%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL518+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 : n001.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 0.11s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL518+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 00:42:28 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.11/0.49 % Refutation found
% 0.11/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.49 fof(f1,axiom,(
% 0.11/0.49 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f16,axiom,(
% 0.11/0.49 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f17,axiom,(
% 0.11/0.49 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f18,axiom,(
% 0.11/0.49 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f22,axiom,(
% 0.11/0.49 ( r1<=> (! [P] : is_a_theorem(implies(or(P,P),P)) )) ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f27,axiom,(
% 0.11/0.49 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f28,axiom,(
% 0.11/0.49 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f29,axiom,(
% 0.11/0.49 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f30,axiom,(
% 0.11/0.49 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f31,axiom,(
% 0.11/0.49 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f32,axiom,(
% 0.11/0.49 op_or ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f33,axiom,(
% 0.11/0.49 op_implies_and ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f34,axiom,(
% 0.11/0.49 op_equiv ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f35,axiom,(
% 0.11/0.49 modus_ponens ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f36,axiom,(
% 0.11/0.49 kn1 ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f37,axiom,(
% 0.11/0.49 kn2 ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f38,axiom,(
% 0.11/0.49 kn3 ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f40,axiom,(
% 0.11/0.49 op_implies_or ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f41,axiom,(
% 0.11/0.49 op_and ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f43,conjecture,(
% 0.11/0.49 r1 ),
% 0.11/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.49 fof(f44,negated_conjecture,(
% 0.11/0.49 ~(r1 )),
% 0.11/0.49 inference(negated_conjecture,[status(cth)],[f43])).
% 0.11/0.49 fof(f45,plain,(
% 0.11/0.49 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.11/0.49 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.11/0.49 fof(f46,plain,(
% 0.11/0.49 (~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))))),
% 0.11/0.49 inference(NNF_transformation,[status(thm)],[f45])).
% 0.11/0.49 fof(f47,plain,(
% 0.11/0.49 (~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))))),
% 0.11/0.49 inference(miniscoping,[status(thm)],[f46])).
% 0.11/0.49 fof(f48,plain,(
% 0.11/0.49 (~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)))),
% 0.11/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f47])).
% 0.11/0.49 fof(f49,plain,(
% 0.11/0.49 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f48])).
% 0.11/0.49 fof(f111,plain,(
% 0.11/0.49 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 0.11/0.49 inference(NNF_transformation,[status(thm)],[f16])).
% 0.11/0.49 fof(f112,plain,(
% 0.11/0.49 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))))),
% 0.11/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f111])).
% 0.11/0.49 fof(f113,plain,(
% 0.11/0.49 ![X0]: (~kn1|is_a_theorem(implies(X0,and(X0,X0))))),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f112])).
% 0.11/0.49 fof(f115,plain,(
% 0.11/0.49 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 0.11/0.49 inference(NNF_transformation,[status(thm)],[f17])).
% 0.11/0.49 fof(f116,plain,(
% 0.11/0.49 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl)))),
% 0.11/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl]),skolemize(P,sK33_skl),skolemize(Q,sK34_skl)],[f115])).
% 0.11/0.49 fof(f117,plain,(
% 0.11/0.49 ![X0,X1]: (~kn2|is_a_theorem(implies(and(X0,X1),X0)))),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f116])).
% 0.11/0.49 fof(f119,plain,(
% 0.11/0.49 (~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)))))))),
% 0.11/0.49 inference(NNF_transformation,[status(thm)],[f18])).
% 0.11/0.49 fof(f120,plain,(
% 0.11/0.49 (~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))))))),
% 0.11/0.49 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])).
% 0.11/0.49 fof(f121,plain,(
% 0.11/0.49 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))))),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f120])).
% 0.11/0.49 fof(f135,plain,(
% 0.11/0.49 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|(?[P]: ~is_a_theorem(implies(or(P,P),P))))),
% 0.11/0.49 inference(NNF_transformation,[status(thm)],[f22])).
% 0.11/0.49 fof(f136,plain,(
% 0.11/0.49 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)))),
% 0.11/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(P,sK44_skl)],[f135])).
% 0.11/0.49 fof(f138,plain,(
% 0.11/0.49 r1|~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f136])).
% 0.11/0.49 fof(f155,plain,(
% 0.11/0.49 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 0.11/0.49 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.11/0.49 fof(f156,plain,(
% 0.11/0.49 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f155])).
% 0.11/0.49 fof(f157,plain,(
% 0.11/0.49 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 0.11/0.49 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.11/0.49 fof(f158,plain,(
% 0.11/0.49 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f157])).
% 0.11/0.49 fof(f159,plain,(
% 0.11/0.49 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 0.11/0.49 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.11/0.49 fof(f160,plain,(
% 0.11/0.49 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f159])).
