%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL294-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 01:07:23 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.67s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 29 unt; 0 def)
% Number of atoms : 59 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 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 : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [P,Q] : and(P,Q) = not(or(not(P),not(Q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [P,Q] : equivalent(P,Q) = and(implies(P,Q),implies(Q,P)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ theorem(equivalent(implies(p,q),or(not(p),q))),
file('/export/starexec/sandbox/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(f15,plain,
! [X0,X1,X2] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
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(implies(p,q),or(not(p),q))),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f25,plain,
! [X0] : axiom(implies(implies(X0,not(X0)),not(X0))),
inference(paramodulation,[status(thm)],[f17,f12]) ).
fof(f28,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))),
inference(paramodulation,[status(thm)],[f17,f15]) ).
fof(f32,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f17,f28]) ).
fof(f36,plain,
! [X0,X1] :
( ~ axiom(implies(X1,X0))
| ~ theorem(X1)
| theorem(X0) ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f38,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f36,f14]) ).
fof(f39,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f36,f12]) ).
fof(f61,plain,
! [X0,X1] :
( ~ axiom(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f38,f18]) ).
fof(f86,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[status(thm)],[f17,f21]) ).
fof(f89,plain,
! [X0,X1,X2] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(paramodulation,[status(thm)],[f86,f17]) ).
fof(f135,plain,
! [X0,X1] :
( ~ axiom(or(X1,not(X0)))
| theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f17,f61]) ).
fof(f136,plain,
~ theorem(equivalent(implies(p,q),implies(p,q))),
inference(forward_demodulation,[status(thm)],[f17,f23]) ).
fof(f201,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f32,f36]) ).
fof(f394,plain,
! [X0] : axiom(or(and(X0,X0),not(X0))),
inference(backward_demodulation,[status(thm)],[f89,f25]) ).
fof(f454,plain,
! [X0] : theorem(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[f394,f135]) ).
fof(f472,plain,
! [X0] :
( ~ theorem(X0)
| theorem(and(X0,X0)) ),
inference(resolution,[status(thm)],[f454,f20]) ).
fof(f501,plain,
! [X0] :
( ~ theorem(implies(X0,X0))
| theorem(equivalent(X0,X0)) ),
inference(paramodulation,[status(thm)],[f22,f472]) ).
fof(f897,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f18,f13]) ).
fof(f1643,plain,
! [X0,X1] : theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f201,f897]) ).
fof(f1650,plain,
! [X0] : theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f1643,f39]) ).
fof(f1666,plain,
! [X0] : theorem(equivalent(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[f501,f1650]) ).
fof(f1687,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f136,f1666]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL294-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 % Computer : n009.cluster.edu
% 0.19/0.49 % Model : x86_64 x86_64
% 0.19/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.49 % Memory : 8046.5625MB
% 0.19/0.49 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 00:19:28 UTC 2026
% 0.19/0.50 % CPUTime :
% 0.19/0.53 % Drodi V4.1.1
% 0.23/0.67 % Refutation found
% 0.23/0.67 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.23/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.73 % Elapsed time: 0.204249 seconds
% 0.23/0.73 % CPU time: 1.156210 seconds
% 0.23/0.73 % Total memory used: 95.045 MB
% 0.23/0.73 % Net memory used: 94.232 MB
%------------------------------------------------------------------------------