%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL109-3 : 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 19.86s 3.01s
% Output : CNFRefutation 19.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : implies(truth,X) = X,
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(f8,axiom,
! [X,Y] : implies(X,implies(Y,X)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] : implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : not(not(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y] : implies(not(X),not(Y)) = implies(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X0] : implies(truth,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = truth,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0] : not(not(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
! [X0,X1] : implies(not(X0),not(X1)) = implies(X1,X0),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f34,plain,
implies(b,implies(implies(implies(a,b),implies(b,a)),a)) != truth,
inference(forward_demodulation,[status(thm)],[f27,f31]) ).
fof(f35,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(forward_demodulation,[status(thm)],[f27,f34]) ).
fof(f81,plain,
! [X0,X1] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(paramodulation,[status(thm)],[f29,f30]) ).
fof(f82,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(paramodulation,[status(thm)],[f29,f30]) ).
fof(f161,plain,
! [X0,X1] : implies(implies(X0,X1),not(X0)) = implies(implies(not(X0),not(X1)),not(X1)),
inference(paramodulation,[status(thm)],[f30,f18]) ).
fof(f195,plain,
! [X0,X1] : implies(X0,not(implies(X0,X1))) = implies(implies(not(X0),not(X1)),not(X1)),
inference(forward_demodulation,[status(thm)],[f81,f161]) ).
fof(f196,plain,
! [X0,X1] : implies(X0,not(implies(X0,X1))) = implies(X1,not(implies(not(X0),not(X1)))),
inference(forward_demodulation,[status(thm)],[f81,f195]) ).
fof(f197,plain,
! [X0,X1] : implies(X0,not(implies(X0,X1))) = implies(X1,not(implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f30,f196]) ).
fof(f228,plain,
! [X0,X1,X2] : implies(not(implies(X0,X1)),X2) = implies(X0,implies(not(X2),X1)),
inference(paramodulation,[status(thm)],[f82,f27]) ).
fof(f448,plain,
! [X0,X1,X2] : implies(not(implies(X0,not(implies(X0,X1)))),X2) = implies(X1,implies(not(X2),not(implies(X1,X0)))),
inference(paramodulation,[status(thm)],[f197,f228]) ).
fof(f505,plain,
! [X0,X1,X2] : implies(X0,implies(not(X1),not(implies(X0,X2)))) = implies(X2,implies(not(X1),not(implies(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f228,f448]) ).
fof(f506,plain,
! [X0,X1,X2] : implies(X0,implies(implies(X0,X1),X2)) = implies(X1,implies(not(X2),not(implies(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f30,f505]) ).
fof(f507,plain,
! [X0,X1,X2] : implies(X0,implies(implies(X0,X1),X2)) = implies(X1,implies(implies(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f30,f506]) ).
fof(f648,plain,
! [X0,X1] : implies(implies(implies(X0,X1),X1),X1) = implies(truth,implies(X0,X1)),
inference(paramodulation,[status(thm)],[f23,f18]) ).
fof(f677,plain,
! [X0,X1] : implies(implies(implies(X0,X1),X1),X1) = implies(X0,X1),
inference(forward_demodulation,[status(thm)],[f16,f648]) ).
fof(f685,plain,
! [X0,X1] : implies(implies(implies(X0,X1),X1),X0) = implies(X1,X0),
inference(paramodulation,[status(thm)],[f18,f677]) ).
fof(f8699,plain,
! [X0,X1] : implies(implies(X0,X1),implies(X1,X0)) = implies(X1,implies(implies(X1,implies(X0,X1)),X0)),
inference(paramodulation,[status(thm)],[f685,f507]) ).
fof(f8989,plain,
! [X0,X1] : implies(X0,implies(implies(X1,X0),X1)) = implies(X0,implies(implies(X0,implies(X1,X0)),X1)),
inference(forward_demodulation,[status(thm)],[f27,f8699]) ).
fof(f8990,plain,
! [X0,X1] : implies(X0,implies(implies(X1,X0),X1)) = implies(X0,implies(truth,X1)),
inference(forward_demodulation,[status(thm)],[f23,f8989]) ).
fof(f8991,plain,
implies(b,implies(implies(b,a),a)) != truth,
inference(backward_demodulation,[status(thm)],[f8994,f35]) ).
fof(f8994,plain,
! [X0,X1] : implies(X0,implies(implies(X1,X0),X1)) = implies(X0,X1),
inference(forward_demodulation,[status(thm)],[f16,f8990]) ).
fof(f9208,plain,
implies(a,implies(implies(a,b),a)) != truth,
inference(forward_demodulation,[status(thm)],[f507,f8991]) ).
fof(f9209,plain,
truth != truth,
inference(forward_demodulation,[status(thm)],[f23,f9208]) ).
fof(f9210,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f9209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL109-3 : 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 00:06:03 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 19.86/3.01 % Refutation found
% 19.86/3.01 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 19.86/3.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.86/3.05 % Elapsed time: 2.683787 seconds
% 19.86/3.05 % CPU time: 20.928155 seconds
% 19.86/3.05 % Total memory used: 204.093 MB
% 19.86/3.05 % Net memory used: 199.596 MB
%------------------------------------------------------------------------------