%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL513+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 01:10:12 PM UTC 2026
% Result : Theorem 36.37s 5.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL513+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 00:36:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.41 % Drodi V4.1.1
% 36.37/5.39 % Refutation found
% 36.37/5.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 36.37/5.39 % SZS output start CNFRefutation for theBenchmark
% 36.37/5.39 fof(f1,axiom,(
% 36.37/5.39 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f14,axiom,(
% 36.37/5.39 ( equivalence_2<=> (! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) )) ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f16,axiom,(
% 36.37/5.39 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f17,axiom,(
% 36.37/5.39 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f18,axiom,(
% 36.37/5.39 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f27,axiom,(
% 36.37/5.39 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f29,axiom,(
% 36.37/5.39 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f31,axiom,(
% 36.37/5.39 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f32,axiom,(
% 36.37/5.39 op_or ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f33,axiom,(
% 36.37/5.39 op_implies_and ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f34,axiom,(
% 36.37/5.39 op_equiv ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f35,axiom,(
% 36.37/5.39 modus_ponens ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f36,axiom,(
% 36.37/5.39 kn1 ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f37,axiom,(
% 36.37/5.39 kn2 ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f38,axiom,(
% 36.37/5.39 kn3 ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f43,conjecture,(
% 36.37/5.39 equivalence_2 ),
% 36.37/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 36.37/5.39 fof(f44,negated_conjecture,(
% 36.37/5.39 ~(equivalence_2 )),
% 36.37/5.39 inference(negated_conjecture,[status(cth)],[f43])).
% 36.37/5.39 fof(f45,plain,(
% 36.37/5.39 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 36.37/5.39 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 36.37/5.39 fof(f46,plain,(
% 36.37/5.39 (~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))))),
% 36.37/5.39 inference(NNF_transformation,[status(thm)],[f45])).
% 36.37/5.39 fof(f47,plain,(
% 36.37/5.39 (~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))))),
% 36.37/5.39 inference(miniscoping,[status(thm)],[f46])).
% 36.37/5.39 fof(f48,plain,(
% 36.37/5.39 (~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)))),
% 36.37/5.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f47])).
% 36.37/5.39 fof(f49,plain,(
% 36.37/5.39 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f48])).
% 36.37/5.39 fof(f103,plain,(
% 36.37/5.39 (~equivalence_2|(![X,Y]: is_a_theorem(implies(equiv(X,Y),implies(Y,X)))))&(equivalence_2|(?[X,Y]: ~is_a_theorem(implies(equiv(X,Y),implies(Y,X)))))),
% 36.37/5.39 inference(NNF_transformation,[status(thm)],[f14])).
% 36.37/5.39 fof(f104,plain,(
% 36.37/5.39 (~equivalence_2|(![X,Y]: is_a_theorem(implies(equiv(X,Y),implies(Y,X)))))&(equivalence_2|~is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl))))),
% 36.37/5.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK28_skl,sK29_skl]),skolemize(X,sK28_skl),skolemize(Y,sK29_skl)],[f103])).
% 36.37/5.39 fof(f106,plain,(
% 36.37/5.39 equivalence_2|~is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl)))),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f104])).
% 36.37/5.39 fof(f111,plain,(
% 36.37/5.39 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 36.37/5.39 inference(NNF_transformation,[status(thm)],[f16])).
% 36.37/5.39 fof(f112,plain,(
% 36.37/5.39 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))))),
% 36.37/5.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f111])).
% 36.37/5.39 fof(f113,plain,(
% 36.37/5.39 ![X0]: (~kn1|is_a_theorem(implies(X0,and(X0,X0))))),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f112])).
% 36.37/5.39 fof(f115,plain,(
% 36.37/5.39 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 36.37/5.39 inference(NNF_transformation,[status(thm)],[f17])).
% 36.37/5.39 fof(f116,plain,(
% 36.37/5.39 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl)))),
% 36.37/5.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl]),skolemize(P,sK33_skl),skolemize(Q,sK34_skl)],[f115])).
% 36.37/5.39 fof(f117,plain,(
% 36.37/5.39 ![X0,X1]: (~kn2|is_a_theorem(implies(and(X0,X1),X0)))),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f116])).
% 36.37/5.39 fof(f119,plain,(
% 36.37/5.39 (~kn3|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))))&(kn3|(?[P,Q,R]: ~is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))))),
% 36.37/5.39 inference(NNF_transformation,[status(thm)],[f18])).
