%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL498+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 : n011.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 23.08s 3.32s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL498+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
% 0.08/0.35 % Computer : n011.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 00:36:11 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 23.08/3.32 % Refutation found
% 23.08/3.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 23.08/3.32 % SZS output start CNFRefutation for theBenchmark
% 23.08/3.32 fof(f1,axiom,(
% 23.08/3.32 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f21,axiom,(
% 23.08/3.32 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f22,axiom,(
% 23.08/3.32 ( r1<=> (! [P] : is_a_theorem(implies(or(P,P),P)) )) ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f23,axiom,(
% 23.08/3.32 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f24,axiom,(
% 23.08/3.32 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f25,axiom,(
% 23.08/3.32 ( r4<=> (! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )) ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f26,axiom,(
% 23.08/3.32 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f27,axiom,(
% 23.08/3.32 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f28,axiom,(
% 23.08/3.32 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f30,axiom,(
% 23.08/3.32 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f32,axiom,(
% 23.08/3.32 op_implies_or ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f33,axiom,(
% 23.08/3.32 op_and ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f35,axiom,(
% 23.08/3.32 modus_ponens ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f36,axiom,(
% 23.08/3.32 r1 ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f37,axiom,(
% 23.08/3.32 r2 ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f38,axiom,(
% 23.08/3.32 r3 ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f39,axiom,(
% 23.08/3.32 r4 ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f40,axiom,(
% 23.08/3.32 r5 ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f42,axiom,(
% 23.08/3.32 op_or ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f45,conjecture,(
% 23.08/3.32 cn3 ),
% 23.08/3.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.08/3.32 fof(f46,negated_conjecture,(
% 23.08/3.32 ~(cn3 )),
% 23.08/3.32 inference(negated_conjecture,[status(cth)],[f45])).
% 23.08/3.32 fof(f47,plain,(
% 23.08/3.32 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 23.08/3.32 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 23.08/3.32 fof(f48,plain,(
% 23.08/3.32 (~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))))),
% 23.08/3.32 inference(NNF_transformation,[status(thm)],[f47])).
% 23.08/3.32 fof(f49,plain,(
% 23.08/3.32 (~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))))),
% 23.08/3.32 inference(miniscoping,[status(thm)],[f48])).
% 23.08/3.32 fof(f50,plain,(
% 23.08/3.32 (~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)))),
% 23.08/3.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f49])).
% 23.08/3.32 fof(f51,plain,(
% 23.08/3.32 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f50])).
% 23.08/3.32 fof(f133,plain,(
% 23.08/3.32 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 23.08/3.32 inference(NNF_transformation,[status(thm)],[f21])).
% 23.08/3.32 fof(f134,plain,(
% 23.08/3.32 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 23.08/3.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f133])).
% 23.08/3.32 fof(f136,plain,(
% 23.08/3.32 cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f134])).
% 23.08/3.32 fof(f137,plain,(
% 23.08/3.32 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|(?[P]: ~is_a_theorem(implies(or(P,P),P))))),
% 23.08/3.32 inference(NNF_transformation,[status(thm)],[f22])).
% 23.08/3.32 fof(f138,plain,(
% 23.08/3.32 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)))),
% 23.08/3.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(P,sK44_skl)],[f137])).
% 23.08/3.32 fof(f139,plain,(
% 23.08/3.32 ![X0]: (~r1|is_a_theorem(implies(or(X0,X0),X0)))),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f138])).
% 23.08/3.32 fof(f141,plain,(
% 23.08/3.32 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 23.08/3.32 inference(NNF_transformation,[status(thm)],[f23])).
% 23.08/3.32 fof(f142,plain,(
% 23.08/3.32 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))))),
% 23.08/3.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(P,sK45_skl),skolemize(Q,sK46_skl)],[f141])).
% 23.08/3.32 fof(f143,plain,(
% 23.08/3.32 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f142])).
% 23.08/3.32 fof(f145,plain,(
% 23.08/3.32 (~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)))))),
% 23.08/3.32 inference(NNF_transformation,[status(thm)],[f24])).
