%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL546+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 01:10:15 PM UTC 2026
% Result : Theorem 4.64s 1.08s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL546+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:37:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 4.64/1.08 % Refutation found
% 4.64/1.08 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.64/1.08 % SZS output start CNFRefutation for theBenchmark
% 4.64/1.08 fof(f1,axiom,(
% 4.64/1.08 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f6,axiom,(
% 4.64/1.08 ( implies_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )) ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f35,axiom,(
% 4.64/1.08 modus_ponens ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f39,axiom,(
% 4.64/1.08 implies_3 ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f50,axiom,(
% 4.64/1.08 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f55,axiom,(
% 4.64/1.08 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f57,axiom,(
% 4.64/1.08 ( axiom_B<=> (! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) )) ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f68,axiom,(
% 4.64/1.08 ( axiom_m6<=> (! [X] : is_a_theorem(strict_implies(X,possibly(X))) )) ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f75,axiom,(
% 4.64/1.08 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f78,axiom,(
% 4.64/1.08 necessitation ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f80,axiom,(
% 4.64/1.08 axiom_M ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f82,axiom,(
% 4.64/1.08 axiom_B ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f86,axiom,(
% 4.64/1.08 op_strict_implies ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f89,conjecture,(
% 4.64/1.08 axiom_m6 ),
% 4.64/1.08 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.64/1.08 fof(f90,negated_conjecture,(
% 4.64/1.08 ~(axiom_m6 )),
% 4.64/1.08 inference(negated_conjecture,[status(cth)],[f89])).
% 4.64/1.08 fof(f91,plain,(
% 4.64/1.08 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 4.64/1.08 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 4.64/1.08 fof(f92,plain,(
% 4.64/1.08 (~modus_ponens|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y))))&(modus_ponens|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(implies(X,Y)))&~is_a_theorem(Y))))),
% 4.64/1.08 inference(NNF_transformation,[status(thm)],[f91])).
% 4.64/1.08 fof(f93,plain,(
% 4.64/1.08 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|(?[Y]: ((?[X]: (is_a_theorem(X)&is_a_theorem(implies(X,Y))))&~is_a_theorem(Y))))),
% 4.64/1.08 inference(miniscoping,[status(thm)],[f92])).
% 4.64/1.08 fof(f94,plain,(
% 4.64/1.08 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|((is_a_theorem(sK1_skl)&is_a_theorem(implies(sK1_skl,sK0_skl)))&~is_a_theorem(sK0_skl)))),
% 4.64/1.08 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f93])).
% 4.64/1.08 fof(f95,plain,(
% 4.64/1.08 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f94])).
% 4.64/1.08 fof(f117,plain,(
% 4.64/1.08 (~implies_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))&(implies_3|(?[X,Y,Z]: ~is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))),
% 4.64/1.08 inference(NNF_transformation,[status(thm)],[f6])).
% 4.64/1.08 fof(f118,plain,(
% 4.64/1.08 (~implies_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))&(implies_3|~is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl)))))),
% 4.64/1.08 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(X,sK10_skl),skolemize(Y,sK11_skl),skolemize(Z,sK12_skl)],[f117])).
% 4.64/1.08 fof(f119,plain,(
% 4.64/1.08 ![X0,X1,X2]: (~implies_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f118])).
% 4.64/1.08 fof(f214,plain,(
% 4.64/1.08 modus_ponens),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f35])).
% 4.64/1.08 fof(f218,plain,(
% 4.64/1.08 implies_3),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f39])).
% 4.64/1.08 fof(f229,plain,(
% 4.64/1.08 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 4.64/1.08 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 4.64/1.08 fof(f230,plain,(
% 4.64/1.08 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 4.64/1.08 inference(NNF_transformation,[status(thm)],[f229])).
% 4.64/1.08 fof(f231,plain,(
% 4.64/1.08 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 4.64/1.08 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f230])).
% 4.64/1.08 fof(f232,plain,(
% 4.64/1.08 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f231])).
% 4.64/1.08 fof(f260,plain,(
% 4.64/1.08 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 4.64/1.08 inference(NNF_transformation,[status(thm)],[f55])).
% 4.64/1.08 fof(f261,plain,(
% 4.64/1.08 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 4.64/1.08 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f260])).
% 4.64/1.08 fof(f262,plain,(
% 4.64/1.08 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f261])).
% 4.64/1.08 fof(f268,plain,(
% 4.64/1.08 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|(?[X]: ~is_a_theorem(implies(X,necessarily(possibly(X))))))),
% 4.64/1.08 inference(NNF_transformation,[status(thm)],[f57])).
% 4.64/1.08 fof(f269,plain,(
% 4.64/1.08 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|~is_a_theorem(implies(sK66_skl,necessarily(possibly(sK66_skl)))))),
% 4.64/1.08 inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl]),skolemize(X,sK66_skl)],[f268])).
% 4.64/1.08 fof(f270,plain,(
% 4.64/1.08 ![X0]: (~axiom_B|is_a_theorem(implies(X0,necessarily(possibly(X0)))))),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f269])).
