%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL287-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 01:07:22 PM UTC 2026
% Result : Unsatisfiable 0.26s 0.63s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 35 unt; 0 def)
% Number of atoms : 54 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 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(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,axiom,
! [P,Q] : and(P,Q) = not(or(not(P),not(Q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [P,Q] : equivalent(P,Q) = and(implies(P,Q),implies(Q,P)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ theorem(equivalent(and(p,q),not(or(not(p),not(q))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0] : axiom(implies(or(X0,X0),X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0] :
( ~ axiom(X0)
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [Y] :
( ~ theorem(Y)
| ! [X] :
( ~ theorem(implies(Y,X))
| theorem(X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0,X1] :
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
! [X0,X1] : equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
~ theorem(equivalent(and(p,q),not(or(not(p),not(q))))),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f24,plain,
~ theorem(equivalent(and(p,q),not(implies(p,not(q))))),
inference(backward_demodulation,[status(thm)],[f17,f23]) ).
fof(f25,plain,
~ theorem(equivalent(and(p,q),and(p,q))),
inference(backward_demodulation,[status(thm)],[f26,f24]) ).
fof(f26,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[status(thm)],[f17,f21]) ).
fof(f55,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f12,f18]) ).
fof(f58,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f13,f18]) ).
fof(f61,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f14,f18]) ).
fof(f82,plain,
! [X0,X1] :
( ~ theorem(implies(implies(or(X1,X1),X1),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f55,f20]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ theorem(implies(implies(X1,or(X2,X1)),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f58,f20]) ).
fof(f108,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[f16,f18]) ).
fof(f140,plain,
! [X0,X1] : theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f17,f61]) ).
fof(f270,plain,
! [X0] : theorem(or(X0,not(or(X0,X0)))),
inference(resolution,[status(thm)],[f82,f140]) ).
fof(f278,plain,
! [X0] : theorem(implies(X0,not(or(not(X0),not(X0))))),
inference(paramodulation,[status(thm)],[f17,f270]) ).
fof(f280,plain,
! [X0] : theorem(implies(X0,not(implies(X0,not(X0))))),
inference(forward_demodulation,[status(thm)],[f17,f278]) ).
fof(f281,plain,
! [X0] : theorem(implies(X0,and(X0,X0))),
inference(forward_demodulation,[status(thm)],[f26,f280]) ).
fof(f285,plain,
! [X0,X1] : theorem(implies(or(X0,or(X1,X1)),or(X0,X1))),
inference(resolution,[status(thm)],[f108,f82]) ).
fof(f300,plain,
! [X0] : theorem(implies(implies(X0,X0),equivalent(X0,X0))),
inference(paramodulation,[status(thm)],[f22,f281]) ).
fof(f531,plain,
! [X0,X1] : theorem(implies(implies(X0,or(X1,X1)),or(not(X0),X1))),
inference(paramodulation,[status(thm)],[f17,f285]) ).
fof(f534,plain,
! [X0,X1] : theorem(implies(implies(X0,or(X1,X1)),implies(X0,X1))),
inference(forward_demodulation,[status(thm)],[f17,f531]) ).
fof(f708,plain,
! [X0] : theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f534,f85]) ).
fof(f728,plain,
! [X0,X1] :
( ~ theorem(implies(implies(X1,X1),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f708,f20]) ).
fof(f733,plain,
! [X0] : theorem(equivalent(X0,X0)),
inference(resolution,[status(thm)],[f728,f300]) ).
fof(f751,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f25,f733]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL287-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 00:18:34 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.26/0.63 % Refutation found
% 0.26/0.63 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.26/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.66 % Elapsed time: 0.203004 seconds
% 0.26/0.66 % CPU time: 1.329403 seconds
% 0.26/0.66 % Total memory used: 97.674 MB
% 0.26/0.66 % Net memory used: 96.697 MB
%------------------------------------------------------------------------------