%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL207-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 01:07:08 PM UTC 2026
% Result : Unsatisfiable 15.22s 2.43s
% Output : CNFRefutation 15.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 70 ( 36 unt; 0 def)
% Number of atoms : 112 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 86 ( 44 ~; 42 |; 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 : 150 ( 150 !; 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(not(implies(p,q)),implies(q,p))),
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(not(implies(p,q)),implies(q,p))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f21,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f26,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f30,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f18,f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f18,f21]) ).
fof(f44,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f53,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f26,f18]) ).
fof(f54,plain,
! [X0,X1] : theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f15,f26]) ).
fof(f55,plain,
! [X0,X1] : theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15,f26]) ).
fof(f57,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| theorem(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f15,f53]) ).
fof(f70,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f88,plain,
! [X0,X1] :
( ~ theorem(or(X1,not(X0)))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f55,f18]) ).
fof(f92,plain,
! [X0,X1] :
( ~ theorem(implies(X1,not(X0)))
| theorem(implies(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f15,f57]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f44,f18]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[f70,f18]) ).
fof(f135,plain,
! [X0,X1,X2] :
( ~ theorem(or(X0,X2))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f93,f32]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,or(not(X1),X2))) ),
inference(paramodulation,[status(thm)],[f15,f93]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f136]) ).
fof(f279,plain,
! [X0,X1,X2] :
( ~ theorem(or(not(X0),X2))
| theorem(implies(X0,or(X1,X2))) ),
inference(paramodulation,[status(thm)],[f15,f135]) ).
fof(f281,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X0,X2))
| theorem(implies(X0,or(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f279]) ).
fof(f313,plain,
! [X0,X1,X2] :
( ~ theorem(X0)
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f281,f18]) ).
fof(f370,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X1))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f313,f26]) ).
fof(f532,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X0))
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f128,f18]) ).
fof(f613,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X0))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f93,f370]) ).
fof(f646,plain,
! [X0,X1] :
( theorem(or(X1,X0))
| ~ theorem(or(X0,or(X1,X0))) ),
inference(resolution,[status(thm)],[f613,f30]) ).
fof(f726,plain,
! [X0,X1] :
( theorem(or(not(X1),X0))
| ~ theorem(or(X0,implies(X1,X0))) ),
inference(paramodulation,[status(thm)],[f15,f646]) ).
fof(f727,plain,
! [X0,X1] :
( theorem(implies(X1,X0))
| ~ theorem(or(X0,implies(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f15,f726]) ).
fof(f999,plain,
! [X0,X1] : theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f138,f21]) ).
fof(f1002,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,implies(X0,X2)))
| theorem(or(not(X0),implies(X1,X2))) ),
inference(paramodulation,[status(thm)],[f15,f138]) ).
fof(f1003,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,implies(X0,X2)))
| theorem(implies(X0,implies(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f1002]) ).
fof(f1006,plain,
! [X0] : theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f999,f727]) ).
fof(f1013,plain,
! [X0] : theorem(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[f1006,f92]) ).
fof(f1575,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X0,X2))
| theorem(or(X2,X1))
| ~ theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f532,f57]) ).
fof(f1584,plain,
! [X0,X1,X2] :
( theorem(or(X2,X1))
| ~ theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f532,f999]) ).
fof(f1606,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X2,X0))
| theorem(or(not(X2),X1))
| ~ theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f15,f532]) ).
fof(f1607,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X2,X0))
| theorem(implies(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f15,f1606]) ).
fof(f1612,plain,
! [X0,X1] : theorem(or(X0,or(X1,not(X1)))),
inference(resolution,[status(thm)],[f1584,f54]) ).
fof(f1693,plain,
! [X0] : theorem(or(X0,not(X0))),
inference(resolution,[status(thm)],[f1612,f30]) ).
fof(f1910,plain,
! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f532,f1693]) ).
fof(f2147,plain,
! [X0] : theorem(or(X0,not(not(not(X0))))),
inference(resolution,[status(thm)],[f1910,f1013]) ).
fof(f2186,plain,
! [X0] : theorem(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[f2147,f88]) ).
fof(f2748,plain,
! [X0,X1] :
( ~ theorem(implies(not(X1),X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f1575,f2186]) ).
fof(f3082,plain,
! [X0,X1,X2] :
( theorem(implies(X1,X2))
| ~ theorem(implies(or(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f1607,f21]) ).
fof(f4854,plain,
! [X0,X1] : theorem(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[f3082,f26]) ).
fof(f4921,plain,
! [X0,X1] : theorem(or(or(not(X0),X1),X0)),
inference(resolution,[status(thm)],[f4854,f2748]) ).
fof(f4932,plain,
! [X0,X1] : theorem(or(implies(X0,X1),X0)),
inference(forward_demodulation,[status(thm)],[f15,f4921]) ).
fof(f5004,plain,
! [X0,X1] : theorem(implies(X0,implies(not(X0),X1))),
inference(resolution,[status(thm)],[f4932,f88]) ).
fof(f5035,plain,
! [X0,X1,X2] : theorem(implies(X0,implies(not(or(X1,X0)),X2))),
inference(resolution,[status(thm)],[f5004,f3082]) ).
fof(f6066,plain,
! [X0,X1,X2] : theorem(implies(not(or(X0,X1)),implies(X1,X2))),
inference(resolution,[status(thm)],[f5035,f1003]) ).
fof(f6343,plain,
! [X0,X1,X2] : theorem(implies(not(implies(X0,X1)),implies(X1,X2))),
inference(paramodulation,[status(thm)],[f15,f6066]) ).
fof(f6521,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f19,f6343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL207-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 00:11:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 15.22/2.43 % Refutation found
% 15.22/2.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 15.22/2.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.87/2.46 % Elapsed time: 2.082307 seconds
% 1.87/2.46 % CPU time: 16.087718 seconds
% 1.87/2.46 % Total memory used: 178.745 MB
% 1.87/2.46 % Net memory used: 162.086 MB
%------------------------------------------------------------------------------