%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL516+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 4.69s 1.22s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL516+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:32:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 4.69/1.22 % Refutation found
% 4.69/1.22 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.69/1.22 % SZS output start CNFRefutation for theBenchmark
% 4.69/1.22 fof(f1,axiom,(
% 4.69/1.22 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f16,axiom,(
% 4.69/1.22 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f17,axiom,(
% 4.69/1.22 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f18,axiom,(
% 4.69/1.22 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f20,axiom,(
% 4.69/1.22 ( cn2<=> (! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) )) ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f27,axiom,(
% 4.69/1.22 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f29,axiom,(
% 4.69/1.22 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f31,axiom,(
% 4.69/1.22 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f32,axiom,(
% 4.69/1.22 op_or ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f33,axiom,(
% 4.69/1.22 op_implies_and ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f34,axiom,(
% 4.69/1.22 op_equiv ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f35,axiom,(
% 4.69/1.22 modus_ponens ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f36,axiom,(
% 4.69/1.22 kn1 ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f37,axiom,(
% 4.69/1.22 kn2 ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f38,axiom,(
% 4.69/1.22 kn3 ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f43,conjecture,(
% 4.69/1.22 cn2 ),
% 4.69/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.22 fof(f44,negated_conjecture,(
% 4.69/1.22 ~(cn2 )),
% 4.69/1.22 inference(negated_conjecture,[status(cth)],[f43])).
% 4.69/1.22 fof(f45,plain,(
% 4.69/1.22 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 4.69/1.22 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 4.69/1.22 fof(f46,plain,(
% 4.69/1.22 (~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))))),
% 4.69/1.22 inference(NNF_transformation,[status(thm)],[f45])).
% 4.69/1.22 fof(f47,plain,(
% 4.69/1.22 (~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))))),
% 4.69/1.22 inference(miniscoping,[status(thm)],[f46])).
% 4.69/1.22 fof(f48,plain,(
% 4.69/1.22 (~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)))),
% 4.69/1.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f47])).
% 4.69/1.22 fof(f49,plain,(
% 4.69/1.22 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 4.69/1.22 inference(cnf_transformation,[status(thm)],[f48])).
% 4.69/1.22 fof(f111,plain,(
% 4.69/1.22 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 4.69/1.22 inference(NNF_transformation,[status(thm)],[f16])).
% 4.69/1.22 fof(f112,plain,(
% 4.69/1.22 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))))),
% 4.69/1.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f111])).
% 4.69/1.22 fof(f113,plain,(
% 4.69/1.22 ![X0]: (~kn1|is_a_theorem(implies(X0,and(X0,X0))))),
% 4.69/1.22 inference(cnf_transformation,[status(thm)],[f112])).
% 4.69/1.22 fof(f115,plain,(
% 4.69/1.22 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 4.69/1.22 inference(NNF_transformation,[status(thm)],[f17])).
% 4.69/1.22 fof(f116,plain,(
% 4.69/1.23 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl)))),
% 4.69/1.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl]),skolemize(P,sK33_skl),skolemize(Q,sK34_skl)],[f115])).
% 4.69/1.23 fof(f117,plain,(
% 4.69/1.23 ![X0,X1]: (~kn2|is_a_theorem(implies(and(X0,X1),X0)))),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f116])).
% 4.69/1.23 fof(f119,plain,(
% 4.69/1.23 (~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)))))))),
% 4.69/1.23 inference(NNF_transformation,[status(thm)],[f18])).
% 4.69/1.23 fof(f120,plain,(
% 4.69/1.23 (~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))))))),
% 4.69/1.23 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])).
% 4.69/1.23 fof(f121,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))))),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f120])).
% 4.69/1.23 fof(f127,plain,(
% 4.69/1.23 (~cn2|(![P,Q]: is_a_theorem(implies(P,implies(not(P),Q)))))&(cn2|(?[P,Q]: ~is_a_theorem(implies(P,implies(not(P),Q)))))),
% 4.69/1.23 inference(NNF_transformation,[status(thm)],[f20])).
