%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL544+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 : 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 01:10:14 PM UTC 2026
% Result : Theorem 0.19s 0.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL544+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n019.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 00:37:50 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.49 % Drodi V4.1.1
% 0.19/0.58 % Refutation found
% 0.19/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.58 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.58 fof(f1,axiom,(
% 0.19/0.58 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f5,axiom,(
% 0.19/0.58 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f9,axiom,(
% 0.19/0.58 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f35,axiom,(
% 0.19/0.58 modus_ponens ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f38,axiom,(
% 0.19/0.58 implies_2 ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f42,axiom,(
% 0.19/0.58 and_3 ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f50,axiom,(
% 0.19/0.58 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f66,axiom,(
% 0.19/0.58 ( axiom_m4<=> (! [X] : is_a_theorem(strict_implies(X,and(X,X))) )) ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f75,axiom,(
% 0.19/0.58 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f78,axiom,(
% 0.19/0.58 necessitation ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f86,axiom,(
% 0.19/0.58 op_strict_implies ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f89,conjecture,(
% 0.19/0.58 axiom_m4 ),
% 0.19/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.58 fof(f90,negated_conjecture,(
% 0.19/0.58 ~(axiom_m4 )),
% 0.19/0.58 inference(negated_conjecture,[status(cth)],[f89])).
% 0.19/0.58 fof(f91,plain,(
% 0.19/0.58 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.19/0.58 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.19/0.58 fof(f92,plain,(
% 0.19/0.58 (~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))))),
% 0.19/0.58 inference(NNF_transformation,[status(thm)],[f91])).
% 0.19/0.58 fof(f93,plain,(
% 0.19/0.58 (~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))))),
% 0.19/0.58 inference(miniscoping,[status(thm)],[f92])).
% 0.19/0.58 fof(f94,plain,(
% 0.19/0.58 (~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)))),
% 0.19/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f93])).
% 0.19/0.58 fof(f95,plain,(
% 0.19/0.58 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f94])).
% 0.19/0.58 fof(f113,plain,(
% 0.19/0.58 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|(?[X,Y]: ~is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))),
% 0.19/0.58 inference(NNF_transformation,[status(thm)],[f5])).
% 0.19/0.58 fof(f114,plain,(
% 0.19/0.58 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl))))),
% 0.19/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f113])).
% 0.19/0.58 fof(f115,plain,(
% 0.19/0.58 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f114])).
% 0.19/0.58 fof(f129,plain,(
% 0.19/0.58 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,and(X,Y))))))),
% 0.19/0.58 inference(NNF_transformation,[status(thm)],[f9])).
% 0.19/0.58 fof(f130,plain,(
% 0.19/0.58 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|~is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl)))))),
% 0.19/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f129])).
% 0.19/0.58 fof(f131,plain,(
% 0.19/0.58 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f130])).
% 0.19/0.58 fof(f214,plain,(
% 0.19/0.58 modus_ponens),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f35])).
% 0.19/0.58 fof(f217,plain,(
% 0.19/0.58 implies_2),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f38])).
% 0.19/0.58 fof(f221,plain,(
% 0.19/0.58 and_3),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f42])).
% 0.19/0.58 fof(f229,plain,(
% 0.19/0.58 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 0.19/0.58 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 0.19/0.58 fof(f230,plain,(
% 0.19/0.58 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 0.19/0.58 inference(NNF_transformation,[status(thm)],[f229])).
% 0.19/0.58 fof(f231,plain,(
% 0.19/0.58 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 0.19/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f230])).
% 0.19/0.58 fof(f232,plain,(
% 0.19/0.58 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f231])).
% 0.19/0.58 fof(f304,plain,(
% 0.19/0.58 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|(?[X]: ~is_a_theorem(strict_implies(X,and(X,X)))))),
% 0.19/0.58 inference(NNF_transformation,[status(thm)],[f66])).
% 0.19/0.58 fof(f305,plain,(
% 0.19/0.58 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|~is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl))))),
% 0.19/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK83_skl]),skolemize(X,sK83_skl)],[f304])).
% 0.19/0.58 fof(f307,plain,(
% 0.19/0.58 axiom_m4|~is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl)))),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f305])).
% 0.19/0.58 fof(f336,plain,(
% 0.19/0.58 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 0.19/0.58 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 0.19/0.58 fof(f337,plain,(
% 0.19/0.58 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f336])).
% 0.19/0.58 fof(f341,plain,(
% 0.19/0.58 necessitation),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f78])).
% 0.19/0.58 fof(f349,plain,(
% 0.19/0.58 op_strict_implies),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f86])).
% 0.19/0.58 fof(f352,plain,(
% 0.19/0.58 ~axiom_m4),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f90])).
% 0.19/0.58 fof(f356,plain,(
% 0.19/0.58 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.19/0.58 inference(backward_subsumption_resolution,[status(thm)],[f95,f214])).
% 0.19/0.58 fof(f359,plain,(
% 0.19/0.58 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 0.19/0.58 inference(backward_subsumption_resolution,[status(thm)],[f115,f217])).
% 0.19/0.58 fof(f363,plain,(
% 0.19/0.58 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 0.19/0.58 inference(backward_subsumption_resolution,[status(thm)],[f131,f221])).
% 0.19/0.58 fof(f372,plain,(
% 0.19/0.58 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.19/0.58 inference(backward_subsumption_resolution,[status(thm)],[f232,f341])).
% 0.19/0.58 fof(f377,plain,(
% 0.19/0.58 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.19/0.58 inference(backward_subsumption_resolution,[status(thm)],[f337,f349])).
% 0.19/0.58 fof(f379,plain,(
% 0.19/0.58 ~is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl)))),
% 0.19/0.58 inference(backward_subsumption_resolution,[status(thm)],[f307,f352])).
% 0.19/0.58 fof(f402,plain,(
% 0.19/0.58 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1)))),
% 0.19/0.58 inference(paramodulation,[status(thm)],[f377,f372])).
% 0.19/0.58 fof(f455,plain,(
% 0.19/0.58 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 0.19/0.58 inference(resolution,[status(thm)],[f359,f356])).
% 0.19/0.58 fof(f536,plain,(
% 0.19/0.58 ~is_a_theorem(implies(sK83_skl,and(sK83_skl,sK83_skl)))),
% 0.19/0.58 inference(resolution,[status(thm)],[f402,f379])).
% 0.19/0.58 fof(f790,plain,(
% 0.19/0.58 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 0.19/0.58 inference(resolution,[status(thm)],[f455,f363])).
% 0.19/0.58 fof(f798,plain,(
% 0.19/0.58 $false),
% 0.19/0.58 inference(backward_subsumption_resolution,[status(thm)],[f536,f790])).
% 0.19/0.60 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.63 % Elapsed time: 0.166464 seconds
% 0.19/0.63 % CPU time: 0.603806 seconds
% 0.19/0.63 % Total memory used: 68.450 MB
% 0.19/0.63 % Net memory used: 67.956 MB
%------------------------------------------------------------------------------