% 23.08/3.32 fof(f146,plain,(
% 23.08/3.32 (~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))))),
% 23.08/3.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f145])).
% 23.08/3.32 fof(f147,plain,(
% 23.08/3.32 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f146])).
% 23.08/3.32 fof(f149,plain,(
% 23.08/3.32 (~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))))))),
% 23.08/3.32 inference(NNF_transformation,[status(thm)],[f25])).
% 23.08/3.32 fof(f150,plain,(
% 23.08/3.32 (~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)))))),
% 23.08/3.32 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])).
% 23.08/3.32 fof(f151,plain,(
% 23.08/3.32 ![X0,X1,X2]: (~r4|is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f150])).
% 23.08/3.32 fof(f153,plain,(
% 23.08/3.32 (~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))))))),
% 23.08/3.32 inference(NNF_transformation,[status(thm)],[f26])).
% 23.08/3.32 fof(f154,plain,(
% 23.08/3.32 (~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)))))),
% 23.08/3.32 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])).
% 23.08/3.32 fof(f155,plain,(
% 23.08/3.32 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f154])).
% 23.08/3.32 fof(f157,plain,(
% 23.08/3.32 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 23.08/3.32 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 23.08/3.32 fof(f158,plain,(
% 23.08/3.32 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f157])).
% 23.08/3.32 fof(f159,plain,(
% 23.08/3.32 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 23.08/3.32 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 23.08/3.32 fof(f160,plain,(
% 23.08/3.32 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f159])).
% 23.08/3.32 fof(f163,plain,(
% 23.08/3.32 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 23.08/3.32 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 23.08/3.32 fof(f164,plain,(
% 23.08/3.32 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f163])).
% 23.08/3.32 fof(f167,plain,(
% 23.08/3.32 op_implies_or),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f32])).
% 23.08/3.32 fof(f168,plain,(
% 23.08/3.32 op_and),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f33])).
% 23.08/3.32 fof(f170,plain,(
% 23.08/3.32 modus_ponens),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f35])).
% 23.08/3.32 fof(f171,plain,(
% 23.08/3.32 r1),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f36])).
% 23.08/3.32 fof(f172,plain,(
% 23.08/3.32 r2),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f37])).
% 23.08/3.32 fof(f173,plain,(
% 23.08/3.32 r3),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f38])).
% 23.08/3.32 fof(f174,plain,(
% 23.08/3.32 r4),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f39])).
% 23.08/3.32 fof(f175,plain,(
% 23.08/3.32 r5),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f40])).
% 23.08/3.32 fof(f177,plain,(
% 23.08/3.32 op_or),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f42])).
% 23.08/3.32 fof(f180,plain,(
% 23.08/3.32 ~cn3),
% 23.08/3.32 inference(cnf_transformation,[status(thm)],[f46])).
% 23.08/3.32 fof(f181,plain,(
% 23.08/3.32 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 23.08/3.32 inference(backward_subsumption_resolution,[status(thm)],[f164,f167])).
% 23.08/3.32 fof(f182,plain,(
% 23.08/3.32 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1))))),
% 23.08/3.32 inference(backward_subsumption_resolution,[status(thm)],[f160,f168])).
% 23.08/3.32 fof(f184,plain,(
% 23.08/3.32 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 23.08/3.32 inference(backward_subsumption_resolution,[status(thm)],[f51,f170])).
% 23.08/3.32 fof(f185,plain,(
% 23.08/3.32 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 23.08/3.32 inference(backward_subsumption_resolution,[status(thm)],[f139,f171])).
% 23.08/3.32 fof(f186,plain,(
% 23.08/3.32 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 23.08/3.32 inference(backward_subsumption_resolution,[status(thm)],[f143,f172])).
% 23.08/3.32 fof(f187,plain,(
% 23.08/3.32 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 23.08/3.32 inference(backward_subsumption_resolution,[status(thm)],[f147,f173])).
% 23.08/3.32 fof(f188,plain,(
% 23.08/3.32 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 23.08/3.32 inference(backward_subsumption_resolution,[status(thm)],[f151,f174])).
