]) ).
fof(f174,plain,
~ is_a_theorem(implies(implies(y,implies(x,z)),implies(x,implies(y,z)))),
inference(resolution,[status(thm)],[f115,f39]) ).
fof(f187,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))),
inference(resolution,[status(thm)],[f119,f115]) ).
fof(f192,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X0)),X1)),
inference(resolution,[status(thm)],[f187,f78]) ).
fof(f232,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f110,f192]) ).
fof(f253,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)],[f12,f7]) ).
fof(f345,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)],[f253,f103]) ).
fof(f349,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)],[f253,f232]) ).
fof(f405,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1)) ),
inference(resolution,[status(thm)],[f349,f77]) ).
fof(f440,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)],[f102,f7]) ).
fof(f505,plain,
! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f405,f106]) ).
fof(f511,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(not(X1),X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f405,f12]) ).
fof(f528,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f505,f103]) ).
fof(f559,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)],[f15,f12]) ).
fof(f583,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f528,f9]) ).
fof(f1383,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f511,f12]) ).
fof(f2215,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(resolution,[status(thm)],[f1383,f583]) ).
fof(f2458,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f2215,f15]) ).
fof(f2870,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f2458,f15]) ).
fof(f3018,plain,
~ is_a_theorem(implies(x,implies(implies(x,z),z))),
inference(resolution,[status(thm)],[f559,f174]) ).
fof(f3851,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(implies(X0,X1),X1),X2)) ),
inference(resolution,[status(thm)],[f2870,f345]) ).
fof(f11577,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(implies(implies(X2,X0),X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f3851,f440]) ).
fof(f12217,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f11577,f2870]) ).
fof(f12294,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f3018,f12217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL368-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:27:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 36.42/5.07 % Refutation found
% 36.42/5.07 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 36.42/5.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 36.42/5.12 % Elapsed time: 4.745149 seconds
% 36.42/5.12 % CPU time: 37.285071 seconds
% 36.42/5.12 % Total memory used: 390.138 MB
% 36.42/5.12 % Net memory used: 338.718 MB
%------------------------------------------------------------------------------