%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL378-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 01:07:33 PM UTC 2026
% Result : Unsatisfiable 7.32s 1.49s
% Output : CNFRefutation 7.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 41 unt; 0 def)
% Number of atoms : 78 ( 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 : 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 : 149 ( 149 !; 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(not(x),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(not(x),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(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(f18,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f14,f9]) ).
fof(f19,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(f20,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f14,f10]) ).
fof(f72,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)],[f20,f14]) ).
fof(f73,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f20,f7]) ).
fof(f76,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)],[f19,f7]) ).
fof(f100,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f73,f9]) ).
fof(f108,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X0)),X1)),
inference(resolution,[status(thm)],[f100,f13]) ).
fof(f112,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(implies(X2,X2)),X1))),
inference(resolution,[status(thm)],[f108,f14]) ).
fof(f160,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))),
inference(resolution,[status(thm)],[f112,f73]) ).
fof(f170,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(not(implies(X0,X0)),X1),X2),implies(X3,X2))),
inference(resolution,[status(thm)],[f160,f14]) ).
fof(f443,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)],[f170,f7]) ).
fof(f459,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f443,f9]) ).
fof(f476,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1))),
inference(resolution,[status(thm)],[f459,f14]) ).
fof(f501,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f476,f7]) ).
fof(f511,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f501,f18]) ).
fof(f560,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),implies(X2,X1))),
inference(resolution,[status(thm)],[f511,f14]) ).
fof(f797,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X0,X1)))),
inference(resolution,[status(thm)],[f76,f476]) ).
fof(f820,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(resolution,[status(thm)],[f797,f73]) ).
fof(f836,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,implies(not(X1),X2)),X3),implies(X1,X3))),
inference(resolution,[status(thm)],[f820,f14]) ).
fof(f1277,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X2,implies(X0,X1)))),
inference(resolution,[status(thm)],[f560,f76]) ).
fof(f1283,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)],[f560,f7]) ).
fof(f1404,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)],[f836,f7]) ).
fof(f1615,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(not(X0),X1),implies(X2,implies(implies(X1,X0),X0)))),
inference(resolution,[status(thm)],[f1277,f76]) ).
fof(f1623,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)],[f1277,f7]) ).
fof(f1633,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(implies(implies(not(not(X1)),X2),X1),X1))),
inference(resolution,[status(thm)],[f1283,f72]) ).
fof(f1685,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(not(not(X0)),X1),X0),X0)),
inference(resolution,[status(thm)],[f1633,f12]) ).
fof(f1720,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(implies(not(not(X0)),X1),X0)) ),
inference(resolution,[status(thm)],[f1685,f7]) ).
fof(f1857,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X0)))),
inference(resolution,[status(thm)],[f1404,f1277]) ).
fof(f1908,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,implies(X1,X2)),X3),implies(X2,X3))),
inference(resolution,[status(thm)],[f1857,f14]) ).
fof(f2284,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f1908,f1283]) ).
fof(f2303,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f2284,f1720]) ).
fof(f2339,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(resolution,[status(thm)],[f2303,f14]) ).
fof(f2628,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f2339,f7]) ).
fof(f5491,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(implies(X0,X2),X2)))),
inference(resolution,[status(thm)],[f1615,f2628]) ).
fof(f10656,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(implies(X1,X2),X2)))),
inference(resolution,[status(thm)],[f1623,f5491]) ).
fof(f10729,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f10656,f1720]) ).
fof(f10817,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f10729,f14]) ).
fof(f10818,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f10729,f7]) ).
fof(f11088,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,implies(not(X0),X1)),X2),X2)),
inference(resolution,[status(thm)],[f10818,f10]) ).
fof(f11745,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)) ),
inference(resolution,[status(thm)],[f11088,f7]) ).
fof(f14561,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f10817,f76]) ).
fof(f16094,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[f14561,f11745]) ).
fof(f16149,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f11,f16094]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL378-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 % Computer : n006.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Mon Sep 21 00:25:15 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.50 % Drodi V4.1.1
% 7.32/1.49 % Refutation found
% 7.32/1.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.32/1.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.50/1.53 % Elapsed time: 1.031429 seconds
% 3.50/1.53 % CPU time: 7.753654 seconds
% 3.50/1.53 % Total memory used: 126.974 MB
% 3.50/1.53 % Net memory used: 115.931 MB
%------------------------------------------------------------------------------