% 4.64/1.08 fof(f312,plain,(
% 4.64/1.08 (~axiom_m6|(![X]: is_a_theorem(strict_implies(X,possibly(X)))))&(axiom_m6|(?[X]: ~is_a_theorem(strict_implies(X,possibly(X)))))),
% 4.64/1.08 inference(NNF_transformation,[status(thm)],[f68])).
% 4.64/1.08 fof(f313,plain,(
% 4.64/1.08 (~axiom_m6|(![X]: is_a_theorem(strict_implies(X,possibly(X)))))&(axiom_m6|~is_a_theorem(strict_implies(sK87_skl,possibly(sK87_skl))))),
% 4.64/1.08 inference(skolemize,[status(esa),new_symbols(skolem,[sK87_skl]),skolemize(X,sK87_skl)],[f312])).
% 4.64/1.08 fof(f315,plain,(
% 4.64/1.08 axiom_m6|~is_a_theorem(strict_implies(sK87_skl,possibly(sK87_skl)))),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f313])).
% 4.64/1.08 fof(f336,plain,(
% 4.64/1.08 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 4.64/1.08 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 4.64/1.08 fof(f337,plain,(
% 4.64/1.08 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f336])).
% 4.64/1.08 fof(f341,plain,(
% 4.64/1.08 necessitation),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f78])).
% 4.64/1.08 fof(f343,plain,(
% 4.64/1.08 axiom_M),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f80])).
% 4.64/1.08 fof(f345,plain,(
% 4.64/1.08 axiom_B),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f82])).
% 4.64/1.08 fof(f349,plain,(
% 4.64/1.08 op_strict_implies),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f86])).
% 4.64/1.08 fof(f352,plain,(
% 4.64/1.08 ~axiom_m6),
% 4.64/1.08 inference(cnf_transformation,[status(thm)],[f90])).
% 4.64/1.08 fof(f356,plain,(
% 4.64/1.08 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 4.64/1.08 inference(backward_subsumption_resolution,[status(thm)],[f95,f214])).
% 4.64/1.08 fof(f360,plain,(
% 4.64/1.08 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 4.64/1.08 inference(backward_subsumption_resolution,[status(thm)],[f119,f218])).
% 4.64/1.08 fof(f372,plain,(
% 4.64/1.08 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 4.64/1.08 inference(backward_subsumption_resolution,[status(thm)],[f232,f341])).
% 4.64/1.08 fof(f374,plain,(
% 4.64/1.08 ![X0]: (is_a_theorem(implies(necessarily(X0),X0)))),
% 4.64/1.08 inference(backward_subsumption_resolution,[status(thm)],[f262,f343])).
% 4.64/1.10 fof(f376,plain,(
% 4.64/1.10 ![X0]: (is_a_theorem(implies(X0,necessarily(possibly(X0)))))),
% 4.64/1.10 inference(backward_subsumption_resolution,[status(thm)],[f270,f345])).
% 4.64/1.10 fof(f377,plain,(
% 4.64/1.10 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 4.64/1.10 inference(backward_subsumption_resolution,[status(thm)],[f337,f349])).
% 4.64/1.10 fof(f379,plain,(
% 4.64/1.10 ~is_a_theorem(strict_implies(sK87_skl,possibly(sK87_skl)))),
% 4.64/1.10 inference(backward_subsumption_resolution,[status(thm)],[f315,f352])).
% 4.64/1.10 fof(f402,plain,(
% 4.64/1.10 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1)))),
% 4.64/1.10 inference(paramodulation,[status(thm)],[f377,f372])).
% 4.64/1.10 fof(f465,plain,(
% 4.64/1.10 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X2),implies(X0,X2))))),
% 4.64/1.10 inference(resolution,[status(thm)],[f360,f356])).
% 4.64/1.10 fof(f536,plain,(
% 4.64/1.10 ~is_a_theorem(implies(sK87_skl,possibly(sK87_skl)))),
% 4.64/1.10 inference(resolution,[status(thm)],[f402,f379])).
% 4.64/1.10 fof(f831,plain,(
% 4.64/1.10 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(X0,X2)))),
% 4.64/1.10 inference(resolution,[status(thm)],[f465,f356])).
% 4.64/1.10 fof(f4202,plain,(
% 4.64/1.10 ![X0]: (~is_a_theorem(implies(sK87_skl,X0))|~is_a_theorem(implies(X0,possibly(sK87_skl))))),
% 4.64/1.10 inference(resolution,[status(thm)],[f831,f536])).
% 4.64/1.10 fof(f4237,plain,(
% 4.64/1.10 ~is_a_theorem(implies(sK87_skl,necessarily(possibly(sK87_skl))))),
% 4.64/1.10 inference(resolution,[status(thm)],[f4202,f374])).
% 4.64/1.10 fof(f4243,plain,(
% 4.64/1.10 $false),
% 4.64/1.10 inference(forward_subsumption_resolution,[status(thm)],[f4237,f376])).
% 4.64/1.10 % SZS output end CNFRefutation for theBenchmark.p
% 2.57/1.11 % Elapsed time: 0.717619 seconds
% 2.57/1.11 % CPU time: 5.394096 seconds
% 2.57/1.11 % Total memory used: 194.550 MB
% 2.57/1.11 % Net memory used: 188.629 MB
%------------------------------------------------------------------------------