%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL235-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 01:07:15 PM UTC 2026
% Result : Unsatisfiable 218.40s 28.12s
% Output : CNFRefutation 96.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 45 unt; 0 def)
% Number of atoms : 113 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 43 ~; 39 |; 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; 2 con; 0-2 aty)
% Number of variables : 144 ( 144 !; 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,axiom,
! [P,Q] : and(P,Q) = not(or(not(P),not(Q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ theorem(implies(not(and(p,q)),or(not(p),not(q)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0] : axiom(implies(or(X0,X0),X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0] :
( ~ axiom(X0)
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
! [Y] :
( ~ theorem(Y)
| ! [X] :
( ~ theorem(implies(Y,X))
| theorem(X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f19,plain,
! [X0,X1] :
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f21,plain,
~ theorem(implies(not(and(p,q)),or(not(p),not(q)))),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f22,plain,
~ theorem(implies(not(and(p,q)),implies(p,not(q)))),
inference(backward_demodulation,[status(thm)],[f16,f21]) ).
fof(f23,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[status(thm)],[f16,f20]) ).
fof(f25,plain,
! [X0,X1,X2] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(paramodulation,[status(thm)],[f23,f16]) ).
fof(f26,plain,
! [X0,X1,X2,X3] : implies(or(and(X0,X1),not(X2)),X3) = or(and(implies(X0,not(X1)),X2),X3),
inference(paramodulation,[status(thm)],[f25,f25]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ~ theorem(or(and(X1,X2),not(X3)))
| ~ theorem(or(and(implies(X1,not(X2)),X3),X0))
| theorem(X0) ),
inference(paramodulation,[status(thm)],[f26,f19]) ).
fof(f60,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f11,f17]) ).
fof(f63,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f12,f17]) ).
fof(f67,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f60,f19]) ).
fof(f68,plain,
! [X0] : theorem(implies(implies(X0,not(X0)),not(X0))),
inference(paramodulation,[status(thm)],[f16,f60]) ).
fof(f69,plain,
! [X0] : theorem(or(and(X0,X0),not(X0))),
inference(forward_demodulation,[status(thm)],[f25,f68]) ).
fof(f73,plain,
! [X0,X1,X2] : theorem(or(and(X0,X1),or(X2,implies(X0,not(X1))))),
inference(paramodulation,[status(thm)],[f25,f63]) ).
fof(f74,plain,
! [X0,X1] : theorem(implies(X0,implies(X1,X0))),
inference(paramodulation,[status(thm)],[f16,f63]) ).
fof(f82,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f74,f19]) ).
fof(f91,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f13,f17]) ).
fof(f96,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f14,f17]) ).
fof(f105,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[f15,f17]) ).
fof(f136,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f91,f19]) ).
fof(f141,plain,
! [X0,X1] : theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f16,f91]) ).
fof(f220,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| theorem(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f16,f136]) ).
fof(f242,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f96,f19]) ).
fof(f361,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[f105,f19]) ).
fof(f364,plain,
! [X0,X1,X2] : theorem(or(and(X0,X1),implies(or(X2,X0),or(X2,not(X1))))),
inference(paramodulation,[status(thm)],[f25,f105]) ).
fof(f428,plain,
! [X0,X1] :
( ~ theorem(or(X1,not(X0)))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f141,f19]) ).
fof(f512,plain,
! [X0,X1] :
( ~ theorem(implies(X1,not(X0)))
| theorem(implies(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f16,f220]) ).
fof(f667,plain,
! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(or(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f242,f67]) ).
fof(f671,plain,
! [X0,X1,X2] :
( ~ theorem(or(not(X1),or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(paramodulation,[status(thm)],[f16,f242]) ).
fof(f673,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f16,f671]) ).
fof(f1026,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X0))
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f361,f19]) ).
fof(f1035,plain,
! [X0,X1,X2] : theorem(or(implies(or(X0,X1),or(X0,not(X2))),and(X1,X2))),
inference(resolution,[status(thm)],[f364,f136]) ).