% 23.08/3.32 fof(f189,plain,(
% 23.08/3.32 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 23.08/3.32 inference(backward_subsumption_resolution,[status(thm)],[f155,f175])).
% 23.08/3.32 fof(f191,plain,(
% 23.08/3.32 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 23.08/3.32 inference(backward_subsumption_resolution,[status(thm)],[f158,f177])).
% 23.08/3.32 fof(f192,plain,(
% 23.08/3.32 ~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 23.08/3.32 inference(backward_subsumption_resolution,[status(thm)],[f136,f180])).
% 23.08/3.32 fof(f193,plain,(
% 23.08/3.32 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1))))),
% 23.08/3.32 inference(forward_demodulation,[status(thm)],[f181,f182])).
% 23.08/3.32 fof(f199,plain,(
% 23.08/3.32 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(and(X0,X1),X2))),
% 23.08/3.32 inference(paramodulation,[status(thm)],[f193,f181])).
% 23.08/3.32 fof(f204,plain,(
% 23.08/3.32 ![X0]: (~is_a_theorem(or(X0,X0))|is_a_theorem(X0))),
% 23.08/3.32 inference(resolution,[status(thm)],[f184,f185])).
% 23.08/3.32 fof(f206,plain,(
% 23.08/3.32 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(or(X1,X0)))),
% 23.08/3.32 inference(resolution,[status(thm)],[f184,f186])).
% 23.08/3.32 fof(f215,plain,(
% 23.08/3.32 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0)))),
% 23.08/3.32 inference(resolution,[status(thm)],[f187,f184])).
% 23.08/3.32 fof(f221,plain,(
% 23.08/3.32 ![X0,X1]: (~is_a_theorem(or(X0,not(X1)))|is_a_theorem(implies(X1,X0)))),
% 23.08/3.32 inference(paramodulation,[status(thm)],[f181,f215])).
% 23.08/3.32 fof(f245,plain,(
% 23.08/3.32 ![X0,X1,X2]: (implies(and(not(X0),not(X1)),X2)=or(or(X0,X1),X2))),
% 23.08/3.32 inference(paramodulation,[status(thm)],[f191,f181])).
% 23.08/3.32 fof(f269,plain,(
% 23.08/3.32 ![X0,X1]: (is_a_theorem(implies(X0,X1))|~is_a_theorem(not(X0)))),
% 23.08/3.32 inference(resolution,[status(thm)],[f221,f206])).
% 23.08/3.32 fof(f270,plain,(
% 23.08/3.32 ![X0,X1]: (~is_a_theorem(implies(X0,not(X1)))|is_a_theorem(implies(X1,not(X0))))),
% 23.08/3.32 inference(paramodulation,[status(thm)],[f181,f221])).
% 23.08/3.32 fof(f379,plain,(
% 23.08/3.32 ![X0,X1,X2]: (~is_a_theorem(implies(X0,not(X1)))|~is_a_theorem(or(and(X0,X1),X2))|is_a_theorem(X2))),
% 23.08/3.32 inference(paramodulation,[status(thm)],[f199,f184])).
% 23.08/3.32 fof(f397,plain,(
% 23.08/3.32 ![X0,X1,X2]: (~is_a_theorem(or(X0,or(X1,X2)))|is_a_theorem(or(X1,or(X0,X2))))),
% 23.08/3.32 inference(resolution,[status(thm)],[f188,f184])).
% 23.08/3.32 fof(f398,plain,(
% 23.08/3.32 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))))),
% 23.08/3.34 inference(paramodulation,[status(thm)],[f181,f188])).
% 23.08/3.34 fof(f402,plain,(
% 23.08/3.34 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))))),
% 23.08/3.34 inference(forward_demodulation,[status(thm)],[f181,f398])).
% 23.08/3.34 fof(f406,plain,(
% 23.08/3.34 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X2,X0),or(X2,X1))))),
% 23.08/3.34 inference(resolution,[status(thm)],[f189,f184])).
