%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 01:09:14 PM UTC 2026
% Result : Unsatisfiable 0.20s 6.08s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.43 % Computer : n019.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Mon Sep 21 00:01:45 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.44 % Drodi V4.1.1
% 0.20/6.08 % Refutation found
% 0.20/6.08 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/6.08 % SZS output start CNFRefutation for theBenchmark
% 0.20/6.08 fof(f1,axiom,(
% 0.20/6.08 (![X,Y]: (( ~ is_a_theorem(implies(X,Y))| ~ is_a_theorem(X)| is_a_theorem(Y) ) ))),
% 0.20/6.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/6.08 fof(f2,axiom,(
% 0.20/6.08 (![X,Y]: (is_a_theorem(implies(X,implies(Y,X))) ))),
% 0.20/6.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/6.08 fof(f3,axiom,(
% 0.20/6.08 (![X,Y,Z]: (is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ))),
% 0.20/6.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/6.08 fof(f4,axiom,(
% 0.20/6.08 (![X,Y]: (is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ))),
% 0.20/6.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/6.08 fof(f6,axiom,(
% 0.20/6.08 (![X]: (is_a_theorem(implies(necessary(X),X)) ))),
% 0.20/6.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/6.08 fof(f8,negated_conjecture,(
% 0.20/6.08 ~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))) ),
% 0.20/6.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/6.08 fof(f9,plain,(
% 0.20/6.08 ![Y]: ((![X]: (~is_a_theorem(implies(X,Y))|~is_a_theorem(X)))|is_a_theorem(Y))),
% 0.20/6.08 inference(miniscoping,[status(thm)],[f1])).
% 0.20/6.08 fof(f10,plain,(
% 0.20/6.08 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(X0)|is_a_theorem(X1))),
% 0.20/6.08 inference(cnf_transformation,[status(thm)],[f9])).
% 0.20/6.08 fof(f11,plain,(
% 0.20/6.08 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 0.20/6.08 inference(cnf_transformation,[status(thm)],[f2])).
% 0.20/6.08 fof(f12,plain,(
% 0.20/6.08 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))))),
% 0.20/6.08 inference(cnf_transformation,[status(thm)],[f3])).
% 0.20/6.08 fof(f13,plain,(
% 0.20/6.08 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 0.20/6.08 inference(cnf_transformation,[status(thm)],[f4])).
% 0.20/6.08 fof(f15,plain,(
% 0.20/6.08 ![X0]: (is_a_theorem(implies(necessary(X0),X0)))),
% 0.20/6.08 inference(cnf_transformation,[status(thm)],[f6])).
% 0.20/6.08 fof(f17,plain,(
% 0.20/6.08 ~is_a_theorem(implies(necessary(a),not(necessary(not(a)))))),
% 0.20/6.08 inference(cnf_transformation,[status(thm)],[f8])).
% 0.20/6.08 fof(f18,plain,(
% 0.20/6.08 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,X0)))),
% 0.20/6.08 inference(resolution,[status(thm)],[f11,f10])).
% 0.20/6.08 fof(f20,plain,(
% 0.20/6.08 ![X0,X1,X2]: (~is_a_theorem(implies(X0,implies(X1,X2)))|is_a_theorem(implies(implies(X0,X1),implies(X0,X2))))),
% 0.20/6.08 inference(resolution,[status(thm)],[f12,f10])).
% 0.20/6.08 fof(f21,plain,(
% 0.20/6.08 ![X0,X1]: (~is_a_theorem(implies(not(X0),not(X1)))|is_a_theorem(implies(X1,X0)))),
% 0.20/6.08 inference(resolution,[status(thm)],[f13,f10])).
% 0.20/6.08 fof(f34,plain,(
% 0.20/6.08 ![X0,X1,X2]: (~is_a_theorem(implies(X0,implies(X1,X2)))|~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(X0,X2)))),
% 0.20/6.08 inference(resolution,[status(thm)],[f20,f10])).
% 0.20/6.08 fof(f42,plain,(
% 0.20/6.08 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(X0,X2))|~is_a_theorem(implies(X1,X2)))),
% 0.20/6.08 inference(resolution,[status(thm)],[f34,f18])).
% 0.20/6.08 fof(f62,plain,(
% 0.20/6.08 ![X0]: (~is_a_theorem(implies(necessary(a),X0))|~is_a_theorem(implies(X0,not(necessary(not(a))))))),
% 0.20/6.08 inference(resolution,[status(thm)],[f42,f17])).
% 0.20/6.08 fof(f95,plain,(
% 0.20/6.08 ~is_a_theorem(implies(a,not(necessary(not(a)))))),
% 0.20/6.08 inference(resolution,[status(thm)],[f15,f62])).
% 0.20/6.08 fof(f116,plain,(
% 0.20/6.08 ![X0,X1,X2]: (~is_a_theorem(implies(X0,implies(implies(X1,X0),X2)))|is_a_theorem(implies(X0,X2)))),
% 0.20/6.08 inference(resolution,[status(thm)],[f34,f11])).
% 0.20/6.08 fof(f171,plain,(
% 0.20/6.08 ![X0,X1]: (~is_a_theorem(implies(X0,necessary(X1)))|is_a_theorem(implies(X0,X1)))),
% 0.20/6.08 inference(resolution,[status(thm)],[f42,f15])).
% 0.20/6.08 fof(f172,plain,(
% 0.20/6.08 ![X0,X1,X2]: (~is_a_theorem(implies(X0,implies(not(X1),not(X2))))|is_a_theorem(implies(X0,implies(X2,X1))))),
% 0.20/6.08 inference(resolution,[status(thm)],[f42,f13])).
% 0.20/6.08 fof(f406,plain,(
% 0.20/6.08 ![X0,X1]: (is_a_theorem(implies(not(X0),implies(X0,X1))))),
% 0.20/6.08 inference(resolution,[status(thm)],[f172,f11])).
% 0.20/6.08 fof(f432,plain,(
% 0.20/6.08 ![X0,X1]: (is_a_theorem(implies(not(not(X0)),implies(X1,X0))))),
% 0.20/6.08 inference(resolution,[status(thm)],[f406,f172])).
% 0.20/6.08 fof(f1564,plain,(
% 0.20/6.08 ![X0]: (is_a_theorem(implies(not(not(X0)),X0)))),
% 0.20/6.08 inference(resolution,[status(thm)],[f432,f116])).
% 0.20/6.08 fof(f1584,plain,(
% 0.20/6.08 ![X0]: (is_a_theorem(implies(not(not(necessary(X0))),X0)))),
% 0.20/6.09 inference(resolution,[status(thm)],[f1564,f171])).
% 0.20/6.09 fof(f1681,plain,(
% 0.20/6.09 ![X0]: (is_a_theorem(implies(X0,not(necessary(not(X0))))))),
% 0.20/6.09 inference(resolution,[status(thm)],[f1584,f21])).
% 0.20/6.09 fof(f1719,plain,(
% 0.20/6.09 $false),
% 0.20/6.09 inference(backward_subsumption_resolution,[status(thm)],[f95,f1681])).
% 0.20/6.09 % SZS output end CNFRefutation for theBenchmark.p
% 0.20/6.12 % Elapsed time: 0.680094 seconds
% 0.20/6.12 % CPU time: 4.871553 seconds
% 0.20/6.12 % Total memory used: 97.688 MB
% 0.20/6.12 % Net memory used: 88.941 MB
%------------------------------------------------------------------------------