% 4.69/1.23 fof(f128,plain,(
% 4.69/1.23 (~cn2|(![P,Q]: is_a_theorem(implies(P,implies(not(P),Q)))))&(cn2|~is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl))))),
% 4.69/1.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK41_skl,sK42_skl]),skolemize(P,sK41_skl),skolemize(Q,sK42_skl)],[f127])).
% 4.69/1.23 fof(f130,plain,(
% 4.69/1.23 cn2|~is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl)))),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f128])).
% 4.69/1.23 fof(f155,plain,(
% 4.69/1.23 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 4.69/1.23 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 4.69/1.23 fof(f156,plain,(
% 4.69/1.23 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f155])).
% 4.69/1.23 fof(f159,plain,(
% 4.69/1.23 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 4.69/1.23 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 4.69/1.23 fof(f160,plain,(
% 4.69/1.23 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f159])).
% 4.69/1.23 fof(f163,plain,(
% 4.69/1.23 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 4.69/1.23 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 4.69/1.23 fof(f164,plain,(
% 4.69/1.23 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f163])).
% 4.69/1.23 fof(f165,plain,(
% 4.69/1.23 op_or),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f32])).
% 4.69/1.23 fof(f166,plain,(
% 4.69/1.23 op_implies_and),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f33])).
% 4.69/1.23 fof(f167,plain,(
% 4.69/1.23 op_equiv),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f34])).
% 4.69/1.23 fof(f168,plain,(
% 4.69/1.23 modus_ponens),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f35])).
% 4.69/1.23 fof(f169,plain,(
% 4.69/1.23 kn1),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f36])).
% 4.69/1.23 fof(f170,plain,(
% 4.69/1.23 kn2),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f37])).
% 4.69/1.23 fof(f171,plain,(
% 4.69/1.23 kn3),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f38])).
% 4.69/1.23 fof(f176,plain,(
% 4.69/1.23 ~cn2),
% 4.69/1.23 inference(cnf_transformation,[status(thm)],[f44])).
% 4.69/1.23 fof(f177,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 4.69/1.23 inference(forward_subsumption_resolution,[status(thm)],[f49,f168])).
% 4.69/1.23 fof(f178,plain,(
% 4.69/1.23 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 4.69/1.23 inference(forward_subsumption_resolution,[status(thm)],[f117,f170])).
% 4.69/1.23 fof(f180,plain,(
% 4.69/1.23 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 4.69/1.23 inference(forward_subsumption_resolution,[status(thm)],[f160,f166])).
% 4.69/1.23 fof(f181,plain,(
% 4.69/1.23 ![X0,X1,X2]: (implies(X0,and(X1,not(X2)))=not(and(X0,implies(X1,X2))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f180,f180])).
% 4.69/1.23 fof(f182,plain,(
% 4.69/1.23 ~is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl)))),
% 4.69/1.23 inference(forward_subsumption_resolution,[status(thm)],[f130,f176])).
% 4.69/1.23 fof(f183,plain,(
% 4.69/1.23 ![X0,X1]: (~op_or|or(X0,X1)=implies(not(X0),X1))),
% 4.69/1.23 inference(forward_demodulation,[status(thm)],[f180,f156])).
% 4.69/1.23 fof(f184,plain,(
% 4.69/1.23 ~is_a_theorem(implies(sK41_skl,or(sK41_skl,sK42_skl)))),
% 4.69/1.23 inference(backward_demodulation,[status(thm)],[f185,f182])).
% 4.69/1.23 fof(f185,plain,(
% 4.69/1.23 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 4.69/1.23 inference(forward_subsumption_resolution,[status(thm)],[f183,f165])).
% 4.69/1.23 fof(f186,plain,(
% 4.69/1.23 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f180,f185])).
% 4.69/1.23 fof(f187,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(not(X0))|~is_a_theorem(or(X0,X1))|is_a_theorem(X1))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f185,f177])).
% 4.69/1.23 fof(f189,plain,(
% 4.69/1.23 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 4.69/1.23 inference(forward_subsumption_resolution,[status(thm)],[f113,f169])).