% 23.08/3.34 fof(f883,plain,(
% 23.08/3.34 ![X0,X1]: (~is_a_theorem(or(X0,or(or(X0,X1),X1)))|is_a_theorem(or(X0,X1)))),
% 23.08/3.34 inference(resolution,[status(thm)],[f397,f204])).
% 23.08/3.34 fof(f1279,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(X0,X1))|~is_a_theorem(or(or(X0,X1),X1)))),
% 23.08/3.34 inference(resolution,[status(thm)],[f883,f206])).
% 23.08/3.34 fof(f1322,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(X0,X1))|~is_a_theorem(or(X1,or(X0,X1))))),
% 23.08/3.34 inference(resolution,[status(thm)],[f1279,f215])).
% 23.08/3.34 fof(f1545,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(X0,X1))|~is_a_theorem(or(X0,or(X1,X1))))),
% 23.08/3.34 inference(resolution,[status(thm)],[f1322,f397])).
% 23.08/3.34 fof(f1551,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(not(X0),X1))|~is_a_theorem(or(X1,implies(X0,X1))))),
% 23.08/3.34 inference(paramodulation,[status(thm)],[f181,f1322])).
% 23.08/3.34 fof(f1553,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(implies(X0,X1))|~is_a_theorem(or(X1,implies(X0,X1))))),
% 23.08/3.34 inference(forward_demodulation,[status(thm)],[f181,f1551])).
% 23.08/3.34 fof(f1582,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(not(X0),X1))|~is_a_theorem(implies(X0,or(X1,X1))))),
% 23.08/3.34 inference(paramodulation,[status(thm)],[f181,f1545])).
% 23.08/3.34 fof(f1586,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X0,or(X1,X1))))),
% 23.08/3.34 inference(forward_demodulation,[status(thm)],[f181,f1582])).
% 23.08/3.34 fof(f1809,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),X0))|~is_a_theorem(implies(X1,X0)))),
% 23.08/3.34 inference(resolution,[status(thm)],[f1586,f406])).
% 23.08/3.34 fof(f1812,plain,(
% 23.08/3.34 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 23.08/3.34 inference(resolution,[status(thm)],[f1586,f186])).
% 23.08/3.34 fof(f1832,plain,(
% 23.08/3.34 ![X0,X1]: (~is_a_theorem(or(and(not(X0),X0),X1))|is_a_theorem(X1))),
% 23.08/3.34 inference(resolution,[status(thm)],[f1812,f379])).
% 23.08/3.34 fof(f1833,plain,(
% 23.08/3.34 ![X0]: (is_a_theorem(implies(X0,not(not(X0)))))),
% 23.08/3.34 inference(resolution,[status(thm)],[f1812,f270])).
% 23.08/3.34 fof(f1857,plain,(
% 23.08/3.34 ![X0,X1]: (~is_a_theorem(or(and(X0,not(X0)),X1))|is_a_theorem(X1))),
% 23.08/3.34 inference(resolution,[status(thm)],[f1833,f379])).
% 23.08/3.34 fof(f1862,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(and(X0,X1),not(not(implies(X0,not(X1)))))))),
% 23.08/3.34 inference(paramodulation,[status(thm)],[f199,f1833])).
% 23.08/3.34 fof(f1873,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(and(X0,X1),not(and(X0,X1)))))),
% 23.08/3.34 inference(forward_demodulation,[status(thm)],[f193,f1862])).
% 23.08/3.34 fof(f2654,plain,(
% 23.08/3.34 ![X0]: (is_a_theorem(not(and(not(X0),X0))))),
% 23.08/3.34 inference(resolution,[status(thm)],[f1873,f1832])).
% 23.08/3.34 fof(f2655,plain,(
% 23.08/3.34 ![X0]: (is_a_theorem(not(and(X0,not(X0)))))),
% 23.08/3.34 inference(resolution,[status(thm)],[f1873,f1857])).
% 23.08/3.34 fof(f2694,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(implies(and(not(X0),X0),X1)))),
% 23.08/3.34 inference(resolution,[status(thm)],[f2654,f269])).
