%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL157-1 : 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 01:06:56 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.54s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 55 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 62 !; 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(f5,axiom,
! [X,Y] : or(X,Y) = implies(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : or(X,Y) = or(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : and(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : and(X,Y) = and(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : and_star(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
and_star(x,falsehood) != falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : implies(truth,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
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)],[f3]) ).
fof(f22,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1] : and(X0,X1) = and(X1,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
! [X0,X1] : and_star(X0,X1) = not(or(not(X0),not(X1))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f33,plain,
not(truth) = falsehood,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
and_star(x,falsehood) != falsehood,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f38,plain,
! [X0,X1] : and_star(X0,X1) = and(X0,X1),
inference(forward_demodulation,[status(thm)],[f25,f30]) ).
fof(f45,plain,
and(x,falsehood) != falsehood,
inference(forward_demodulation,[status(thm)],[f38,f34]) ).
fof(f46,plain,
and(falsehood,x) != falsehood,
inference(forward_demodulation,[status(thm)],[f27,f45]) ).
fof(f52,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f59,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f52]) ).
fof(f70,plain,
! [X0] : or(truth,X0) = implies(falsehood,X0),
inference(paramodulation,[status(thm)],[f33,f22]) ).
fof(f76,plain,
! [X0] : or(X0,truth) = implies(falsehood,X0),
inference(paramodulation,[status(thm)],[f24,f70]) ).
fof(f86,plain,
! [X0,X1] : or(X0,implies(implies(not(X0),X1),X1)) = truth,
inference(paramodulation,[status(thm)],[f22,f59]) ).
fof(f87,plain,
! [X0] : implies(implies(truth,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f18,f59]) ).
fof(f98,plain,
! [X0,X1] : or(X0,implies(or(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f22,f86]) ).
fof(f99,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f87]) ).
fof(f108,plain,
! [X0] : or(X0,not(X0)) = truth,
inference(paramodulation,[status(thm)],[f22,f99]) ).
fof(f131,plain,
! [X0] : or(X0,implies(implies(falsehood,X0),truth)) = truth,
inference(paramodulation,[status(thm)],[f76,f98]) ).
fof(f155,plain,
! [X0] : implies(X0,X0) = implies(implies(X0,truth),truth),
inference(paramodulation,[status(thm)],[f18,f20]) ).
fof(f163,plain,
or(truth,implies(implies(truth,falsehood),falsehood)) = truth,
inference(paramodulation,[status(thm)],[f20,f131]) ).
fof(f176,plain,
! [X0] : truth = implies(implies(X0,truth),truth),
inference(forward_demodulation,[status(thm)],[f99,f155]) ).
fof(f181,plain,
implies(falsehood,implies(implies(truth,falsehood),falsehood)) = truth,
inference(forward_demodulation,[status(thm)],[f70,f163]) ).
fof(f182,plain,
implies(falsehood,implies(falsehood,falsehood)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f181]) ).
fof(f183,plain,
implies(falsehood,truth) = truth,
inference(forward_demodulation,[status(thm)],[f99,f182]) ).
fof(f189,plain,
! [X0] : implies(implies(falsehood,X0),implies(implies(X0,truth),truth)) = truth,
inference(paramodulation,[status(thm)],[f183,f19]) ).
fof(f199,plain,
! [X0] : or(X0,truth) = truth,
inference(backward_demodulation,[status(thm)],[f200,f131]) ).
fof(f200,plain,
! [X0] : implies(implies(falsehood,X0),truth) = truth,
inference(forward_demodulation,[status(thm)],[f176,f189]) ).
fof(f209,plain,
! [X0] : implies(falsehood,X0) = truth,
inference(forward_demodulation,[status(thm)],[f76,f199]) ).
fof(f224,plain,
! [X0] : implies(implies(X0,falsehood),falsehood) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f209,f20]) ).
fof(f231,plain,
! [X0] : implies(implies(X0,falsehood),falsehood) = X0,
inference(forward_demodulation,[status(thm)],[f18,f224]) ).
fof(f377,plain,
! [X0] : implies(or(X0,falsehood),falsehood) = not(X0),
inference(paramodulation,[status(thm)],[f22,f231]) ).
fof(f445,plain,
! [X0] : implies(or(falsehood,X0),falsehood) = not(X0),
inference(paramodulation,[status(thm)],[f24,f377]) ).
fof(f466,plain,
implies(truth,falsehood) = not(not(falsehood)),
inference(paramodulation,[status(thm)],[f108,f445]) ).
fof(f482,plain,
falsehood = not(not(falsehood)),
inference(forward_demodulation,[status(thm)],[f18,f466]) ).
fof(f493,plain,
! [X0] : or(not(falsehood),X0) = implies(falsehood,X0),
inference(paramodulation,[status(thm)],[f482,f22]) ).
fof(f499,plain,
! [X0] : or(not(falsehood),X0) = truth,
inference(forward_demodulation,[status(thm)],[f209,f493]) ).
fof(f577,plain,
! [X0] : and(falsehood,X0) = not(truth),
inference(paramodulation,[status(thm)],[f499,f25]) ).
fof(f592,plain,
falsehood != falsehood,
inference(backward_demodulation,[status(thm)],[f593,f46]) ).
fof(f593,plain,
! [X0] : and(falsehood,X0) = falsehood,
inference(forward_demodulation,[status(thm)],[f33,f577]) ).
fof(f614,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL157-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 % Computer : n020.cluster.edu
% 0.19/0.47 % Model : x86_64 x86_64
% 0.19/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47 % Memory : 8046.5625MB
% 0.19/0.47 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Mon Sep 21 00:08:32 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.49 % Drodi V4.1.1
% 0.19/0.54 % Refutation found
% 0.19/0.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.57 % Elapsed time: 0.081352 seconds
% 0.19/0.57 % CPU time: 0.269017 seconds
% 0.19/0.57 % Total memory used: 7.647 MB
% 0.19/0.57 % Net memory used: 7.541 MB
%------------------------------------------------------------------------------