%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 01:06:49 PM UTC 2026
% Result : Unsatisfiable 60.01s 8.03s
% Output : CNFRefutation 60.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 46 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : implies(truth,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : implies(X,X) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : implies(X,truth) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] : implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : implies(X,not(truth)) = not(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : not(not(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] : implies(not(X),not(Y)) = implies(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : implies(truth,X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [X0] : implies(X0,X0) = truth,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0] : implies(X0,truth) = truth,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
! [X0] : implies(X0,not(truth)) = not(X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
! [X0] : not(not(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
! [X0,X1] : implies(not(X0),not(X1)) = implies(X1,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f32,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f171,plain,
! [X0,X1] : implies(X0,implies(X1,not(truth))) = implies(X1,not(X0)),
inference(paramodulation,[status(thm)],[f29,f28]) ).
fof(f180,plain,
! [X0,X1] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(forward_demodulation,[status(thm)],[f29,f171]) ).
fof(f218,plain,
! [X0,X1,X2] : implies(X0,implies(X1,not(X2))) = implies(X1,implies(X2,not(X0))),
inference(paramodulation,[status(thm)],[f180,f28]) ).
fof(f348,plain,
! [X0,X1,X2] : implies(not(X0),implies(X1,not(X2))) = implies(X1,implies(X2,X0)),
inference(paramodulation,[status(thm)],[f30,f218]) ).
fof(f405,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(paramodulation,[status(thm)],[f30,f31]) ).
fof(f411,plain,
! [X0,X1] : implies(implies(not(X0),not(X1)),not(X1)) = implies(implies(X0,X1),not(X0)),
inference(paramodulation,[status(thm)],[f31,f20]) ).
fof(f429,plain,
! [X0,X1] : implies(implies(X0,X1),not(X0)) = implies(implies(X1,X0),not(X1)),
inference(forward_demodulation,[status(thm)],[f31,f411]) ).
fof(f572,plain,
! [X0,X1,X2] : implies(X0,implies(not(X1),not(X2))) = implies(not(implies(X2,not(X0))),X1),
inference(paramodulation,[status(thm)],[f405,f218]) ).
fof(f618,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(not(implies(X1,not(X0))),X2),
inference(forward_demodulation,[status(thm)],[f31,f572]) ).
fof(f814,plain,
! [X0,X1] : implies(not(X0),truth) = implies(not(X1),implies(X1,X0)),
inference(paramodulation,[status(thm)],[f22,f348]) ).
fof(f855,plain,
! [X0,X1] : truth = implies(not(X0),implies(X0,X1)),
inference(forward_demodulation,[status(thm)],[f24,f814]) ).
fof(f871,plain,
! [X0,X1] : implies(implies(implies(X0,X1),not(X0)),not(implies(X1,X0))) = implies(implies(not(X1),implies(X1,X0)),not(not(X1))),
inference(paramodulation,[status(thm)],[f429,f429]) ).
fof(f959,plain,
! [X0,X1] : implies(implies(implies(X0,X1),not(X0)),not(implies(X1,X0))) = implies(truth,not(not(X1))),
inference(forward_demodulation,[status(thm)],[f855,f871]) ).
fof(f960,plain,
! [X0,X1] : implies(implies(implies(X0,X1),not(X0)),not(implies(X1,X0))) = not(not(X1)),
inference(forward_demodulation,[status(thm)],[f18,f959]) ).
fof(f961,plain,
! [X0,X1] : implies(implies(implies(X0,X1),not(X0)),not(implies(X1,X0))) = X1,
inference(forward_demodulation,[status(thm)],[f30,f960]) ).
fof(f1248,plain,
! [X0,X1,X2] : implies(X0,implies(implies(X0,X1),X2)) = implies(not(implies(implies(X1,X0),not(X1))),X2),
inference(paramodulation,[status(thm)],[f429,f618]) ).
fof(f1298,plain,
! [X0,X1,X2] : implies(X0,implies(implies(X0,X1),X2)) = implies(X1,implies(implies(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f618,f1248]) ).
fof(f1915,plain,
! [X0,X1] : implies(implies(implies(not(X0),implies(X0,X1)),not(not(X0))),not(implies(implies(X1,X0),not(X1)))) = implies(X0,X1),
inference(paramodulation,[status(thm)],[f429,f961]) ).
fof(f1977,plain,
! [X0,X1] : implies(implies(truth,not(not(X0))),not(implies(implies(X1,X0),not(X1)))) = implies(X0,X1),
inference(forward_demodulation,[status(thm)],[f855,f1915]) ).
fof(f1978,plain,
! [X0,X1] : implies(not(not(X0)),not(implies(implies(X1,X0),not(X1)))) = implies(X0,X1),
inference(forward_demodulation,[status(thm)],[f18,f1977]) ).
fof(f1980,plain,
! [X0,X1] : implies(implies(implies(X0,X1),not(X0)),not(X1)) = implies(X1,X0),
inference(forward_demodulation,[status(thm)],[f31,f1978]) ).
fof(f14125,plain,
! [X0,X1] : implies(implies(X0,X1),implies(X1,X0)) = implies(not(X0),implies(implies(not(X0),implies(X0,X1)),not(X1))),
inference(paramodulation,[status(thm)],[f1980,f1298]) ).
fof(f14587,plain,
! [X0,X1] : implies(implies(X0,X1),implies(X1,X0)) = implies(implies(not(X0),implies(X0,X1)),implies(X1,X0)),
inference(forward_demodulation,[status(thm)],[f348,f14125]) ).
fof(f14588,plain,
! [X0,X1] : implies(implies(X0,X1),implies(X1,X0)) = implies(truth,implies(X1,X0)),
inference(forward_demodulation,[status(thm)],[f855,f14587]) ).
fof(f14590,plain,
implies(implies(b,a),implies(b,a)) != truth,
inference(backward_demodulation,[status(thm)],[f14591,f32]) ).
fof(f14591,plain,
! [X0,X1] : implies(implies(X0,X1),implies(X1,X0)) = implies(X1,X0),
inference(forward_demodulation,[status(thm)],[f18,f14588]) ).
fof(f14618,plain,
truth != truth,
inference(forward_demodulation,[status(thm)],[f22,f14590]) ).
fof(f14619,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f14618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 00:04:55 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 60.01/8.03 % Refutation found
% 60.01/8.03 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 60.01/8.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 25.07/8.16 % Elapsed time: 7.801678 seconds
% 25.07/8.16 % CPU time: 61.634101 seconds
% 25.07/8.16 % Total memory used: 592.895 MB
% 25.07/8.16 % Net memory used: 573.265 MB
%------------------------------------------------------------------------------