%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL459+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 01:10:07 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL459+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
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 00:32:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.39 fof(f1,axiom,(
% 0.13/0.39 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f5,axiom,(
% 0.13/0.39 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f9,axiom,(
% 0.13/0.39 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f16,axiom,(
% 0.13/0.39 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f35,axiom,(
% 0.13/0.39 modus_ponens ),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f38,axiom,(
% 0.13/0.39 implies_2 ),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f42,axiom,(
% 0.13/0.39 and_3 ),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f53,conjecture,(
% 0.13/0.39 kn1 ),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f54,negated_conjecture,(
% 0.13/0.39 ~(kn1 )),
% 0.13/0.39 inference(negated_conjecture,[status(cth)],[f53])).
% 0.13/0.39 fof(f55,plain,(
% 0.13/0.39 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.13/0.39 fof(f56,plain,(
% 0.13/0.39 (~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))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f55])).
% 0.13/0.39 fof(f57,plain,(
% 0.13/0.39 (~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))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f56])).
% 0.13/0.39 fof(f58,plain,(
% 0.13/0.39 (~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)))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f57])).
% 0.13/0.39 fof(f59,plain,(
% 0.13/0.39 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f58])).
% 0.13/0.39 fof(f77,plain,(
% 0.13/0.39 (~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)))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f5])).
% 0.13/0.39 fof(f78,plain,(
% 0.13/0.39 (~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))))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f77])).
% 0.13/0.39 fof(f79,plain,(
% 0.13/0.39 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f78])).
% 0.13/0.39 fof(f93,plain,(
% 0.13/0.39 (~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))))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f9])).
% 0.13/0.39 fof(f94,plain,(
% 0.13/0.39 (~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)))))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f93])).
% 0.13/0.39 fof(f95,plain,(
% 0.13/0.39 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f94])).
% 0.13/0.39 fof(f121,plain,(
% 0.13/0.39 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f16])).
% 0.13/0.39 fof(f122,plain,(
% 0.13/0.39 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))))),
% 0.13/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f121])).
% 0.13/0.40 fof(f124,plain,(
% 0.13/0.40 kn1|~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f122])).
% 0.13/0.40 fof(f178,plain,(
% 0.13/0.40 modus_ponens),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f35])).
% 0.13/0.40 fof(f181,plain,(
% 0.13/0.40 implies_2),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f38])).
% 0.13/0.40 fof(f185,plain,(
% 0.13/0.40 and_3),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f42])).
% 0.13/0.40 fof(f196,plain,(
% 0.13/0.40 ~kn1),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f54])).
% 0.13/0.40 fof(f197,plain,(
% 0.13/0.40 ~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f124,f196])).
% 0.13/0.40 fof(f198,plain,(
% 0.13/0.40 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.13/0.40 inference(backward_subsumption_resolution,[status(thm)],[f59,f178])).
% 0.13/0.40 fof(f206,plain,(
% 0.13/0.40 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f79,f181])).
% 0.13/0.40 fof(f208,plain,(
% 0.13/0.40 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 0.13/0.40 inference(resolution,[status(thm)],[f198,f206])).
% 0.13/0.40 fof(f290,plain,(
% 0.13/0.40 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f95,f185])).
% 0.13/0.40 fof(f340,plain,(
% 0.13/0.40 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 0.13/0.40 inference(resolution,[status(thm)],[f208,f290])).
% 0.13/0.40 fof(f358,plain,(
% 0.13/0.40 $false),
% 0.13/0.40 inference(backward_subsumption_resolution,[status(thm)],[f197,f340])).
% 0.13/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.42 % Elapsed time: 0.054962 seconds
% 0.13/0.42 % CPU time: 0.181452 seconds
% 0.13/0.42 % Total memory used: 84.561 MB
% 0.13/0.42 % Net memory used: 84.471 MB
%------------------------------------------------------------------------------