%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL198-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 01:07:06 PM UTC 2026
% Result : Unsatisfiable 6.72s 1.44s
% Output : CNFRefutation 6.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 45 unt; 0 def)
% Number of atoms : 96 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 35 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 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 : 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,negated_conjecture,
~ theorem(implies(or(not(p),implies(p,q)),implies(p,q))),
file('/export/starexec/sandbox2/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(or(not(p),implies(p,q)),implies(p,q))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
~ theorem(implies(implies(p,implies(p,q)),implies(p,q))),
inference(forward_demodulation,[status(thm)],[f15,f19]) ).
fof(f21,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f23,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f21,f18]) ).
fof(f25,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f28,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f25,f18]) ).
fof(f29,plain,
! [X0,X1] : theorem(implies(X0,implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15,f25]) ).
fof(f30,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f33,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f42,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f50,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f15,f28]) ).
fof(f52,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f30,f18]) ).
fof(f54,plain,
! [X0,X1] : theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15,f30]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f33,f18]) ).
fof(f77,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| theorem(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f15,f52]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[f42,f18]) ).
fof(f87,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f15,f42]) ).
fof(f89,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f15,f87]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ theorem(or(X0,X2))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f62,f28]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,or(not(X1),X2))) ),
inference(paramodulation,[status(thm)],[f15,f62]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,implies(X0,X2)))
| theorem(or(not(X0),or(X1,X2))) ),
inference(paramodulation,[status(thm)],[f15,f62]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f101]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,implies(X0,X2)))
| theorem(implies(X0,or(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f102]) ).
fof(f141,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,not(X2))),or(X0,implies(X2,X1)))),
inference(resolution,[status(thm)],[f86,f54]) ).
fof(f145,plain,
! [X0,X1,X2] : theorem(implies(or(X0,X1),or(X0,implies(X2,X1)))),
inference(resolution,[status(thm)],[f86,f29]) ).
fof(f149,plain,
! [X0,X1,X2,X3] : theorem(implies(or(X0,implies(X1,X2)),or(X0,implies(implies(X3,X1),implies(X3,X2))))),
inference(resolution,[status(thm)],[f89,f86]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X2,X0))
| theorem(or(X0,or(X1,not(X2)))) ),
inference(resolution,[status(thm)],[f100,f77]) ).
fof(f173,plain,
! [X0,X1,X2,X3] :
( theorem(or(X1,or(X3,implies(X0,X2))))
| ~ theorem(implies(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f103,f100]) ).
fof(f175,plain,
! [X0,X1] :
( theorem(implies(X0,X1))
| ~ theorem(implies(X0,or(implies(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f103,f23]) ).
fof(f263,plain,
! [X0,X1,X2] :
( ~ theorem(or(X0,X2))
| theorem(or(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f145,f18]) ).
fof(f269,plain,
! [X0,X1,X2] :
( ~ theorem(or(X0,or(X2,not(X1))))
| theorem(or(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f141,f18]) ).
fof(f305,plain,
! [X0,X1,X2,X3] :
( ~ theorem(or(X0,implies(X2,X3)))
| theorem(or(X0,implies(implies(X1,X2),implies(X1,X3)))) ),
inference(resolution,[status(thm)],[f149,f18]) ).
fof(f431,plain,
! [X0,X1] : theorem(or(X0,or(X1,not(or(X0,X0))))),
inference(resolution,[status(thm)],[f155,f21]) ).
fof(f464,plain,
! [X0,X1,X2] : theorem(or(X0,or(X1,implies(X2,X2)))),
inference(resolution,[status(thm)],[f173,f25]) ).
fof(f501,plain,
~ theorem(implies(implies(p,implies(p,q)),or(implies(implies(p,implies(p,q)),implies(p,q)),implies(p,q)))),
inference(resolution,[status(thm)],[f175,f20]) ).
fof(f588,plain,
~ theorem(or(implies(implies(p,implies(p,q)),implies(p,q)),implies(p,q))),
inference(resolution,[status(thm)],[f501,f50]) ).
fof(f593,plain,
! [X0,X1] : theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f464,f23]) ).
fof(f600,plain,
! [X0] : theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f593,f23]) ).
fof(f629,plain,
! [X0,X1] : theorem(or(X0,or(X1,not(X0)))),
inference(resolution,[status(thm)],[f600,f155]) ).
fof(f888,plain,
~ theorem(implies(p,or(implies(implies(p,implies(p,q)),implies(p,q)),q))),
inference(resolution,[status(thm)],[f588,f103]) ).
fof(f1050,plain,
! [X0,X1] : theorem(or(X0,implies(X0,X1))),
inference(resolution,[status(thm)],[f269,f629]) ).
fof(f1070,plain,
! [X0,X1] : theorem(or(implies(X0,X1),X0)),
inference(resolution,[status(thm)],[f1050,f52]) ).
fof(f1085,plain,
! [X0,X1,X2] : theorem(or(implies(X0,X1),implies(X2,X0))),
inference(resolution,[status(thm)],[f1070,f263]) ).
fof(f1460,plain,
! [X0,X1,X2] : theorem(or(implies(X0,X1),implies(X1,X2))),
inference(resolution,[status(thm)],[f1085,f52]) ).
fof(f1651,plain,
~ theorem(or(implies(implies(p,implies(p,q)),implies(p,q)),q)),
inference(resolution,[status(thm)],[f888,f50]) ).
fof(f1806,plain,
! [X0,X1,X2,X3] : theorem(or(implies(X0,X1),implies(implies(X2,X1),implies(X2,X3)))),
inference(resolution,[status(thm)],[f1460,f305]) ).
fof(f2429,plain,
! [X0,X1] : theorem(or(X0,implies(or(X0,X0),X1))),
inference(resolution,[status(thm)],[f431,f269]) ).
fof(f2444,plain,
! [X0,X1] : theorem(implies(or(X0,X0),or(X0,X1))),
inference(resolution,[status(thm)],[f2429,f104]) ).
fof(f2457,plain,
! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f2444,f18]) ).
fof(f2516,plain,
~ theorem(or(implies(implies(p,implies(p,q)),implies(p,q)),implies(implies(p,implies(p,q)),implies(p,q)))),
inference(resolution,[status(thm)],[f2457,f1651]) ).
fof(f2546,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2516,f1806]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL198-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n010.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 00:10:54 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 6.72/1.44 % Refutation found
% 6.72/1.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.72/1.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.72/1.48 % Elapsed time: 1.043780 seconds
% 6.72/1.48 % CPU time: 7.902393 seconds
% 6.72/1.48 % Total memory used: 127.692 MB
% 6.72/1.48 % Net memory used: 118.394 MB
%------------------------------------------------------------------------------