%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL183-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 01:07:02 PM UTC 2026
% Result : Unsatisfiable 10.30s 1.78s
% Output : CNFRefutation 10.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 35 unt; 0 def)
% Number of atoms : 93 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 73 ( 39 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 112 !; 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(f5,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
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,negated_conjecture,
~ theorem(implies(implies(not(q),not(p)),implies(p,q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : axiom(implies(or(X0,X0),X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
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(implies(not(q),not(p)),implies(p,q))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f22,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f27,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f29,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f27,f18]) ).
fof(f46,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f49,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f46,f18]) ).
fof(f50,plain,
! [X0,X1] : theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f15,f46]) ).
fof(f51,plain,
! [X0,X1] : theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15,f46]) ).
fof(f53,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| theorem(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f15,f49]) ).
fof(f62,plain,
! [X0,X1] : theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f15,f50]) ).
fof(f63,plain,
! [X0,X1] :
( ~ theorem(or(X1,not(X0)))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f51,f18]) ).
fof(f67,plain,
! [X0,X1] :
( ~ theorem(implies(X1,not(X0)))
| theorem(implies(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f15,f53]) ).
fof(f71,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(X0)
| ~ theorem(or(X0,not(X1))) ),
inference(resolution,[status(thm)],[f63,f18]) ).
fof(f88,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f98,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f100,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f15,f98]) ).
fof(f103,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))),
inference(paramodulation,[status(thm)],[f15,f88]) ).
fof(f107,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f15,f103]) ).
fof(f136,plain,
! [X0,X1,X2] : theorem(or(X0,implies(X1,or(X2,X1)))),
inference(resolution,[status(thm)],[f27,f29]) ).
fof(f142,plain,
! [X0,X1] :
( ~ axiom(implies(X1,X0))
| ~ theorem(X1)
| theorem(X0) ),
inference(resolution,[status(thm)],[f18,f16]) ).
fof(f251,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[f142,f14]) ).
fof(f293,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(implies(X0,X1),implies(X0,X2))) ),
inference(resolution,[status(thm)],[f100,f142]) ).
fof(f331,plain,
! [X0,X1] :
( theorem(X0)
| ~ theorem(X1)
| ~ theorem(or(or(X0,X0),not(X1))) ),
inference(resolution,[status(thm)],[f71,f22]) ).
fof(f738,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X0))
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f251,f18]) ).
fof(f970,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X2,X0))
| theorem(implies(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f293,f18]) ).
fof(f1016,plain,
! [X0,X1] :
( ~ theorem(implies(X0,or(X1,X1)))
| theorem(X1)
| ~ theorem(X0) ),
inference(resolution,[status(thm)],[f331,f53]) ).
fof(f1042,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| theorem(X0)
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f1016,f251]) ).
fof(f1073,plain,
! [X0,X1,X2] :
( ~ theorem(implies(implies(X1,or(X2,X1)),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f1042,f136]) ).
fof(f1236,plain,
! [X0,X1] : theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f1073,f107]) ).
fof(f1262,plain,
! [X0,X1] :
( ~ theorem(implies(implies(X1,X1),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f1236,f1042]) ).
fof(f1263,plain,
! [X0] : theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f1236,f22]) ).
fof(f1276,plain,
! [X0] : theorem(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[f1263,f67]) ).
fof(f1329,plain,
! [X0] : theorem(or(X0,not(X0))),
inference(resolution,[status(thm)],[f1262,f50]) ).
fof(f2031,plain,
! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f738,f1329]) ).
fof(f2122,plain,
! [X0] : theorem(or(X0,not(not(not(X0))))),
inference(resolution,[status(thm)],[f2031,f1276]) ).
fof(f2522,plain,
! [X0,X1,X2] :
( theorem(implies(implies(X1,not(X0)),X2))
| ~ theorem(implies(implies(X0,not(X1)),X2)) ),
inference(resolution,[status(thm)],[f970,f62]) ).
fof(f4820,plain,
~ theorem(implies(implies(p,not(not(q))),implies(p,q))),
inference(resolution,[status(thm)],[f2522,f19]) ).
fof(f4916,plain,
~ theorem(implies(not(not(q)),q)),
inference(resolution,[status(thm)],[f4820,f293]) ).
fof(f4926,plain,
~ theorem(or(q,not(not(not(q))))),
inference(resolution,[status(thm)],[f4916,f63]) ).
fof(f4931,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4926,f2122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL183-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 00:11:01 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 10.30/1.78 % Refutation found
% 10.30/1.78 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.30/1.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.82/1.81 % Elapsed time: 1.438913 seconds
% 0.82/1.81 % CPU time: 11.057178 seconds
% 0.82/1.81 % Total memory used: 171.576 MB
% 0.82/1.81 % Net memory used: 155.217 MB
%------------------------------------------------------------------------------