% 4.69/1.23 fof(f191,plain,(
% 4.69/1.23 ![X0]: (is_a_theorem(or(X0,and(not(X0),not(X0)))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f185,f189])).
% 4.69/1.23 fof(f203,plain,(
% 4.69/1.23 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 4.69/1.23 inference(forward_subsumption_resolution,[status(thm)],[f164,f167])).
% 4.69/1.23 fof(f207,plain,(
% 4.69/1.23 ![X0]: (is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f203,f189])).
% 4.69/1.23 fof(f209,plain,(
% 4.69/1.23 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f203,f178])).
% 4.69/1.23 fof(f212,plain,(
% 4.69/1.23 ![X0]: (is_a_theorem(implies(or(X0,not(X0)),equiv(not(X0),not(X0)))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f185,f207])).
% 4.69/1.23 fof(f214,plain,(
% 4.69/1.23 ![X0,X1]: (is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f185,f209])).
% 4.69/1.23 fof(f215,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(equiv(not(X0),X1))|is_a_theorem(or(X0,X1)))),
% 4.69/1.23 inference(resolution,[status(thm)],[f214,f177])).
% 4.69/1.23 fof(f229,plain,(
% 4.69/1.23 ![X0]: (is_a_theorem(not(and(not(X0),implies(not(X0),X0)))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f181,f189])).
% 4.69/1.23 fof(f237,plain,(
% 4.69/1.23 ![X0]: (is_a_theorem(not(and(not(X0),or(X0,X0)))))),
% 4.69/1.23 inference(forward_demodulation,[status(thm)],[f185,f229])).
% 4.69/1.23 fof(f239,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(or(and(not(X0),or(X0,X0)),X1))|is_a_theorem(X1))),
% 4.69/1.23 inference(resolution,[status(thm)],[f237,f187])).
% 4.69/1.23 fof(f311,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))))),
% 4.69/1.23 inference(forward_demodulation,[status(thm)],[f185,f121])).
% 4.69/1.23 fof(f312,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))))),
% 4.69/1.23 inference(forward_subsumption_resolution,[status(thm)],[f311,f171])).
% 4.69/1.23 fof(f313,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(and(X1,X2),not(and(X2,X0)))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f312,f177])).
% 4.69/1.23 fof(f314,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0)))))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f185,f312])).
% 4.69/1.23 fof(f316,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),not(and(not(X2),X0))))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f186,f312])).
% 4.69/1.23 fof(f324,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))))),
% 4.69/1.23 inference(forward_demodulation,[status(thm)],[f180,f314])).
% 4.69/1.23 fof(f327,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(and(X1,X2),implies(X2,X0))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f324,f177])).
% 4.69/1.23 fof(f329,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0)))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f186,f324])).
% 4.69/1.23 fof(f336,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))))),
% 4.69/1.23 inference(forward_demodulation,[status(thm)],[f185,f329])).
% 4.69/1.23 fof(f342,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(implies(implies(X1,X2),or(X2,X0))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f336,f177])).
% 4.69/1.23 fof(f351,plain,(
% 4.69/1.23 ![X0,X1]: (is_a_theorem(implies(implies(and(not(X0),not(X0)),X1),or(X1,X0))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f342,f191])).
% 4.69/1.23 fof(f368,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(implies(and(not(X0),not(X0)),X1))|is_a_theorem(or(X1,X0)))),
% 4.69/1.23 inference(resolution,[status(thm)],[f351,f177])).
% 4.69/1.23 fof(f379,plain,(
% 4.69/1.23 ![X0]: (is_a_theorem(or(not(X0),X0)))),
% 4.69/1.23 inference(resolution,[status(thm)],[f368,f178])).
% 4.69/1.23 fof(f387,plain,(
% 4.69/1.23 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f379,f342])).
% 4.69/1.23 fof(f391,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(X1,not(X0))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f387,f177])).
% 4.69/1.23 fof(f433,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(not(X0),X2),or(X2,X1))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f391,f342])).
