%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL525+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 : n005.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 01:10:13 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL525+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 00:37:18 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.49 % Refutation found
% 0.18/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.49 fof(f1,axiom,(
% 0.18/0.49 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f35,axiom,(
% 0.18/0.49 modus_ponens ),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f51,axiom,(
% 0.18/0.49 ( modus_ponens_strict_implies<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(strict_implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f55,axiom,(
% 0.18/0.49 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f75,axiom,(
% 0.18/0.49 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f80,axiom,(
% 0.18/0.49 axiom_M ),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f85,axiom,(
% 0.18/0.49 op_strict_implies ),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f88,conjecture,(
% 0.18/0.49 modus_ponens_strict_implies ),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f89,negated_conjecture,(
% 0.18/0.49 ~(modus_ponens_strict_implies )),
% 0.18/0.49 inference(negated_conjecture,[status(cth)],[f88])).
% 0.18/0.49 fof(f90,plain,(
% 0.18/0.49 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.18/0.49 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.18/0.49 fof(f91,plain,(
% 0.18/0.49 (~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))))),
% 0.18/0.49 inference(NNF_transformation,[status(thm)],[f90])).
% 0.18/0.49 fof(f92,plain,(
% 0.18/0.49 (~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))))),
% 0.18/0.49 inference(miniscoping,[status(thm)],[f91])).
% 0.18/0.49 fof(f93,plain,(
% 0.18/0.49 (~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)))),
% 0.18/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f92])).
% 0.18/0.49 fof(f94,plain,(
% 0.18/0.49 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f93])).
% 0.18/0.49 fof(f213,plain,(
% 0.18/0.49 modus_ponens),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f35])).
% 0.18/0.49 fof(f234,plain,(
% 0.18/0.49 modus_ponens_strict_implies<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y)))|is_a_theorem(Y)))),
% 0.18/0.49 inference(pre_NNF_transformation,[status(thm)],[f51])).
% 0.18/0.49 fof(f235,plain,(
% 0.18/0.49 (~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))))),
% 0.18/0.49 inference(NNF_transformation,[status(thm)],[f234])).
% 0.18/0.49 fof(f236,plain,(
% 0.18/0.49 (~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))))),
% 0.18/0.49 inference(miniscoping,[status(thm)],[f235])).
% 0.18/0.49 fof(f237,plain,(
% 0.18/0.49 (~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)))),
% 0.18/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl,sK57_skl]),skolemize(Y,sK56_skl),skolemize(X,sK57_skl)],[f236])).
% 0.18/0.49 fof(f239,plain,(
% 0.18/0.49 modus_ponens_strict_implies|is_a_theorem(sK57_skl)),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f237])).
% 0.18/0.49 fof(f240,plain,(
% 0.18/0.49 modus_ponens_strict_implies|is_a_theorem(strict_implies(sK57_skl,sK56_skl))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f237])).
% 0.18/0.50 fof(f241,plain,(
% 0.18/0.50 modus_ponens_strict_implies|~is_a_theorem(sK56_skl)),
% 0.18/0.50 inference(cnf_transformation,[status(thm)],[f237])).
% 0.18/0.50 fof(f259,plain,(
% 0.18/0.50 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 0.18/0.50 inference(NNF_transformation,[status(thm)],[f55])).
% 0.18/0.50 fof(f260,plain,(
% 0.18/0.50 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 0.18/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f259])).
% 0.18/0.50 fof(f261,plain,(
% 0.18/0.50 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 0.18/0.50 inference(cnf_transformation,[status(thm)],[f260])).
% 0.18/0.50 fof(f335,plain,(
% 0.18/0.50 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 0.18/0.50 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 0.18/0.50 fof(f336,plain,(
% 0.18/0.50 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.18/0.50 inference(cnf_transformation,[status(thm)],[f335])).
% 0.18/0.50 fof(f342,plain,(
% 0.18/0.50 axiom_M),
% 0.18/0.50 inference(cnf_transformation,[status(thm)],[f80])).
% 0.18/0.50 fof(f347,plain,(
% 0.18/0.50 op_strict_implies),
% 0.18/0.50 inference(cnf_transformation,[status(thm)],[f85])).
% 0.18/0.50 fof(f350,plain,(
% 0.18/0.50 ~modus_ponens_strict_implies),
% 0.18/0.50 inference(cnf_transformation,[status(thm)],[f89])).
% 0.18/0.50 fof(f354,plain,(
% 0.18/0.50 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.18/0.50 inference(backward_subsumption_resolution,[status(thm)],[f94,f213])).
% 0.18/0.50 fof(f372,plain,(
% 0.18/0.50 ![X0]: (is_a_theorem(implies(necessarily(X0),X0)))),
% 0.18/0.50 inference(backward_subsumption_resolution,[status(thm)],[f261,f342])).
% 0.18/0.50 fof(f374,plain,(
% 0.18/0.50 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.18/0.50 inference(backward_subsumption_resolution,[status(thm)],[f336,f347])).
% 0.18/0.50 fof(f376,plain,(
% 0.18/0.50 ~is_a_theorem(sK56_skl)),
% 0.18/0.50 inference(backward_subsumption_resolution,[status(thm)],[f241,f350])).
% 0.18/0.50 fof(f377,plain,(
% 0.18/0.50 is_a_theorem(strict_implies(sK57_skl,sK56_skl))),
% 0.18/0.50 inference(backward_subsumption_resolution,[status(thm)],[f240,f350])).
% 0.18/0.50 fof(f378,plain,(
% 0.18/0.50 is_a_theorem(sK57_skl)),
% 0.18/0.50 inference(backward_subsumption_resolution,[status(thm)],[f239,f350])).
% 0.18/0.50 fof(f428,plain,(
% 0.18/0.50 ![X0]: (~is_a_theorem(necessarily(X0))|is_a_theorem(X0))),
% 0.18/0.50 inference(resolution,[status(thm)],[f354,f372])).
% 0.18/0.50 fof(f434,plain,(
% 0.18/0.50 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(X0,X1)))),
% 0.18/0.50 inference(paramodulation,[status(thm)],[f374,f428])).
% 0.18/0.50 fof(f490,plain,(
% 0.18/0.50 is_a_theorem(implies(sK57_skl,sK56_skl))),
% 0.18/0.50 inference(resolution,[status(thm)],[f434,f377])).
% 0.18/0.50 fof(f496,plain,(
% 0.18/0.50 ~is_a_theorem(sK57_skl)|is_a_theorem(sK56_skl)),
% 0.18/0.50 inference(resolution,[status(thm)],[f490,f354])).
% 0.18/0.50 fof(f498,plain,(
% 0.18/0.50 is_a_theorem(sK56_skl)),
% 0.18/0.50 inference(forward_subsumption_resolution,[status(thm)],[f496,f378])).
% 0.18/0.50 fof(f499,plain,(
% 0.18/0.50 $false),
% 0.18/0.50 inference(backward_subsumption_resolution,[status(thm)],[f376,f498])).
% 0.18/0.50 % SZS output end CNFRefutation for theBenchmark.p
% 0.50/0.58 % Elapsed time: 0.124582 seconds
% 0.50/0.58 % CPU time: 0.188609 seconds
% 0.50/0.58 % Total memory used: 20.199 MB
% 0.50/0.58 % Net memory used: 20.175 MB
%------------------------------------------------------------------------------