%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL110-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 01:06:50 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : implies(truth,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
implies(not(not(x)),x) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0] : implies(truth,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
implies(not(not(x)),x) != truth,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [X0] : implies(X0,X0) = implies(implies(X0,truth),truth),
inference(paramodulation,[status(thm)],[f6,f8]) ).
fof(f38,plain,
! [X0] : implies(implies(not(X0),not(truth)),X0) = truth,
inference(paramodulation,[status(thm)],[f6,f9]) ).
fof(f40,plain,
! [X0,X1,X2] : implies(truth,implies(implies(implies(X0,X1),X2),implies(implies(not(X1),not(X0)),X2))) = truth,
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f45,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f55,plain,
! [X0,X1] : implies(implies(X0,truth),implies(X1,implies(X0,X1))) = truth,
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f67,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X2),implies(implies(not(X1),not(X0)),X2)) = truth,
inference(forward_demodulation,[status(thm)],[f6,f40]) ).
fof(f70,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f6,f45]) ).
fof(f76,plain,
! [X0] : implies(implies(truth,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f6,f70]) ).
fof(f77,plain,
! [X0] : implies(X0,implies(X0,X0)) = truth,
inference(paramodulation,[status(thm)],[f17,f70]) ).
fof(f106,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f6,f76]) ).
fof(f115,plain,
! [X0,X1] : implies(truth,implies(X0,implies(X1,X0))) = truth,
inference(backward_demodulation,[status(thm)],[f116,f55]) ).
fof(f116,plain,
! [X0] : implies(X0,truth) = truth,
inference(forward_demodulation,[status(thm)],[f106,f77]) ).
fof(f142,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = truth,
inference(forward_demodulation,[status(thm)],[f6,f115]) ).
fof(f203,plain,
! [X0,X1,X2] : implies(truth,implies(implies(implies(X0,X1),X2),implies(X1,X2))) = truth,
inference(paramodulation,[status(thm)],[f142,f7]) ).
fof(f205,plain,
! [X0,X1] : implies(implies(implies(X0,X1),X1),X1) = implies(truth,implies(X0,X1)),
inference(paramodulation,[status(thm)],[f142,f8]) ).
fof(f210,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X2),implies(X1,X2)) = truth,
inference(forward_demodulation,[status(thm)],[f6,f203]) ).
fof(f211,plain,
! [X0,X1] : implies(implies(implies(X0,X1),X1),X1) = implies(X0,X1),
inference(forward_demodulation,[status(thm)],[f6,f205]) ).
fof(f230,plain,
! [X0,X1] : implies(implies(implies(X0,X1),X1),X0) = implies(X1,X0),
inference(paramodulation,[status(thm)],[f8,f211]) ).
fof(f286,plain,
implies(truth,not(not(truth))) = implies(not(truth),not(not(truth))),
inference(paramodulation,[status(thm)],[f38,f230]) ).
fof(f317,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(forward_demodulation,[status(thm)],[f6,f286]) ).
fof(f352,plain,
! [X0] : implies(truth,implies(not(truth),X0)) = truth,
inference(paramodulation,[status(thm)],[f38,f210]) ).
fof(f403,plain,
not(not(truth)) = truth,
inference(backward_demodulation,[status(thm)],[f407,f317]) ).
fof(f407,plain,
! [X0] : implies(not(truth),X0) = truth,
inference(forward_demodulation,[status(thm)],[f6,f352]) ).
fof(f556,plain,
! [X0] : implies(truth,implies(implies(not(not(truth)),not(not(X0))),X0)) = truth,
inference(paramodulation,[status(thm)],[f38,f67]) ).
fof(f611,plain,
! [X0] : implies(implies(not(not(truth)),not(not(X0))),X0) = truth,
inference(forward_demodulation,[status(thm)],[f6,f556]) ).
fof(f612,plain,
! [X0] : implies(implies(truth,not(not(X0))),X0) = truth,
inference(forward_demodulation,[status(thm)],[f403,f611]) ).
fof(f613,plain,
truth != truth,
inference(backward_demodulation,[status(thm)],[f614,f10]) ).
fof(f614,plain,
! [X0] : implies(not(not(X0)),X0) = truth,
inference(forward_demodulation,[status(thm)],[f6,f612]) ).
fof(f645,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f613]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL110-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 00:06:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.41/1.61 % Elapsed time: 1.033146 seconds
% 1.41/1.61 % CPU time: 0.066885 seconds
% 1.41/1.61 % Total memory used: 2.924 MB
% 1.41/1.61 % Net memory used: 2.878 MB
%------------------------------------------------------------------------------