% 4.69/1.23 fof(f436,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~is_a_theorem(implies(and(X0,not(X1)),X2))|is_a_theorem(or(X2,implies(X0,X1))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f180,f391])).
% 4.69/1.23 fof(f437,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X2),or(X2,X1))))),
% 4.69/1.23 inference(forward_demodulation,[status(thm)],[f185,f433])).
% 4.69/1.23 fof(f471,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(or(X0,X2))|is_a_theorem(or(X2,X1)))),
% 4.69/1.23 inference(resolution,[status(thm)],[f437,f177])).
% 4.69/1.23 fof(f518,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(implies(X0,not(X1)))|is_a_theorem(not(and(or(X1,X1),X0))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f313,f239])).
% 4.69/1.23 fof(f570,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(implies(not(X0),not(X1)))|is_a_theorem(implies(or(X1,X1),X0)))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f180,f518])).
% 4.69/1.23 fof(f573,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(or(X0,not(X1)))|is_a_theorem(implies(or(X1,X1),X0)))),
% 4.69/1.23 inference(forward_demodulation,[status(thm)],[f185,f570])).
% 4.69/1.23 fof(f579,plain,(
% 4.69/1.23 ![X0,X1]: (is_a_theorem(implies(or(X0,X0),X1))|~is_a_theorem(implies(X0,X1)))),
% 4.69/1.23 inference(resolution,[status(thm)],[f573,f391])).
% 4.69/1.23 fof(f594,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(or(X0,X0))|is_a_theorem(X1))),
% 4.69/1.23 inference(resolution,[status(thm)],[f579,f177])).
% 4.69/1.23 fof(f906,plain,(
% 4.69/1.23 ![X0,X1]: (is_a_theorem(or(X0,implies(X0,X1))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f436,f178])).
% 4.69/1.23 fof(f1017,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(X0,X1),X2),or(X2,X0))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f906,f342])).
% 4.69/1.23 fof(f1018,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(or(and(implies(X0,X1),X2),implies(X2,X0))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f906,f327])).
% 4.69/1.23 fof(f1109,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~is_a_theorem(implies(implies(X0,X1),X2))|is_a_theorem(or(X2,X0)))),
% 4.69/1.23 inference(resolution,[status(thm)],[f1017,f177])).
% 4.69/1.23 fof(f1135,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(or(or(X0,X1),implies(X1,X2))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f1109,f1017])).
% 4.69/1.23 fof(f1163,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(or(or(X0,not(X1)),or(X1,X2))))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f185,f1135])).
% 4.69/1.23 fof(f1174,plain,(
% 4.69/1.23 ![X0,X1]: (~is_a_theorem(implies(or(X0,not(X0)),X1))|is_a_theorem(X1))),
% 4.69/1.23 inference(resolution,[status(thm)],[f1163,f594])).
% 4.69/1.23 fof(f1200,plain,(
% 4.69/1.23 ![X0]: (is_a_theorem(equiv(not(X0),not(X0))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f1174,f212])).
% 4.69/1.23 fof(f1207,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~is_a_theorem(implies(implies(implies(X0,X1),not(and(X0,not(X1)))),X2))|is_a_theorem(X2))),
% 4.69/1.23 inference(paramodulation,[status(thm)],[f186,f1174])).
% 4.69/1.23 fof(f1211,plain,(
% 4.69/1.23 ![X0,X1,X2]: (~is_a_theorem(implies(implies(implies(X0,X1),implies(X0,X1)),X2))|is_a_theorem(X2))),
% 4.69/1.23 inference(forward_demodulation,[status(thm)],[f180,f1207])).
% 4.69/1.23 fof(f1215,plain,(
% 4.69/1.23 ![X0,X1]: (is_a_theorem(or(implies(X0,X1),X0)))),
% 4.69/1.23 inference(resolution,[status(thm)],[f1211,f1017])).
% 4.69/1.23 fof(f1279,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(X1,implies(X0,X2)))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f1215,f342])).
% 4.69/1.23 fof(f1280,plain,(
% 4.69/1.23 ![X0,X1,X2]: (is_a_theorem(or(and(X0,X1),implies(X1,implies(X0,X2)))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f1215,f327])).
