%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 0.10s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 00:37:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.42 % Refutation found
% 0.10/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.42 fof(f1,axiom,(
% 0.10/0.42 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f35,axiom,(
% 0.10/0.42 modus_ponens ),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f51,axiom,(
% 0.10/0.42 ( modus_ponens_strict_implies<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(strict_implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f55,axiom,(
% 0.10/0.42 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f75,axiom,(
% 0.10/0.42 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f80,axiom,(
% 0.10/0.42 axiom_M ),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f86,axiom,(
% 0.10/0.42 op_strict_implies ),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f89,conjecture,(
% 0.10/0.42 modus_ponens_strict_implies ),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f90,negated_conjecture,(
% 0.10/0.42 ~(modus_ponens_strict_implies )),
% 0.10/0.42 inference(negated_conjecture,[status(cth)],[f89])).
% 0.10/0.42 fof(f91,plain,(
% 0.10/0.42 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.10/0.42 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.10/0.42 fof(f92,plain,(
% 0.10/0.42 (~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))))),
% 0.10/0.42 inference(NNF_transformation,[status(thm)],[f91])).
% 0.10/0.42 fof(f93,plain,(
% 0.10/0.42 (~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))))),
% 0.10/0.42 inference(miniscoping,[status(thm)],[f92])).
% 0.10/0.42 fof(f94,plain,(
% 0.10/0.42 (~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)))),
% 0.10/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f93])).
% 0.10/0.42 fof(f95,plain,(
% 0.10/0.42 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f94])).
% 0.10/0.42 fof(f214,plain,(
% 0.10/0.42 modus_ponens),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f35])).
% 0.10/0.42 fof(f235,plain,(
% 0.10/0.42 modus_ponens_strict_implies<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y)))|is_a_theorem(Y)))),
% 0.10/0.42 inference(pre_NNF_transformation,[status(thm)],[f51])).
% 0.10/0.42 fof(f236,plain,(
% 0.10/0.42 (~modus_ponens_strict_implies|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y)))|is_a_theorem(Y))))&(modus_ponens_strict_implies|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(strict_implies(X,Y)))&~is_a_theorem(Y))))),
% 0.10/0.42 inference(NNF_transformation,[status(thm)],[f235])).
% 0.10/0.42 fof(f237,plain,(
% 0.10/0.42 (~modus_ponens_strict_implies|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens_strict_implies|(?[Y]: ((?[X]: (is_a_theorem(X)&is_a_theorem(strict_implies(X,Y))))&~is_a_theorem(Y))))),
% 0.10/0.42 inference(miniscoping,[status(thm)],[f236])).
% 0.10/0.42 fof(f238,plain,(
% 0.10/0.42 (~modus_ponens_strict_implies|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens_strict_implies|((is_a_theorem(sK57_skl)&is_a_theorem(strict_implies(sK57_skl,sK56_skl)))&~is_a_theorem(sK56_skl)))),
% 0.10/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl,sK57_skl]),skolemize(Y,sK56_skl),skolemize(X,sK57_skl)],[f237])).
% 0.10/0.42 fof(f240,plain,(
% 0.10/0.42 modus_ponens_strict_implies|is_a_theorem(sK57_skl)),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f238])).
% 0.10/0.42 fof(f241,plain,(
% 0.10/0.42 modus_ponens_strict_implies|is_a_theorem(strict_implies(sK57_skl,sK56_skl))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f238])).
% 0.10/0.42 fof(f242,plain,(
% 0.10/0.42 modus_ponens_strict_implies|~is_a_theorem(sK56_skl)),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f238])).
% 0.10/0.42 fof(f260,plain,(
% 0.10/0.42 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 0.10/0.42 inference(NNF_transformation,[status(thm)],[f55])).
% 0.10/0.42 fof(f261,plain,(
% 0.10/0.42 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 0.10/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f260])).
% 0.10/0.42 fof(f262,plain,(
% 0.10/0.42 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f261])).
% 0.10/0.42 fof(f336,plain,(
% 0.10/0.42 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 0.10/0.42 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 0.10/0.42 fof(f337,plain,(
% 0.10/0.42 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f336])).
% 0.10/0.42 fof(f343,plain,(
% 0.10/0.42 axiom_M),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f80])).
% 0.10/0.42 fof(f349,plain,(
% 0.10/0.42 op_strict_implies),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f86])).
% 0.10/0.42 fof(f352,plain,(
% 0.10/0.42 ~modus_ponens_strict_implies),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f90])).
% 0.10/0.42 fof(f356,plain,(
% 0.10/0.42 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f95,f214])).
% 0.10/0.42 fof(f374,plain,(
% 0.10/0.42 ![X0]: (is_a_theorem(implies(necessarily(X0),X0)))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f262,f343])).
% 0.10/0.42 fof(f377,plain,(
% 0.10/0.42 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f337,f349])).
% 0.10/0.42 fof(f379,plain,(
% 0.10/0.42 ~is_a_theorem(sK56_skl)),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f242,f352])).
% 0.10/0.42 fof(f380,plain,(
% 0.10/0.42 is_a_theorem(strict_implies(sK57_skl,sK56_skl))),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f241,f352])).
% 0.10/0.42 fof(f381,plain,(
% 0.10/0.42 is_a_theorem(sK57_skl)),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f240,f352])).
% 0.10/0.42 fof(f432,plain,(
% 0.10/0.42 ![X0]: (~is_a_theorem(necessarily(X0))|is_a_theorem(X0))),
% 0.10/0.42 inference(resolution,[status(thm)],[f356,f374])).
% 0.10/0.42 fof(f439,plain,(
% 0.10/0.42 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(X0,X1)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f377,f432])).
% 0.10/0.42 fof(f511,plain,(
% 0.10/0.42 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(X0)|is_a_theorem(X1))),
% 0.10/0.42 inference(resolution,[status(thm)],[f439,f356])).
% 0.10/0.42 fof(f537,plain,(
% 0.10/0.42 ~is_a_theorem(sK57_skl)|is_a_theorem(sK56_skl)),
% 0.10/0.42 inference(resolution,[status(thm)],[f511,f380])).
% 0.10/0.42 fof(f545,plain,(
% 0.10/0.42 is_a_theorem(sK56_skl)),
% 0.10/0.42 inference(forward_subsumption_resolution,[status(thm)],[f537,f381])).
% 0.10/0.42 fof(f546,plain,(
% 0.10/0.42 $false),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f379,f545])).
% 0.10/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.45 % Elapsed time: 0.063026 seconds
% 0.10/0.45 % CPU time: 0.197251 seconds
% 0.10/0.45 % Total memory used: 76.885 MB
% 0.10/0.45 % Net memory used: 76.715 MB
%------------------------------------------------------------------------------