fof(f2225,plain,
! [X0,X1] :
( ~ theorem(or(and(implies(X1,not(X1)),X1),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f52,f69]) ).
fof(f3416,plain,
! [X0,X1] : theorem(or(and(X0,X1),implies(X0,not(X1)))),
inference(resolution,[status(thm)],[f667,f73]) ).
fof(f3437,plain,
! [X0,X1] : theorem(or(implies(X0,not(X1)),and(X0,X1))),
inference(resolution,[status(thm)],[f3416,f136]) ).
fof(f3853,plain,
! [X0,X1] : theorem(or(X0,implies(or(X1,X0),X1))),
inference(resolution,[status(thm)],[f673,f91]) ).
fof(f3876,plain,
! [X0,X1] : theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f673,f63]) ).
fof(f4047,plain,
! [X0] : theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f3876,f2225]) ).
fof(f4058,plain,
! [X0] : theorem(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[f4047,f512]) ).
fof(f4666,plain,
! [X0,X1] : theorem(implies(X0,implies(X1,not(not(X1))))),
inference(resolution,[status(thm)],[f4058,f82]) ).
fof(f5292,plain,
! [X0,X1] : theorem(implies(X0,implies(or(X1,not(X0)),X1))),
inference(paramodulation,[status(thm)],[f16,f3853]) ).
fof(f7686,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(implies(or(X0,not(X1)),X0)) ),
inference(resolution,[status(thm)],[f5292,f19]) ).
fof(f8429,plain,
! [X0,X1] :
( ~ theorem(or(X1,not(X0)))
| theorem(X1)
| ~ theorem(X0) ),
inference(resolution,[status(thm)],[f7686,f19]) ).
fof(f11533,plain,
! [X0,X1,X2] :
( theorem(X2)
| ~ theorem(X1)
| ~ theorem(or(X2,X0))
| ~ theorem(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[f1026,f8429]) ).
fof(f11536,plain,
! [X0,X1] :
( theorem(X1)
| ~ theorem(or(X1,X0))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1026,f67]) ).
fof(f11546,plain,
! [X0,X1] :
( theorem(X0)
| ~ theorem(not(X1))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f11533,f4058]) ).
fof(f11589,plain,
! [X0] :
( theorem(not(not(X0)))
| ~ theorem(or(not(not(X0)),X0)) ),
inference(resolution,[status(thm)],[f11536,f4058]) ).
fof(f11672,plain,
! [X0] :
( theorem(not(not(X0)))
| ~ theorem(implies(not(X0),X0)) ),
inference(forward_demodulation,[status(thm)],[f16,f11589]) ).
fof(f11874,plain,
! [X0] : theorem(not(not(implies(X0,not(not(X0)))))),
inference(resolution,[status(thm)],[f11672,f4666]) ).
fof(f11939,plain,
! [X0] : theorem(not(and(X0,not(X0)))),
inference(forward_demodulation,[status(thm)],[f23,f11874]) ).
fof(f11948,plain,
! [X0,X1] :
( theorem(X0)
| ~ theorem(or(X0,and(X1,not(X1)))) ),
inference(resolution,[status(thm)],[f11939,f11546]) ).
fof(f13022,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X0,not(not(X1))))),
inference(resolution,[status(thm)],[f11948,f1035]) ).
fof(f40694,plain,
! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,not(not(X1)))) ),
inference(resolution,[status(thm)],[f13022,f19]) ).
fof(f79086,plain,
! [X0,X1] :
( theorem(implies(not(X1),X0))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f40694,f428]) ).
fof(f79124,plain,
~ theorem(or(implies(p,not(q)),and(p,q))),
inference(resolution,[status(thm)],[f79086,f22]) ).
fof(f79184,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f79124,f3437]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL235-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:13:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 218.40/28.12 % Refutation found
% 218.40/28.12 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 218.40/28.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 99.36/29.36 % Elapsed time: 28.771591 seconds
% 99.36/29.36 % CPU time: 207.078660 seconds
% 99.36/29.36 % Total memory used: 866.065 MB
% 99.36/29.36 % Net memory used: 825.610 MB
%------------------------------------------------------------------------------