% 36.37/5.39 fof(f120,plain,(
% 36.37/5.39 (~kn3|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))))&(kn3|~is_a_theorem(implies(implies(sK35_skl,sK36_skl),implies(not(and(sK36_skl,sK37_skl)),not(and(sK37_skl,sK35_skl))))))),
% 36.37/5.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl,sK36_skl,sK37_skl]),skolemize(P,sK35_skl),skolemize(Q,sK36_skl),skolemize(R,sK37_skl)],[f119])).
% 36.37/5.39 fof(f121,plain,(
% 36.37/5.39 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))))),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f120])).
% 36.37/5.39 fof(f155,plain,(
% 36.37/5.39 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 36.37/5.39 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 36.37/5.39 fof(f156,plain,(
% 36.37/5.39 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f155])).
% 36.37/5.39 fof(f159,plain,(
% 36.37/5.39 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 36.37/5.39 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 36.37/5.39 fof(f160,plain,(
% 36.37/5.39 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f159])).
% 36.37/5.39 fof(f163,plain,(
% 36.37/5.39 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 36.37/5.39 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 36.37/5.39 fof(f164,plain,(
% 36.37/5.39 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f163])).
% 36.37/5.39 fof(f165,plain,(
% 36.37/5.39 op_or),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f32])).
% 36.37/5.39 fof(f166,plain,(
% 36.37/5.39 op_implies_and),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f33])).
% 36.37/5.39 fof(f167,plain,(
% 36.37/5.39 op_equiv),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f34])).
% 36.37/5.39 fof(f168,plain,(
% 36.37/5.39 modus_ponens),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f35])).
% 36.37/5.39 fof(f169,plain,(
% 36.37/5.39 kn1),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f36])).
% 36.37/5.39 fof(f170,plain,(
% 36.37/5.39 kn2),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f37])).
% 36.37/5.39 fof(f171,plain,(
% 36.37/5.39 kn3),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f38])).
% 36.37/5.39 fof(f176,plain,(
% 36.37/5.39 ~equivalence_2),
% 36.37/5.39 inference(cnf_transformation,[status(thm)],[f44])).
% 36.37/5.39 fof(f177,plain,(
% 36.37/5.39 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 36.37/5.39 inference(forward_subsumption_resolution,[status(thm)],[f49,f168])).
% 36.37/5.39 fof(f179,plain,(
% 36.37/5.39 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 36.37/5.39 inference(forward_subsumption_resolution,[status(thm)],[f113,f169])).
% 36.37/5.39 fof(f182,plain,(
% 36.37/5.39 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 36.37/5.39 inference(forward_subsumption_resolution,[status(thm)],[f117,f170])).
% 36.37/5.39 fof(f186,plain,(
% 36.37/5.39 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 36.37/5.39 inference(forward_subsumption_resolution,[status(thm)],[f160,f166])).
% 36.37/5.39 fof(f187,plain,(
% 36.37/5.39 ![X0,X1,X2]: (implies(X0,and(X1,not(X2)))=not(and(X0,implies(X1,X2))))),
% 36.37/5.40 inference(paramodulation,[status(thm)],[f186,f186])).
% 36.37/5.40 fof(f188,plain,(
% 36.37/5.40 ![X0,X1]: (~op_or|or(X0,X1)=implies(not(X0),X1))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f186,f156])).
% 36.37/5.40 fof(f195,plain,(
% 36.37/5.40 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 36.37/5.40 inference(forward_subsumption_resolution,[status(thm)],[f188,f165])).
% 36.37/5.40 fof(f196,plain,(
% 36.37/5.40 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 36.37/5.40 inference(paramodulation,[status(thm)],[f186,f195])).
% 36.37/5.40 fof(f197,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(or(X0,and(not(X0),not(X0)))))),
% 36.37/5.40 inference(paramodulation,[status(thm)],[f195,f179])).
% 36.37/5.40 fof(f198,plain,(
% 36.37/5.40 ![X0,X1]: (~is_a_theorem(not(X0))|~is_a_theorem(or(X0,X1))|is_a_theorem(X1))),
% 36.37/5.40 inference(paramodulation,[status(thm)],[f195,f177])).
% 36.37/5.40 fof(f205,plain,(
% 36.37/5.40 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 36.37/5.40 inference(forward_subsumption_resolution,[status(thm)],[f164,f167])).
% 36.37/5.40 fof(f229,plain,(
% 36.37/5.40 ~is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl)))),
% 36.37/5.40 inference(forward_subsumption_resolution,[status(thm)],[f106,f176])).