% 0.11/0.49 fof(f161,plain,(
% 0.11/0.49 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 0.11/0.49 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.11/0.49 fof(f162,plain,(
% 0.11/0.49 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f161])).
% 0.11/0.49 fof(f163,plain,(
% 0.11/0.49 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 0.11/0.49 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 0.11/0.49 fof(f164,plain,(
% 0.11/0.49 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f163])).
% 0.11/0.49 fof(f165,plain,(
% 0.11/0.49 op_or),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f32])).
% 0.11/0.49 fof(f166,plain,(
% 0.11/0.49 op_implies_and),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f33])).
% 0.11/0.49 fof(f167,plain,(
% 0.11/0.49 op_equiv),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f34])).
% 0.11/0.49 fof(f168,plain,(
% 0.11/0.49 modus_ponens),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f35])).
% 0.11/0.49 fof(f169,plain,(
% 0.11/0.49 kn1),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f36])).
% 0.11/0.49 fof(f170,plain,(
% 0.11/0.49 kn2),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f37])).
% 0.11/0.49 fof(f171,plain,(
% 0.11/0.49 kn3),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f38])).
% 0.11/0.49 fof(f173,plain,(
% 0.11/0.49 op_implies_or),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f40])).
% 0.11/0.49 fof(f174,plain,(
% 0.11/0.49 op_and),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f41])).
% 0.11/0.49 fof(f176,plain,(
% 0.11/0.49 ~r1),
% 0.11/0.49 inference(cnf_transformation,[status(thm)],[f44])).
% 0.11/0.49 fof(f177,plain,(
% 0.11/0.49 ~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))),
% 0.11/0.49 inference(forward_subsumption_resolution,[status(thm)],[f138,f176])).
% 0.11/0.49 fof(f178,plain,(
% 0.11/0.49 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.11/0.49 inference(backward_subsumption_resolution,[status(thm)],[f49,f168])).
% 0.11/0.49 fof(f180,plain,(
% 0.11/0.49 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 0.11/0.49 inference(forward_subsumption_resolution,[status(thm)],[f113,f169])).
% 0.11/0.49 fof(f181,plain,(
% 0.11/0.49 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 0.11/0.49 inference(forward_subsumption_resolution,[status(thm)],[f117,f170])).
% 0.11/0.49 fof(f182,plain,(
% 0.11/0.49 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 0.11/0.49 inference(forward_subsumption_resolution,[status(thm)],[f162,f173])).
% 0.11/0.49 fof(f183,plain,(
% 0.11/0.50 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(X0))),
% 0.11/0.50 inference(resolution,[status(thm)],[f178,f181])).
% 0.11/0.50 fof(f184,plain,(
% 0.11/0.50 ![X0]: (~is_a_theorem(X0)|is_a_theorem(and(X0,X0)))),
% 0.11/0.50 inference(resolution,[status(thm)],[f178,f180])).
% 0.11/0.50 fof(f185,plain,(
% 0.11/0.50 ![X0,X1]: (is_a_theorem(and(implies(and(X0,X1),X0),implies(and(X0,X1),X0))))),
% 0.11/0.50 inference(resolution,[status(thm)],[f184,f181])).
% 0.11/0.50 fof(f186,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(and(implies(X0,and(X0,X0)),implies(X0,and(X0,X0)))))),
% 0.11/0.50 inference(resolution,[status(thm)],[f184,f180])).
% 0.11/0.50 fof(f188,plain,(
% 0.11/0.50 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 0.11/0.50 inference(forward_subsumption_resolution,[status(thm)],[f160,f166])).
% 0.11/0.50 fof(f191,plain,(
% 0.11/0.50 ![X0,X1]: (~op_or|or(X0,X1)=implies(not(X0),X1))),
% 0.11/0.50 inference(forward_demodulation,[status(thm)],[f188,f156])).
% 0.11/0.50 fof(f198,plain,(
% 0.11/0.50 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 0.11/0.50 inference(forward_subsumption_resolution,[status(thm)],[f191,f165])).
% 0.11/0.50 fof(f199,plain,(
% 0.11/0.50 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f188,f198])).
% 0.11/0.50 fof(f200,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(or(X0,and(not(X0),not(X0)))))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f198,f180])).
% 0.11/0.50 fof(f201,plain,(
% 0.11/0.50 ![X0,X1]: (~is_a_theorem(not(X0))|~is_a_theorem(or(X0,X1))|is_a_theorem(X1))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f198,f178])).
% 0.11/0.50 fof(f209,plain,(
% 0.11/0.50 ![X0,X1]: (~op_and|and(X0,X1)=not(implies(X0,not(X1))))),
% 0.11/0.50 inference(forward_demodulation,[status(thm)],[f182,f158])).
% 0.11/0.50 fof(f210,plain,(
% 0.11/0.50 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1))))),
% 0.11/0.50 inference(forward_subsumption_resolution,[status(thm)],[f209,f174])).
