%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL542+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 : n009.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 01:10:14 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL542+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
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 00:37:43 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.39 fof(f7,axiom,(
% 0.12/0.39 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f40,axiom,(
% 0.12/0.39 and_1 ),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f50,axiom,(
% 0.12/0.39 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f64,axiom,(
% 0.12/0.39 ( axiom_m2<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) )) ),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f75,axiom,(
% 0.12/0.39 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f78,axiom,(
% 0.12/0.39 necessitation ),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f86,axiom,(
% 0.12/0.39 op_strict_implies ),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f89,conjecture,(
% 0.12/0.39 axiom_m2 ),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f90,negated_conjecture,(
% 0.12/0.39 ~(axiom_m2 )),
% 0.12/0.39 inference(negated_conjecture,[status(cth)],[f89])).
% 0.12/0.39 fof(f121,plain,(
% 0.12/0.39 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f7])).
% 0.12/0.39 fof(f122,plain,(
% 0.12/0.39 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|~is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl)))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f121])).
% 0.12/0.39 fof(f123,plain,(
% 0.12/0.39 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f122])).
% 0.12/0.39 fof(f219,plain,(
% 0.12/0.39 and_1),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f40])).
% 0.12/0.39 fof(f229,plain,(
% 0.12/0.39 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 0.12/0.39 fof(f230,plain,(
% 0.12/0.39 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f229])).
% 0.12/0.39 fof(f231,plain,(
% 0.12/0.39 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f230])).
% 0.12/0.39 fof(f232,plain,(
% 0.12/0.39 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f231])).
% 0.12/0.39 fof(f296,plain,(
% 0.12/0.39 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|(?[X,Y]: ~is_a_theorem(strict_implies(and(X,Y),X))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f64])).
% 0.12/0.39 fof(f297,plain,(
% 0.12/0.39 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|~is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl)))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK78_skl,sK79_skl]),skolemize(X,sK78_skl),skolemize(Y,sK79_skl)],[f296])).
% 0.12/0.39 fof(f299,plain,(
% 0.12/0.39 axiom_m2|~is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f297])).
% 0.12/0.39 fof(f336,plain,(
% 0.12/0.39 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 0.12/0.39 fof(f337,plain,(
% 0.12/0.39 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f336])).
% 0.12/0.39 fof(f341,plain,(
% 0.12/0.39 necessitation),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f78])).
% 0.12/0.39 fof(f349,plain,(
% 0.12/0.39 op_strict_implies),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f86])).
% 0.12/0.39 fof(f352,plain,(
% 0.12/0.39 ~axiom_m2),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f90])).
% 0.12/0.39 fof(f361,plain,(
% 0.12/0.39 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 0.12/0.39 inference(backward_subsumption_resolution,[status(thm)],[f123,f219])).
% 0.12/0.39 fof(f372,plain,(
% 0.12/0.39 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.12/0.40 inference(backward_subsumption_resolution,[status(thm)],[f232,f341])).
% 0.12/0.40 fof(f377,plain,(
% 0.12/0.40 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.12/0.40 inference(backward_subsumption_resolution,[status(thm)],[f337,f349])).
% 0.12/0.40 fof(f379,plain,(
% 0.12/0.40 ~is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))),
% 0.12/0.40 inference(backward_subsumption_resolution,[status(thm)],[f299,f352])).
% 0.12/0.40 fof(f402,plain,(
% 0.12/0.40 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1)))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f377,f372])).
% 0.12/0.40 fof(f470,plain,(
% 0.12/0.40 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),X0)))),
% 0.12/0.40 inference(resolution,[status(thm)],[f402,f361])).
% 0.12/0.40 fof(f481,plain,(
% 0.12/0.40 $false),
% 0.12/0.40 inference(backward_subsumption_resolution,[status(thm)],[f379,f470])).
% 0.12/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.43 % Elapsed time: 0.059877 seconds
% 0.12/0.43 % CPU time: 0.197664 seconds
% 0.12/0.43 % Total memory used: 87.629 MB
% 0.12/0.43 % Net memory used: 87.541 MB
%------------------------------------------------------------------------------