% 36.37/5.40 fof(f254,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(not(and(not(X0),implies(not(X0),X0)))))),
% 36.37/5.40 inference(paramodulation,[status(thm)],[f187,f179])).
% 36.37/5.40 fof(f268,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(not(and(not(X0),or(X0,X0)))))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f195,f254])).
% 36.37/5.40 fof(f270,plain,(
% 36.37/5.40 ![X0,X1]: (~is_a_theorem(or(and(not(X0),or(X0,X0)),X1))|is_a_theorem(X1))),
% 36.37/5.40 inference(resolution,[status(thm)],[f268,f198])).
% 36.37/5.40 fof(f401,plain,(
% 36.37/5.40 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f195,f121])).
% 36.37/5.40 fof(f402,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))))),
% 36.37/5.40 inference(forward_subsumption_resolution,[status(thm)],[f401,f171])).
% 36.37/5.40 fof(f403,plain,(
% 36.37/5.40 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(and(X1,X2),not(and(X2,X0)))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f402,f177])).
% 36.37/5.40 fof(f405,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0)))))))),
% 36.37/5.40 inference(paramodulation,[status(thm)],[f195,f402])).
% 36.37/5.40 fof(f416,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f186,f405])).
% 36.37/5.40 fof(f421,plain,(
% 36.37/5.40 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(and(X1,X2),implies(X2,X0))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f416,f177])).
% 36.37/5.40 fof(f424,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0)))))),
% 36.37/5.40 inference(paramodulation,[status(thm)],[f196,f416])).
% 36.37/5.40 fof(f431,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f195,f424])).
% 36.37/5.40 fof(f437,plain,(
% 36.37/5.40 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(implies(implies(X1,X2),or(X2,X0))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f431,f177])).
% 36.37/5.40 fof(f447,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(implies(implies(and(not(X0),not(X0)),X1),or(X1,X0))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f437,f197])).
% 36.37/5.40 fof(f469,plain,(
% 36.37/5.40 ![X0,X1]: (~is_a_theorem(implies(and(not(X0),not(X0)),X1))|is_a_theorem(or(X1,X0)))),
% 36.37/5.40 inference(resolution,[status(thm)],[f447,f177])).
% 36.37/5.40 fof(f485,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(or(not(X0),X0)))),
% 36.37/5.40 inference(resolution,[status(thm)],[f469,f182])).
% 36.37/5.40 fof(f497,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f485,f437])).
% 36.37/5.40 fof(f498,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f485,f421])).
% 36.37/5.40 fof(f502,plain,(
% 36.37/5.40 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(X1,not(X0))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f497,f177])).
% 36.37/5.40 fof(f513,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(implies(or(X0,X0),not(not(X0)))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f498,f270])).
% 36.37/5.40 fof(f526,plain,(
% 36.37/5.40 ![X0]: (~is_a_theorem(or(X0,X0))|is_a_theorem(not(not(X0))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f513,f177])).
% 36.37/5.40 fof(f559,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(or(X0,not(and(X0,X1)))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f502,f182])).
% 36.37/5.40 fof(f565,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(implies(not(and(X0,X1)),X2),or(X2,X0))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f559,f437])).
% 36.37/5.40 fof(f570,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(or(X0,implies(X0,X1))))),
% 36.37/5.40 inference(paramodulation,[status(thm)],[f186,f559])).
% 36.37/5.40 fof(f574,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(or(and(X0,X1),X2),or(X2,X0))))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f195,f565])).
% 36.37/5.40 fof(f577,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(or(and(implies(X0,X1),X2),implies(X2,X0))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f570,f421])).
% 36.37/5.40 fof(f659,plain,(
% 36.37/5.40 ![X0,X1,X2]: (~is_a_theorem(or(and(X0,X1),X2))|is_a_theorem(or(X2,X0)))),
% 36.37/5.40 inference(resolution,[status(thm)],[f574,f177])).
% 36.37/5.40 fof(f698,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(or(implies(X0,X1),implies(X1,X2))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f659,f577])).
% 36.37/5.40 fof(f753,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(not(not(implies(X0,X0)))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f698,f526])).
% 36.37/5.40 fof(f761,plain,(
% 36.37/5.40 ![X0,X1]: (~is_a_theorem(or(not(implies(X0,X0)),X1))|is_a_theorem(X1))),
% 36.37/5.40 inference(resolution,[status(thm)],[f753,f198])).
% 36.37/5.40 fof(f802,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 36.37/5.40 inference(resolution,[status(thm)],[f761,f485])).
