%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL486+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 : 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 01:10:09 PM UTC 2026
% Result : Theorem 1.82s 1.02s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL486+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 00:35:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 1.82/1.02 % Refutation found
% 1.82/1.02 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.82/1.02 % SZS output start CNFRefutation for theBenchmark
% 1.82/1.02 fof(f1,axiom,(
% 1.82/1.02 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 1.82/1.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.82/1.02 fof(f6,axiom,(
% 1.82/1.02 ( implies_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )) ),
% 1.82/1.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.82/1.02 fof(f25,axiom,(
% 1.82/1.02 ( r4<=> (! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )) ),
% 1.82/1.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.82/1.02 fof(f26,axiom,(
% 1.82/1.02 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 1.82/1.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.82/1.02 fof(f30,axiom,(
% 1.82/1.02 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 1.82/1.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.82/1.02 fof(f32,axiom,(
% 1.82/1.02 op_implies_or ),
% 1.82/1.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.82/1.02 fof(f35,axiom,(
% 1.82/1.02 modus_ponens ),
% 1.82/1.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.82/1.02 fof(f39,axiom,(
% 1.82/1.02 r4 ),
% 1.82/1.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.82/1.02 fof(f40,axiom,(
% 1.82/1.02 r5 ),
% 1.82/1.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.82/1.02 fof(f45,conjecture,(
% 1.82/1.02 implies_3 ),
% 1.82/1.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.82/1.02 fof(f46,negated_conjecture,(
% 1.82/1.02 ~(implies_3 )),
% 1.82/1.02 inference(negated_conjecture,[status(cth)],[f45])).
% 1.82/1.02 fof(f47,plain,(
% 1.82/1.02 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 1.82/1.02 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 1.82/1.02 fof(f48,plain,(
% 1.82/1.02 (~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))))),
% 1.82/1.02 inference(NNF_transformation,[status(thm)],[f47])).
% 1.82/1.02 fof(f49,plain,(
% 1.82/1.02 (~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))))),
% 1.82/1.02 inference(miniscoping,[status(thm)],[f48])).
% 1.82/1.02 fof(f50,plain,(
% 1.82/1.02 (~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)))),
% 1.82/1.02 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f49])).
% 1.82/1.02 fof(f51,plain,(
% 1.82/1.02 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 1.82/1.02 inference(cnf_transformation,[status(thm)],[f50])).
% 1.82/1.02 fof(f73,plain,(
% 1.82/1.02 (~implies_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))&(implies_3|(?[X,Y,Z]: ~is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))),
% 1.82/1.02 inference(NNF_transformation,[status(thm)],[f6])).
% 1.82/1.02 fof(f74,plain,(
% 1.82/1.02 (~implies_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))&(implies_3|~is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl)))))),
% 1.82/1.02 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(X,sK10_skl),skolemize(Y,sK11_skl),skolemize(Z,sK12_skl)],[f73])).
% 1.82/1.02 fof(f76,plain,(
% 1.82/1.02 implies_3|~is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl))))),
% 1.82/1.02 inference(cnf_transformation,[status(thm)],[f74])).
% 1.82/1.02 fof(f149,plain,(
% 1.82/1.02 (~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))))))),
% 1.82/1.02 inference(NNF_transformation,[status(thm)],[f25])).
% 1.82/1.02 fof(f150,plain,(
% 1.82/1.02 (~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)))))),
% 1.82/1.02 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])).
% 1.82/1.03 fof(f151,plain,(
% 1.82/1.03 ![X0,X1,X2]: (~r4|is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 1.82/1.03 inference(cnf_transformation,[status(thm)],[f150])).
% 1.82/1.03 fof(f153,plain,(
% 1.82/1.03 (~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))))))),
% 1.82/1.03 inference(NNF_transformation,[status(thm)],[f26])).
% 1.82/1.03 fof(f154,plain,(
% 1.82/1.03 (~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)))))),
% 1.82/1.03 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])).
% 1.82/1.03 fof(f155,plain,(
% 1.82/1.03 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 1.82/1.03 inference(cnf_transformation,[status(thm)],[f154])).
