%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL210-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 01:07:09 PM UTC 2026
% Result : Unsatisfiable 7.22s 1.36s
% Output : CNFRefutation 7.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 29 unt; 0 def)
% Number of atoms : 90 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 37 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 109 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ theorem(implies(not(p),implies(or(p,q),q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : axiom(implies(or(X0,X0),X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0] :
( ~ axiom(X0)
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [Y] :
( ~ theorem(Y)
| ! [X] :
( ~ theorem(implies(Y,X))
| theorem(X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f18,plain,
! [X0,X1] :
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
~ theorem(implies(not(p),implies(or(p,q),q))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f22,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f27,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f29,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f27,f18]) ).
fof(f38,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f42,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f51,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f56,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f38,f18]) ).
fof(f57,plain,
! [X0,X1] : theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f15,f38]) ).
fof(f58,plain,
! [X0,X1] : theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15,f38]) ).
fof(f69,plain,
! [X0,X1] : theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f15,f57]) ).
fof(f70,plain,
! [X0,X1] :
( ~ theorem(or(X1,not(X0)))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f58,f18]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f42,f18]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[f51,f18]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ theorem(or(X0,X2))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f75,f29]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,or(not(X1),X2))) ),
inference(paramodulation,[status(thm)],[f15,f75]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f124]) ).
fof(f154,plain,
! [X0,X1,X2] :
( theorem(or(or(X2,X1),X0))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f123,f56]) ).
fof(f155,plain,
! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(or(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f123,f22]) ).
fof(f170,plain,
! [X0,X1] :
( ~ theorem(or(X1,X1))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f155,f154]) ).
fof(f281,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X0))
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f107,f18]) ).
fof(f302,plain,
! [X0,X1] : theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f126,f27]) ).
fof(f332,plain,
! [X0] : theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f302,f22]) ).
fof(f335,plain,
! [X0,X1] : theorem(or(X0,implies(or(X0,X1),X1))),
inference(resolution,[status(thm)],[f332,f126]) ).
fof(f369,plain,
! [X0,X1] : theorem(or(implies(or(X0,X1),X1),X0)),
inference(resolution,[status(thm)],[f335,f56]) ).
fof(f438,plain,
! [X0,X1,X2] :
( theorem(or(X2,X1))
| ~ theorem(or(or(X2,X1),X0))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f281,f155]) ).
fof(f440,plain,
! [X0,X1,X2] :
( theorem(implies(X1,X2))
| ~ theorem(or(X2,X0))
| ~ theorem(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[f281,f70]) ).
fof(f442,plain,
! [X0,X1] :
( theorem(X1)
| ~ theorem(or(X1,X0))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f281,f22]) ).
fof(f754,plain,
! [X0] :
( theorem(X0)
| ~ theorem(or(X0,or(X0,X0))) ),
inference(resolution,[status(thm)],[f442,f20]) ).
fof(f794,plain,
! [X0] :
( ~ theorem(or(or(X0,X0),or(X0,X0)))
| theorem(X0) ),
inference(resolution,[status(thm)],[f754,f170]) ).
fof(f943,plain,
! [X0] :
( ~ theorem(or(or(X0,X0),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f794,f154]) ).
fof(f1359,plain,
! [X0,X1,X2] :
( theorem(or(X2,X1))
| ~ theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f438,f302]) ).
fof(f1804,plain,
! [X0,X1] :
( theorem(X1)
| ~ theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f1359,f943]) ).
fof(f1822,plain,
! [X0] : theorem(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[f1804,f69]) ).
fof(f1876,plain,
! [X0,X1] :
( theorem(implies(not(X1),X0))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f1822,f440]) ).
fof(f2172,plain,
~ theorem(or(implies(or(p,q),q),p)),
inference(resolution,[status(thm)],[f1876,f19]) ).
fof(f2208,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2172,f369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL210-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 00:14:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 7.22/1.36 % Refutation found
% 7.22/1.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.22/1.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.22/1.39 % Elapsed time: 1.013206 seconds
% 7.22/1.39 % CPU time: 7.735181 seconds
% 7.22/1.39 % Total memory used: 148.155 MB
% 7.22/1.39 % Net memory used: 136.449 MB
%------------------------------------------------------------------------------