%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL496+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 : n007.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 01:10:10 PM UTC 2026
% Result : Theorem 0.11s 0.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL496+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
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 00:34:06 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.55 % Refutation found
% 0.11/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.55 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.55 fof(f1,axiom,(
% 0.11/0.55 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.11/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.55 fof(f19,axiom,(
% 0.11/0.55 ( cn1<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) )) ),
% 0.11/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.55 fof(f25,axiom,(
% 0.11/0.55 ( r4<=> (! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )) ),
% 0.11/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.55 fof(f26,axiom,(
% 0.11/0.55 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 0.11/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.55 fof(f30,axiom,(
% 0.11/0.55 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 0.11/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.55 fof(f32,axiom,(
% 0.11/0.55 op_implies_or ),
% 0.11/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.55 fof(f35,axiom,(
% 0.11/0.55 modus_ponens ),
% 0.11/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.55 fof(f39,axiom,(
% 0.11/0.55 r4 ),
% 0.11/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.55 fof(f40,axiom,(
% 0.11/0.55 r5 ),
% 0.11/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.55 fof(f45,conjecture,(
% 0.11/0.55 cn1 ),
% 0.11/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.55 fof(f46,negated_conjecture,(
% 0.11/0.55 ~(cn1 )),
% 0.11/0.55 inference(negated_conjecture,[status(cth)],[f45])).
% 0.11/0.55 fof(f47,plain,(
% 0.11/0.55 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.11/0.55 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.11/0.55 fof(f48,plain,(
% 0.11/0.55 (~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))))),
% 0.11/0.55 inference(NNF_transformation,[status(thm)],[f47])).
% 0.11/0.55 fof(f49,plain,(
% 0.11/0.55 (~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))))),
% 0.11/0.55 inference(miniscoping,[status(thm)],[f48])).
% 0.11/0.55 fof(f50,plain,(
% 0.11/0.55 (~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)))),
% 0.11/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f49])).
% 0.11/0.55 fof(f51,plain,(
% 0.11/0.55 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.11/0.55 inference(cnf_transformation,[status(thm)],[f50])).
% 0.11/0.55 fof(f125,plain,(
% 0.11/0.55 (~cn1|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))&(cn1|(?[P,Q,R]: ~is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))),
% 0.11/0.55 inference(NNF_transformation,[status(thm)],[f19])).
% 0.11/0.55 fof(f126,plain,(
% 0.11/0.55 (~cn1|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))&(cn1|~is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl)))))),
% 0.11/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl,sK39_skl,sK40_skl]),skolemize(P,sK38_skl),skolemize(Q,sK39_skl),skolemize(R,sK40_skl)],[f125])).
% 0.11/0.55 fof(f128,plain,(
% 0.11/0.55 cn1|~is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl))))),
% 0.11/0.55 inference(cnf_transformation,[status(thm)],[f126])).
% 0.11/0.55 fof(f149,plain,(
% 0.11/0.55 (~r4|(![P,Q,R]: is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))&(r4|(?[P,Q,R]: ~is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))),
% 0.11/0.55 inference(NNF_transformation,[status(thm)],[f25])).
% 0.11/0.55 fof(f150,plain,(
% 0.11/0.55 (~r4|(![P,Q,R]: is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))&(r4|~is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl)))))),
% 0.11/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK49_skl,sK50_skl,sK51_skl]),skolemize(P,sK49_skl),skolemize(Q,sK50_skl),skolemize(R,sK51_skl)],[f149])).
% 0.11/0.56 fof(f151,plain,(
% 0.11/0.56 ![X0,X1,X2]: (~r4|is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f150])).
% 0.11/0.56 fof(f153,plain,(
% 0.11/0.56 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|(?[P,Q,R]: ~is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))),
% 0.11/0.56 inference(NNF_transformation,[status(thm)],[f26])).
% 0.11/0.56 fof(f154,plain,(
% 0.11/0.56 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|~is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl)))))),
% 0.11/0.56 inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl]),skolemize(P,sK52_skl),skolemize(Q,sK53_skl),skolemize(R,sK54_skl)],[f153])).
