%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL191-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 01:07:04 PM UTC 2026
% Result : Unsatisfiable 45.22s 6.20s
% Output : CNFRefutation 45.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 19 unt; 0 def)
% Number of atoms : 62 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 33 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(or(p,or(q,r)),or(or(p,q),r))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(or(p,or(q,r)),or(or(p,q),r))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f34,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f43,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f44,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f46,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f15,f44]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f34,f18]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[f43,f18]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,or(not(X1),X2))) ),
inference(paramodulation,[status(thm)],[f15,f56]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,implies(X0,X2)))
| theorem(or(not(X0),or(X1,X2))) ),
inference(paramodulation,[status(thm)],[f15,f56]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f87]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,implies(X0,X2)))
| theorem(implies(X0,or(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f88]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X0))
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f65,f18]) ).
fof(f180,plain,
! [X0] :
( ~ theorem(X0)
| ~ theorem(implies(X0,implies(or(p,or(q,r)),or(or(p,q),r)))) ),
inference(resolution,[status(thm)],[f19,f18]) ).
fof(f197,plain,
! [X0,X1] :
( ~ theorem(X1)
| ~ theorem(implies(X1,implies(X0,implies(or(p,or(q,r)),or(or(p,q),r)))))
| ~ theorem(X0) ),
inference(resolution,[status(thm)],[f180,f18]) ).
fof(f200,plain,
! [X0,X1] :
( ~ axiom(implies(X1,implies(X0,implies(or(p,or(q,r)),or(or(p,q),r)))))
| ~ theorem(X1)
| ~ theorem(X0) ),
inference(resolution,[status(thm)],[f197,f16]) ).
fof(f285,plain,
! [X0] :
( ~ theorem(implies(X0,or(or(p,q),r)))
| ~ theorem(implies(or(p,or(q,r)),X0)) ),
inference(resolution,[status(thm)],[f200,f46]) ).
fof(f392,plain,
! [X0,X1,X2,X3] :
( ~ theorem(implies(X0,or(X3,X1)))
| theorem(or(X3,X2))
| ~ theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f129,f89]) ).
fof(f546,plain,
~ theorem(implies(or(p,or(q,r)),or(r,or(p,q)))),
inference(resolution,[status(thm)],[f285,f31]) ).
fof(f720,plain,
! [X0,X1,X2] :
( theorem(or(X1,X2))
| ~ theorem(implies(implies(or(X0,X1),X0),X2)) ),
inference(resolution,[status(thm)],[f392,f31]) ).
fof(f1877,plain,
~ theorem(or(r,implies(or(p,or(q,r)),or(p,q)))),
inference(resolution,[status(thm)],[f546,f90]) ).
fof(f2215,plain,
! [X0,X1,X2] : theorem(or(X0,implies(or(X1,or(X2,X0)),or(X1,X2)))),
inference(resolution,[status(thm)],[f720,f43]) ).
fof(f2232,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1877,f2215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL191-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 00:09:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 45.22/6.20 % Refutation found
% 45.22/6.20 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 45.22/6.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 35.22/6.29 % Elapsed time: 5.917209 seconds
% 35.22/6.29 % CPU time: 46.359631 seconds
% 35.22/6.29 % Total memory used: 273.503 MB
% 35.22/6.29 % Net memory used: 242.367 MB
%------------------------------------------------------------------------------