% 4.69/1.23 fof(f1290,plain,(
% 4.69/1.23 ![X0]: (is_a_theorem(or(X0,not(X0))))),
% 4.69/1.23 inference(resolution,[status(thm)],[f1200,f215])).
% 4.69/1.23 fof(f1304,plain,(
% 4.69/1.23 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 4.69/1.23 inference(resolution,[status(thm)],[f1290,f573])).
% 4.69/1.23 fof(f1317,plain,(
% 4.69/1.24 ![X0]: (~is_a_theorem(or(X0,X0))|is_a_theorem(X0))),
% 4.69/1.24 inference(resolution,[status(thm)],[f1304,f177])).
% 4.69/1.24 fof(f1329,plain,(
% 4.69/1.24 ![X0,X1]: (is_a_theorem(X0)|~is_a_theorem(implies(X1,X0))|~is_a_theorem(or(X1,X0)))),
% 4.69/1.24 inference(resolution,[status(thm)],[f1317,f471])).
% 4.69/1.24 fof(f1798,plain,(
% 4.69/1.24 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(X1,implies(X0,X2))))),
% 4.69/1.24 inference(resolution,[status(thm)],[f1279,f177])).
% 4.69/1.24 fof(f1919,plain,(
% 4.69/1.24 ![X0,X1]: (is_a_theorem(X0)|~is_a_theorem(or(and(X0,X1),X0)))),
% 4.69/1.24 inference(resolution,[status(thm)],[f1329,f178])).
% 4.69/1.24 fof(f1929,plain,(
% 4.69/1.24 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 4.69/1.24 inference(resolution,[status(thm)],[f1919,f1018])).
% 4.69/1.24 fof(f2091,plain,(
% 4.69/1.24 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 4.69/1.24 inference(resolution,[status(thm)],[f1798,f1317])).
% 4.69/1.24 fof(f2105,plain,(
% 4.69/1.24 ![X0]: (is_a_theorem(implies(implies(X0,X0),not(and(not(X0),X0)))))),
% 4.69/1.24 inference(resolution,[status(thm)],[f2091,f316])).
% 4.69/1.24 fof(f2718,plain,(
% 4.69/1.24 ![X0]: (~is_a_theorem(implies(X0,X0))|is_a_theorem(not(and(not(X0),X0))))),
% 4.69/1.24 inference(resolution,[status(thm)],[f2105,f177])).
% 4.69/1.24 fof(f2726,plain,(
% 4.69/1.24 ![X0]: (is_a_theorem(not(and(not(X0),X0))))),
% 4.69/1.24 inference(forward_subsumption_resolution,[status(thm)],[f2718,f1929])).
% 4.69/1.24 fof(f2736,plain,(
% 4.69/1.24 ![X0,X1]: (~is_a_theorem(or(and(not(X0),X0),X1))|is_a_theorem(X1))),
% 4.69/1.24 inference(resolution,[status(thm)],[f2726,f187])).
% 4.69/1.24 fof(f2812,plain,(
% 4.69/1.24 ![X0,X1]: (is_a_theorem(implies(X0,implies(not(X0),X1))))),
% 4.69/1.24 inference(resolution,[status(thm)],[f2736,f1280])).
% 4.69/1.24 fof(f2835,plain,(
% 4.69/1.24 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1))))),
% 4.69/1.24 inference(forward_demodulation,[status(thm)],[f185,f2812])).
% 4.69/1.24 fof(f2853,plain,(
% 4.69/1.24 $false),
% 4.69/1.24 inference(backward_subsumption_resolution,[status(thm)],[f184,f2835])).
% 4.69/1.24 % SZS output end CNFRefutation for theBenchmark.p
% 5.68/1.28 % Elapsed time: 0.902547 seconds
% 5.68/1.28 % CPU time: 6.797051 seconds
% 5.68/1.28 % Total memory used: 259.234 MB
% 5.68/1.28 % Net memory used: 255.536 MB
%------------------------------------------------------------------------------