% 36.37/5.40 fof(f810,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(or(and(not(X0),not(X0)),X0)))),
% 36.37/5.40 inference(resolution,[status(thm)],[f802,f469])).
% 36.37/5.40 fof(f811,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(or(and(X0,X1),not(and(X1,X0)))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f802,f403])).
% 36.37/5.40 fof(f812,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(or(X0,not(X0))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f802,f502])).
% 36.37/5.40 fof(f817,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f196,f810])).
% 36.37/5.40 fof(f818,plain,(
% 36.37/5.40 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f195,f817])).
% 36.37/5.40 fof(f827,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),X1),or(X1,X0))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f812,f437])).
% 36.37/5.40 fof(f833,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f195,f827])).
% 36.37/5.40 fof(f846,plain,(
% 36.37/5.40 ![X0]: (~is_a_theorem(or(X0,X0))|is_a_theorem(X0))),
% 36.37/5.40 inference(resolution,[status(thm)],[f818,f177])).
% 36.37/5.40 fof(f1016,plain,(
% 36.37/5.40 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0)))),
% 36.37/5.40 inference(resolution,[status(thm)],[f833,f177])).
% 36.37/5.40 fof(f1249,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(or(not(and(X0,X1)),X1)))),
% 36.37/5.40 inference(resolution,[status(thm)],[f811,f659])).
% 36.37/5.40 fof(f1272,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(or(X0,not(and(X1,X0)))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f1249,f1016])).
% 36.37/5.40 fof(f1277,plain,(
% 36.37/5.40 ![X0,X1]: (is_a_theorem(or(implies(X0,X1),not(X1))))),
% 36.37/5.40 inference(paramodulation,[status(thm)],[f186,f1249])).
% 36.37/5.40 fof(f1285,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(implies(not(and(X0,X1)),X2),or(X2,X1))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f1272,f437])).
% 36.37/5.40 fof(f1295,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(or(and(X0,X1),X2),or(X2,X1))))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f195,f1285])).
% 36.37/5.40 fof(f1305,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(implies(not(X0),X1),or(X1,implies(X2,X0)))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f1277,f437])).
% 36.37/5.40 fof(f1312,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(X1,implies(X2,X0)))))),
% 36.37/5.40 inference(forward_demodulation,[status(thm)],[f195,f1305])).
% 36.37/5.40 fof(f3812,plain,(
% 36.37/5.40 ![X0,X1,X2]: (~is_a_theorem(or(and(X0,X1),X2))|is_a_theorem(or(X2,X1)))),
% 36.37/5.40 inference(resolution,[status(thm)],[f1295,f177])).
% 36.37/5.40 fof(f3824,plain,(
% 36.37/5.40 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,implies(X2,X0))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f1312,f177])).
% 36.37/5.40 fof(f8404,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(or(implies(and(X0,X1),X2),X1)))),
% 36.37/5.40 inference(resolution,[status(thm)],[f3812,f570])).
% 36.37/5.40 fof(f8436,plain,(
% 36.37/5.40 ![X0,X1,X2]: (is_a_theorem(or(X0,implies(and(X1,X0),X2))))),
% 36.37/5.40 inference(resolution,[status(thm)],[f8404,f1016])).
% 36.37/5.40 fof(f9856,plain,(
% 36.37/5.51 ![X0,X1,X2,X3]: (is_a_theorem(or(implies(and(X0,X1),X2),implies(X3,X1))))),
% 36.37/5.51 inference(resolution,[status(thm)],[f3824,f8436])).
% 36.37/5.51 fof(f28966,plain,(
% 36.37/5.51 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1)))),
% 36.37/5.51 inference(resolution,[status(thm)],[f9856,f846])).
% 36.37/5.51 fof(f29051,plain,(
% 36.37/5.51 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))))),
% 36.37/5.51 inference(paramodulation,[status(thm)],[f205,f28966])).
% 36.37/5.51 fof(f29207,plain,(
% 36.37/5.51 $false),
% 36.37/5.51 inference(backward_subsumption_resolution,[status(thm)],[f229,f29051])).
% 36.37/5.51 % SZS output end CNFRefutation for theBenchmark.p
% 7.95/5.56 % Elapsed time: 5.151574 seconds
% 7.95/5.56 % CPU time: 39.894451 seconds
% 7.95/5.56 % Total memory used: 568.390 MB
% 7.95/5.56 % Net memory used: 548.942 MB
%------------------------------------------------------------------------------