%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL301-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 0.13s 1.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 41 unt; 0 def)
% Number of atoms : 68 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 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 : 92 ( 92 !; 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(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(not(implies(not(p),not(q))),and(not(p),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(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(not(implies(not(p),not(q))),and(not(p),q))),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f24,plain,
~ theorem(equivalent(and(not(p),q),and(not(p),q))),
inference(backward_demodulation,[status(thm)],[f25,f23]) ).
fof(f25,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[status(thm)],[f17,f21]) ).
fof(f27,plain,
! [X0,X1,X2] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(paramodulation,[status(thm)],[f25,f17]) ).
fof(f291,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f12,f18]) ).
fof(f295,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f13,f18]) ).
fof(f301,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f291,f20]) ).
fof(f303,plain,
! [X0] : theorem(implies(implies(X0,not(X0)),not(X0))),
inference(paramodulation,[status(thm)],[f17,f291]) ).
fof(f304,plain,
! [X0] : theorem(or(and(X0,X0),not(X0))),
inference(forward_demodulation,[status(thm)],[f27,f303]) ).
fof(f305,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f295,f20]) ).
fof(f375,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f14,f18]) ).
fof(f423,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f15,f18]) ).
fof(f455,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f375,f20]) ).
fof(f462,plain,
! [X0,X1] : theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f17,f375]) ).
fof(f507,plain,
! [X0] : theorem(or(not(X0),and(X0,X0))),
inference(resolution,[status(thm)],[f455,f304]) ).
fof(f512,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| theorem(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f17,f455]) ).
fof(f513,plain,
! [X0] : theorem(implies(X0,and(X0,X0))),
inference(forward_demodulation,[status(thm)],[f17,f507]) ).
fof(f521,plain,
! [X0] : theorem(implies(implies(X0,X0),equivalent(X0,X0))),
inference(paramodulation,[status(thm)],[f22,f513]) ).
fof(f609,plain,
! [X0] :
( ~ theorem(implies(X0,X0))
| theorem(equivalent(X0,X0)) ),
inference(resolution,[status(thm)],[f521,f20]) ).
fof(f673,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f423,f20]) ).
fof(f807,plain,
! [X0,X1] :
( ~ theorem(or(X1,not(X0)))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f462,f20]) ).
fof(f864,plain,
! [X0,X1] : theorem(or(or(X0,X1),not(X1))),
inference(resolution,[status(thm)],[f512,f295]) ).
fof(f908,plain,
! [X0,X1,X2] : theorem(or(X0,or(or(X1,X2),not(X2)))),
inference(resolution,[status(thm)],[f864,f305]) ).
fof(f2565,plain,
! [X0,X1,X2] : theorem(or(or(X0,X1),or(X2,not(X1)))),
inference(resolution,[status(thm)],[f673,f908]) ).
fof(f2615,plain,
! [X0,X1,X2] : theorem(or(or(X0,not(X1)),or(X2,X1))),
inference(resolution,[status(thm)],[f2565,f455]) ).
fof(f2930,plain,
! [X0,X1,X2] : theorem(or(X0,or(or(X1,not(X2)),X2))),
inference(resolution,[status(thm)],[f2615,f673]) ).
fof(f3172,plain,
! [X0,X1] : theorem(or(or(X0,not(X1)),X1)),
inference(resolution,[status(thm)],[f2930,f301]) ).
fof(f3188,plain,
! [X0,X1] : theorem(or(X0,or(X1,not(X0)))),
inference(resolution,[status(thm)],[f3172,f455]) ).
fof(f3201,plain,
! [X0,X1] : theorem(or(X0,or(X1,not(X1)))),
inference(resolution,[status(thm)],[f3188,f673]) ).
fof(f3235,plain,
! [X0] : theorem(or(X0,not(X0))),
inference(resolution,[status(thm)],[f3201,f301]) ).
fof(f3250,plain,
! [X0] : theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f3235,f807]) ).
fof(f3264,plain,
! [X0] : theorem(equivalent(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[f609,f3250]) ).
fof(f3280,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f24,f3264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL301-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/1.18 % Computer : n013.cluster.edu
% 0.08/1.18 % Model : x86_64 x86_64
% 0.08/1.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/1.18 % Memory : 8046.5625MB
% 0.08/1.18 % OS : Linux 6.8.0-71-generic
% 0.08/1.18 % CPULimit : 300
% 0.08/1.18 % WCLimit : 300
% 0.08/1.18 % DateTime : Mon Sep 21 00:19:22 UTC 2026
% 0.08/1.18 % CPUTime :
% 0.08/1.19 % Drodi V4.1.1
% 0.13/1.37 % Refutation found
% 0.13/1.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/1.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/1.40 % Elapsed time: 0.203127 seconds
% 0.13/1.40 % CPU time: 1.424781 seconds
% 0.13/1.40 % Total memory used: 117.834 MB
% 0.13/1.40 % Net memory used: 116.193 MB
%------------------------------------------------------------------------------