% 1.82/1.03 fof(f163,plain,(
% 1.82/1.03 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 1.82/1.03 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 1.82/1.03 fof(f164,plain,(
% 1.82/1.03 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 1.82/1.03 inference(cnf_transformation,[status(thm)],[f163])).
% 1.82/1.03 fof(f167,plain,(
% 1.82/1.03 op_implies_or),
% 1.82/1.03 inference(cnf_transformation,[status(thm)],[f32])).
% 1.82/1.03 fof(f170,plain,(
% 1.82/1.03 modus_ponens),
% 1.82/1.03 inference(cnf_transformation,[status(thm)],[f35])).
% 1.82/1.03 fof(f174,plain,(
% 1.82/1.03 r4),
% 1.82/1.03 inference(cnf_transformation,[status(thm)],[f39])).
% 1.82/1.03 fof(f175,plain,(
% 1.82/1.03 r5),
% 1.82/1.03 inference(cnf_transformation,[status(thm)],[f40])).
% 1.82/1.03 fof(f180,plain,(
% 1.82/1.03 ~implies_3),
% 1.82/1.03 inference(cnf_transformation,[status(thm)],[f46])).
% 1.82/1.03 fof(f181,plain,(
% 1.82/1.03 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 1.82/1.03 inference(backward_subsumption_resolution,[status(thm)],[f164,f167])).
% 1.82/1.03 fof(f184,plain,(
% 1.82/1.03 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 1.82/1.03 inference(backward_subsumption_resolution,[status(thm)],[f51,f170])).
% 1.82/1.03 fof(f188,plain,(
% 1.82/1.03 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 1.82/1.03 inference(backward_subsumption_resolution,[status(thm)],[f151,f174])).
% 1.82/1.03 fof(f189,plain,(
% 1.82/1.03 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 1.82/1.03 inference(backward_subsumption_resolution,[status(thm)],[f155,f175])).
% 1.82/1.03 fof(f193,plain,(
% 1.82/1.03 ~is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl))))),
% 1.82/1.03 inference(backward_subsumption_resolution,[status(thm)],[f76,f180])).
% 1.82/1.03 fof(f350,plain,(
% 1.82/1.03 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))))),
% 1.82/1.03 inference(paramodulation,[status(thm)],[f181,f188])).
% 1.82/1.03 fof(f354,plain,(
% 1.82/1.03 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))))),
% 1.82/1.03 inference(forward_demodulation,[status(thm)],[f181,f350])).
% 1.82/1.03 fof(f361,plain,(
% 1.82/1.03 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))))),
% 1.82/1.03 inference(paramodulation,[status(thm)],[f181,f189])).
% 1.82/1.03 fof(f363,plain,(
% 1.82/1.03 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))))),
% 1.82/1.03 inference(forward_demodulation,[status(thm)],[f181,f361])).
% 1.82/1.03 fof(f366,plain,(
% 1.82/1.03 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))),X3))|is_a_theorem(X3))),
% 1.82/1.03 inference(resolution,[status(thm)],[f363,f184])).
% 1.82/1.03 fof(f1601,plain,(
% 1.82/1.03 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(X1,X2)),or(not(X1),implies(X0,X2)))))),
% 1.82/1.03 inference(paramodulation,[status(thm)],[f181,f354])).
% 1.82/1.03 fof(f1609,plain,(
% 1.82/1.03 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))))),
% 1.82/1.03 inference(forward_demodulation,[status(thm)],[f181,f1601])).
% 1.82/1.03 fof(f2785,plain,(
% 1.82/1.03 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 1.82/1.03 inference(resolution,[status(thm)],[f366,f1609])).
% 1.82/1.03 fof(f2822,plain,(
% 1.82/1.03 $false),
% 1.82/1.03 inference(backward_subsumption_resolution,[status(thm)],[f193,f2785])).
% 1.82/1.03 % SZS output end CNFRefutation for theBenchmark.p
% 3.96/1.05 % Elapsed time: 0.682601 seconds
% 3.96/1.05 % CPU time: 5.086888 seconds
% 3.96/1.05 % Total memory used: 177.614 MB
% 3.96/1.05 % Net memory used: 173.152 MB
%------------------------------------------------------------------------------