% 0.11/0.56 fof(f155,plain,(
% 0.11/0.56 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f154])).
% 0.11/0.56 fof(f163,plain,(
% 0.11/0.56 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 0.11/0.56 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.11/0.56 fof(f164,plain,(
% 0.11/0.56 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f163])).
% 0.11/0.56 fof(f167,plain,(
% 0.11/0.56 op_implies_or),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f32])).
% 0.11/0.56 fof(f170,plain,(
% 0.11/0.56 modus_ponens),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f35])).
% 0.11/0.56 fof(f174,plain,(
% 0.11/0.56 r4),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f39])).
% 0.11/0.56 fof(f175,plain,(
% 0.11/0.56 r5),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f40])).
% 0.11/0.56 fof(f180,plain,(
% 0.11/0.56 ~cn1),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f46])).
% 0.11/0.56 fof(f181,plain,(
% 0.11/0.56 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.11/0.56 inference(backward_subsumption_resolution,[status(thm)],[f51,f170])).
% 0.11/0.56 fof(f188,plain,(
% 0.11/0.56 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 0.11/0.56 inference(forward_subsumption_resolution,[status(thm)],[f164,f167])).
% 0.11/0.56 fof(f255,plain,(
% 0.11/0.56 ~is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl))))),
% 0.11/0.56 inference(forward_subsumption_resolution,[status(thm)],[f128,f180])).
% 0.11/0.56 fof(f296,plain,(
% 0.11/0.56 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 0.11/0.56 inference(forward_subsumption_resolution,[status(thm)],[f151,f174])).
% 0.11/0.56 fof(f299,plain,(
% 0.11/0.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))))),
% 0.11/0.56 inference(paramodulation,[status(thm)],[f188,f296])).
% 0.11/0.56 fof(f303,plain,(
% 0.11/0.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))))),
% 0.11/0.56 inference(forward_demodulation,[status(thm)],[f188,f299])).
% 0.11/0.56 fof(f340,plain,(
% 0.11/0.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 0.11/0.56 inference(forward_subsumption_resolution,[status(thm)],[f155,f175])).
% 0.11/0.56 fof(f343,plain,(
% 0.11/0.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))))),
% 0.11/0.56 inference(paramodulation,[status(thm)],[f188,f340])).
% 0.11/0.56 fof(f345,plain,(
% 0.11/0.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))))),
% 0.11/0.56 inference(forward_demodulation,[status(thm)],[f188,f343])).
% 0.11/0.56 fof(f391,plain,(
% 0.11/0.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(X1,X2)),or(not(X1),implies(X0,X2)))))),
% 0.11/0.56 inference(paramodulation,[status(thm)],[f188,f303])).
% 0.11/0.56 fof(f393,plain,(
% 0.11/0.56 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))))),
% 0.11/0.56 inference(forward_demodulation,[status(thm)],[f188,f391])).
% 0.11/0.56 fof(f403,plain,(
% 0.11/0.56 ![X0,X1,X2]: (~is_a_theorem(implies(X0,implies(X1,X2)))|is_a_theorem(implies(X1,implies(X0,X2))))),
% 0.11/0.56 inference(resolution,[status(thm)],[f393,f181])).
% 0.11/0.56 fof(f412,plain,(
% 0.11/0.56 ~is_a_theorem(implies(implies(sK39_skl,sK40_skl),implies(implies(sK38_skl,sK39_skl),implies(sK38_skl,sK40_skl))))),
% 0.11/0.56 inference(resolution,[status(thm)],[f403,f255])).
% 0.11/0.56 fof(f421,plain,(
% 0.11/0.56 $false),
% 0.11/0.56 inference(forward_subsumption_resolution,[status(thm)],[f412,f345])).
% 0.11/0.56 % SZS output end CNFRefutation for theBenchmark.p
% 0.27/0.59 % Elapsed time: 0.206938 seconds
% 0.27/0.59 % CPU time: 1.320449 seconds
% 0.27/0.59 % Total memory used: 122.772 MB
% 0.27/0.59 % Net memory used: 120.691 MB
%------------------------------------------------------------------------------