% 23.08/3.34 fof(f2720,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(implies(and(X0,not(X0)),X1)))),
% 23.08/3.34 inference(resolution,[status(thm)],[f2655,f269])).
% 23.08/3.34 fof(f2757,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(or(not(X0),X0),X1)))),
% 23.08/3.34 inference(paramodulation,[status(thm)],[f245,f2694])).
% 23.08/3.34 fof(f2768,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(implies(X0,X0),X1)))),
% 23.08/3.34 inference(forward_demodulation,[status(thm)],[f181,f2757])).
% 23.08/3.34 fof(f2777,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(X0,implies(X1,X1))))),
% 23.08/3.34 inference(resolution,[status(thm)],[f2768,f1322])).
% 23.08/3.34 fof(f2815,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(or(X0,not(X0)),X1)))),
% 23.08/3.34 inference(paramodulation,[status(thm)],[f245,f2720])).
% 23.08/3.34 fof(f2828,plain,(
% 23.08/3.34 ![X0,X1]: (is_a_theorem(or(X0,or(X1,not(X1)))))),
% 23.08/3.34 inference(resolution,[status(thm)],[f2815,f1322])).
% 23.08/3.34 fof(f3474,plain,(
% 23.08/3.34 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(or(X1,X0))|is_a_theorem(X1))),
% 23.08/3.34 inference(resolution,[status(thm)],[f1809,f184])).
% 23.08/3.34 fof(f3532,plain,(
% 23.08/3.34 ![X0,X1]: (~is_a_theorem(implies(implies(X0,X0),X1))|is_a_theorem(X1))),
% 23.08/3.34 inference(resolution,[status(thm)],[f3474,f2777])).
% 23.08/3.34 fof(f3535,plain,(
% 23.08/3.34 ![X0,X1]: (~is_a_theorem(implies(or(X0,not(X0)),X1))|is_a_theorem(X1))),
% 23.08/3.38 inference(resolution,[status(thm)],[f3474,f2828])).
% 23.08/3.38 fof(f3570,plain,(
% 23.08/3.38 ![X0,X1]: (is_a_theorem(or(X0,implies(or(X0,X1),X1))))),
% 23.08/3.38 inference(resolution,[status(thm)],[f3532,f402])).
% 23.08/3.38 fof(f3921,plain,(
% 23.08/3.38 ![X0,X1]: (is_a_theorem(implies(X0,implies(or(not(X0),X1),X1))))),
% 23.08/3.38 inference(paramodulation,[status(thm)],[f181,f3570])).
% 23.08/3.38 fof(f3930,plain,(
% 23.08/3.38 ![X0,X1]: (is_a_theorem(implies(X0,implies(implies(X0,X1),X1))))),
% 23.08/3.38 inference(forward_demodulation,[status(thm)],[f181,f3921])).
% 23.08/3.38 fof(f4671,plain,(
% 23.08/3.38 ![X0,X1]: (is_a_theorem(or(X0,X1))|~is_a_theorem(implies(not(X0),X1)))),
% 23.08/3.38 inference(resolution,[status(thm)],[f3535,f406])).
% 23.08/3.38 fof(f5646,plain,(
% 23.08/3.38 ![X0,X1]: (is_a_theorem(or(X0,implies(implies(not(X0),X1),X1))))),
% 23.08/3.38 inference(resolution,[status(thm)],[f4671,f3930])).
% 23.08/3.38 fof(f8229,plain,(
% 23.08/3.38 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 23.08/3.38 inference(resolution,[status(thm)],[f5646,f1553])).
% 23.08/3.38 fof(f8253,plain,(
% 23.08/3.38 $false),
% 23.08/3.38 inference(backward_subsumption_resolution,[status(thm)],[f192,f8229])).
% 23.08/3.38 % SZS output end CNFRefutation for theBenchmark.p
% 23.08/3.42 % Elapsed time: 3.051780 seconds
% 23.08/3.42 % CPU time: 23.874169 seconds
% 23.08/3.42 % Total memory used: 526.570 MB
% 23.08/3.42 % Net memory used: 505.113 MB
%------------------------------------------------------------------------------