%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL156-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 53 unt; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 71 ( 71 !; 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,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(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,truth) != x,
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(f21,plain,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(cnf_transformation,[status(thm)],[f4]) ).
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(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,truth) != x,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f44,plain,
! [X0,X1,X2] : and_star(X0,or(not(X1),not(X2))) = not(or(not(X0),and_star(X1,X2))),
inference(paramodulation,[status(thm)],[f30,f30]) ).
fof(f46,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f53,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f18,f46]) ).
fof(f56,plain,
! [X0] : implies(implies(truth,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f18,f53]) ).
fof(f65,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f18,f56]) ).
fof(f329,plain,
! [X0,X1] : implies(or(X0,not(X1)),implies(X1,X0)) = truth,
inference(backward_demodulation,[status(thm)],[f22,f21]) ).
fof(f331,plain,
! [X0] : or(X0,not(X0)) = truth,
inference(paramodulation,[status(thm)],[f65,f22]) ).
fof(f345,plain,
! [X0] : or(not(X0),X0) = truth,
inference(paramodulation,[status(thm)],[f24,f331]) ).
fof(f359,plain,
! [X0] : and_star(not(X0),X0) = not(truth),
inference(paramodulation,[status(thm)],[f345,f30]) ).
fof(f362,plain,
! [X0] : and_star(not(X0),X0) = falsehood,
inference(forward_demodulation,[status(thm)],[f33,f359]) ).
fof(f490,plain,
! [X0] : and(not(X0),X0) = falsehood,
inference(backward_demodulation,[status(thm)],[f502,f362]) ).
fof(f497,plain,
and(x,truth) != x,
inference(backward_demodulation,[status(thm)],[f502,f34]) ).
fof(f502,plain,
! [X0,X1] : and(X0,X1) = and_star(X0,X1),
inference(forward_demodulation,[status(thm)],[f30,f25]) ).
fof(f529,plain,
! [X0] : implies(truth,implies(X0,not(not(X0)))) = truth,
inference(paramodulation,[status(thm)],[f345,f329]) ).
fof(f546,plain,
! [X0] : implies(X0,not(not(X0))) = truth,
inference(forward_demodulation,[status(thm)],[f18,f529]) ).
fof(f567,plain,
not(not(truth)) = truth,
inference(paramodulation,[status(thm)],[f18,f546]) ).
fof(f572,plain,
! [X0] : implies(implies(not(not(X0)),X0),X0) = implies(truth,not(not(X0))),
inference(paramodulation,[status(thm)],[f546,f20]) ).
fof(f578,plain,
not(falsehood) = truth,
inference(forward_demodulation,[status(thm)],[f33,f567]) ).
fof(f582,plain,
! [X0] : implies(or(not(X0),X0),X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f22,f572]) ).
fof(f583,plain,
! [X0] : implies(truth,X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f345,f582]) ).
fof(f584,plain,
! [X0] : X0 = implies(truth,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f18,f583]) ).
fof(f585,plain,
! [X0] : X0 = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f18,f584]) ).
fof(f650,plain,
! [X0] : or(falsehood,X0) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f578,f22]) ).
fof(f652,plain,
! [X0] : or(falsehood,X0) = X0,
inference(forward_demodulation,[status(thm)],[f18,f650]) ).
fof(f670,plain,
! [X0] : or(X0,falsehood) = X0,
inference(paramodulation,[status(thm)],[f24,f652]) ).
fof(f785,plain,
! [X0,X1,X2] : and(X0,or(not(X1),not(X2))) = not(or(not(X0),and_star(X1,X2))),
inference(forward_demodulation,[status(thm)],[f502,f44]) ).
fof(f786,plain,
! [X0,X1,X2] : and(X0,or(not(X1),not(X2))) = not(or(not(X0),and(X1,X2))),
inference(forward_demodulation,[status(thm)],[f502,f785]) ).
fof(f791,plain,
! [X0,X1] : and(X0,truth) = not(or(not(X0),and(not(X1),X1))),
inference(paramodulation,[status(thm)],[f345,f786]) ).
fof(f812,plain,
! [X0] : and(X0,truth) = not(or(not(X0),falsehood)),
inference(forward_demodulation,[status(thm)],[f490,f791]) ).
fof(f813,plain,
! [X0] : and(X0,truth) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f670,f812]) ).
fof(f814,plain,
! [X0] : and(X0,truth) = X0,
inference(forward_demodulation,[status(thm)],[f585,f813]) ).
fof(f831,plain,
x != x,
inference(backward_demodulation,[status(thm)],[f814,f497]) ).
fof(f843,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f831]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL156-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 00:09:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.032674 seconds
% 0.13/0.39 % CPU time: 0.088603 seconds
% 0.13/0.39 % Total memory used: 3.564 MB
% 0.13/0.39 % Net memory used: 3.522 MB
%------------------------------------------------------------------------------