%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL499+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 : n018.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 01:10:11 PM UTC 2026
% Result : Theorem 0.13s 5.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL499+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
% 0.10/5.38 % Computer : n018.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 00:38:21 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.13/5.42 % Refutation found
% 0.13/5.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.42 % SZS output start CNFRefutation for theBenchmark
% 0.13/5.42 fof(f1,axiom,(
% 0.13/5.42 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f16,axiom,(
% 0.13/5.42 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f22,axiom,(
% 0.13/5.42 ( r1<=> (! [P] : is_a_theorem(implies(or(P,P),P)) )) ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f24,axiom,(
% 0.13/5.42 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f28,axiom,(
% 0.13/5.42 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f30,axiom,(
% 0.13/5.42 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f32,axiom,(
% 0.13/5.42 op_implies_or ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f33,axiom,(
% 0.13/5.42 op_and ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f35,axiom,(
% 0.13/5.42 modus_ponens ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f36,axiom,(
% 0.13/5.42 r1 ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f38,axiom,(
% 0.13/5.42 r3 ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f45,conjecture,(
% 0.13/5.42 kn1 ),
% 0.13/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.42 fof(f46,negated_conjecture,(
% 0.13/5.42 ~(kn1 )),
% 0.13/5.42 inference(negated_conjecture,[status(cth)],[f45])).
% 0.13/5.42 fof(f47,plain,(
% 0.13/5.42 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.13/5.42 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.13/5.42 fof(f48,plain,(
% 0.13/5.42 (~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))))),
% 0.13/5.42 inference(NNF_transformation,[status(thm)],[f47])).
% 0.13/5.42 fof(f49,plain,(
% 0.13/5.42 (~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))))),
% 0.13/5.42 inference(miniscoping,[status(thm)],[f48])).
% 0.13/5.42 fof(f50,plain,(
% 0.13/5.42 (~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)))),
% 0.13/5.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f49])).
% 0.13/5.42 fof(f51,plain,(
% 0.13/5.42 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f50])).
% 0.13/5.42 fof(f113,plain,(
% 0.13/5.42 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 0.13/5.42 inference(NNF_transformation,[status(thm)],[f16])).
% 0.13/5.42 fof(f114,plain,(
% 0.13/5.42 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))))),
% 0.13/5.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f113])).
% 0.13/5.42 fof(f116,plain,(
% 0.13/5.42 kn1|~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f114])).
% 0.13/5.42 fof(f137,plain,(
% 0.13/5.42 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|(?[P]: ~is_a_theorem(implies(or(P,P),P))))),
% 0.13/5.42 inference(NNF_transformation,[status(thm)],[f22])).
% 0.13/5.42 fof(f138,plain,(
% 0.13/5.42 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)))),
% 0.13/5.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(P,sK44_skl)],[f137])).
% 0.13/5.42 fof(f139,plain,(
% 0.13/5.42 ![X0]: (~r1|is_a_theorem(implies(or(X0,X0),X0)))),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f138])).
% 0.13/5.42 fof(f145,plain,(
% 0.13/5.42 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|(?[P,Q]: ~is_a_theorem(implies(or(P,Q),or(Q,P)))))),
% 0.13/5.42 inference(NNF_transformation,[status(thm)],[f24])).
% 0.13/5.42 fof(f146,plain,(
% 0.13/5.42 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))))),
% 0.13/5.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f145])).
% 0.13/5.42 fof(f147,plain,(
% 0.13/5.42 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f146])).
% 0.13/5.42 fof(f159,plain,(
% 0.13/5.42 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 0.13/5.42 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.13/5.42 fof(f160,plain,(
% 0.13/5.42 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f159])).
% 0.13/5.42 fof(f163,plain,(
% 0.13/5.42 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 0.13/5.42 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.13/5.42 fof(f164,plain,(
% 0.13/5.42 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f163])).
% 0.13/5.42 fof(f167,plain,(
% 0.13/5.42 op_implies_or),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f32])).
% 0.13/5.42 fof(f168,plain,(
% 0.13/5.42 op_and),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f33])).
% 0.13/5.42 fof(f170,plain,(
% 0.13/5.42 modus_ponens),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f35])).
% 0.13/5.42 fof(f171,plain,(
% 0.13/5.42 r1),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f36])).
% 0.13/5.42 fof(f173,plain,(
% 0.13/5.42 r3),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f38])).
% 0.13/5.42 fof(f180,plain,(
% 0.13/5.42 ~kn1),
% 0.13/5.42 inference(cnf_transformation,[status(thm)],[f46])).
% 0.13/5.42 fof(f181,plain,(
% 0.13/5.42 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 0.13/5.42 inference(backward_subsumption_resolution,[status(thm)],[f164,f167])).
% 0.13/5.42 fof(f182,plain,(
% 0.13/5.42 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1))))),
% 0.13/5.42 inference(backward_subsumption_resolution,[status(thm)],[f160,f168])).
% 0.13/5.42 fof(f184,plain,(
% 0.13/5.42 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.13/5.42 inference(backward_subsumption_resolution,[status(thm)],[f51,f170])).
% 0.13/5.42 fof(f185,plain,(
% 0.13/5.42 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 0.13/5.42 inference(backward_subsumption_resolution,[status(thm)],[f139,f171])).
% 0.13/5.42 fof(f187,plain,(
% 0.13/5.42 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 0.13/5.42 inference(backward_subsumption_resolution,[status(thm)],[f147,f173])).
% 0.13/5.42 fof(f193,plain,(
% 0.13/5.42 ~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))),
% 0.13/5.42 inference(backward_subsumption_resolution,[status(thm)],[f116,f180])).
% 0.13/5.42 fof(f194,plain,(
% 0.13/5.42 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1))))),
% 0.13/5.42 inference(forward_demodulation,[status(thm)],[f181,f182])).
% 0.13/5.42 fof(f207,plain,(
% 0.13/5.42 ![X0]: (is_a_theorem(implies(implies(X0,not(X0)),not(X0))))),
% 0.13/5.42 inference(paramodulation,[status(thm)],[f181,f185])).
% 0.13/5.42 fof(f221,plain,(
% 0.13/5.42 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(and(X0,X1),X2))),
% 0.13/5.42 inference(paramodulation,[status(thm)],[f194,f181])).
% 0.13/5.42 fof(f224,plain,(
% 0.13/5.42 ![X0]: (is_a_theorem(or(and(X0,X0),not(X0))))),
% 0.13/5.42 inference(backward_demodulation,[status(thm)],[f221,f207])).
% 0.13/5.42 fof(f241,plain,(
% 0.13/5.42 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0)))),
% 0.13/5.42 inference(resolution,[status(thm)],[f187,f184])).
% 0.13/5.42 fof(f257,plain,(
% 0.13/5.42 ![X0,X1]: (~is_a_theorem(or(X0,not(X1)))|is_a_theorem(implies(X1,X0)))),
% 0.13/5.42 inference(paramodulation,[status(thm)],[f181,f241])).
% 0.13/5.42 fof(f365,plain,(
% 0.13/5.42 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 0.13/5.42 inference(resolution,[status(thm)],[f257,f224])).
% 0.13/5.42 fof(f374,plain,(
% 0.13/5.42 $false),
% 0.13/5.42 inference(backward_subsumption_resolution,[status(thm)],[f193,f365])).
% 0.13/5.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/5.45 % Elapsed time: 0.059667 seconds
% 0.13/5.45 % CPU time: 0.188582 seconds
% 0.13/5.45 % Total memory used: 84.852 MB
% 0.13/5.45 % Net memory used: 84.741 MB
%------------------------------------------------------------------------------