% 0.11/0.50 fof(f211,plain,(
% 0.11/0.50 ![X0,X1]: (and(not(X0),X1)=not(or(X0,not(X1))))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f198,f210])).
% 0.11/0.50 fof(f219,plain,(
% 0.11/0.50 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(and(X0,X1),X2))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f210,f182])).
% 0.11/0.50 fof(f222,plain,(
% 0.11/0.50 ![X0,X1]: (and(not(not(X0)),X1)=not(implies(X0,not(X1))))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f182,f211])).
% 0.11/0.50 fof(f233,plain,(
% 0.11/0.50 ![X0,X1]: (and(not(not(X0)),X1)=and(X0,X1))),
% 0.11/0.50 inference(forward_demodulation,[status(thm)],[f210,f222])).
% 0.11/0.50 fof(f239,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(or(not(X0),and(X0,not(not(X0))))))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f233,f200])).
% 0.11/0.50 fof(f241,plain,(
% 0.11/0.50 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(not(not(X0))))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f233,f183])).
% 0.11/0.50 fof(f244,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(implies(X0,and(X0,not(not(X0))))))),
% 0.11/0.50 inference(forward_demodulation,[status(thm)],[f182,f239])).
% 0.11/0.50 fof(f251,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(or(X0,and(not(X0),not(not(not(X0)))))))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f198,f244])).
% 0.11/0.50 fof(f272,plain,(
% 0.11/0.50 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 0.11/0.50 inference(forward_subsumption_resolution,[status(thm)],[f164,f167])).
% 0.11/0.50 fof(f276,plain,(
% 0.11/0.50 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|is_a_theorem(not(not(implies(X0,X1)))))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f272,f241])).
% 0.11/0.50 fof(f279,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f272,f180])).
% 0.11/0.50 fof(f284,plain,(
% 0.11/0.50 ![X0]: (~is_a_theorem(implies(X0,X0))|is_a_theorem(equiv(X0,X0)))),
% 0.11/0.50 inference(resolution,[status(thm)],[f279,f178])).
% 0.11/0.50 fof(f605,plain,(
% 0.11/0.50 ![X0,X1]: (is_a_theorem(not(not(implies(and(X0,X1),X0)))))),
% 0.11/0.50 inference(resolution,[status(thm)],[f185,f241])).
% 0.11/0.50 fof(f626,plain,(
% 0.11/0.50 ![X0,X1]: (is_a_theorem(not(and(and(not(X0),X1),X0))))),
% 0.11/0.50 inference(paramodulation,[status(thm)],[f210,f605])).
% 0.11/0.50 fof(f636,plain,(
% 0.11/0.50 ![X0,X1,X2]: (~is_a_theorem(or(and(and(not(X0),X1),X0),X2))|is_a_theorem(X2))),
% 0.11/0.50 inference(resolution,[status(thm)],[f626,f201])).
% 0.11/0.50 fof(f675,plain,(
% 0.11/0.50 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))))),
% 0.11/0.50 inference(forward_demodulation,[status(thm)],[f198,f121])).
% 0.11/0.50 fof(f676,plain,(
% 0.11/0.50 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))))),
% 0.11/0.50 inference(forward_subsumption_resolution,[status(thm)],[f675,f171])).
% 0.11/0.50 fof(f884,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(not(not(implies(X0,and(X0,X0))))))),
% 0.11/0.50 inference(resolution,[status(thm)],[f186,f241])).
% 0.11/0.50 fof(f917,plain,(
% 0.11/0.50 ![X0,X1]: (~is_a_theorem(or(not(implies(X0,and(X0,X0))),X1))|is_a_theorem(X1))),
% 0.11/0.50 inference(resolution,[status(thm)],[f884,f201])).
% 0.11/0.50 fof(f926,plain,(
% 0.11/0.50 ![X0,X1]: (~is_a_theorem(implies(implies(X0,and(X0,X0)),X1))|is_a_theorem(X1))),
% 0.11/0.50 inference(forward_demodulation,[status(thm)],[f182,f917])).
% 0.11/0.50 fof(f932,plain,(
% 0.11/0.50 ![X0,X1]: (is_a_theorem(or(and(and(X0,X0),X1),not(and(X1,X0)))))),
% 0.11/0.50 inference(resolution,[status(thm)],[f926,f676])).
% 0.11/0.50 fof(f1030,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(not(and(X0,not(X0)))))),
% 0.11/0.50 inference(resolution,[status(thm)],[f932,f636])).
% 0.11/0.50 fof(f1040,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 0.11/0.50 inference(forward_demodulation,[status(thm)],[f188,f1030])).
% 0.11/0.50 fof(f1046,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(equiv(X0,X0)))),
% 0.11/0.50 inference(backward_subsumption_resolution,[status(thm)],[f284,f1040])).
% 0.11/0.50 fof(f1063,plain,(
% 0.11/0.50 ![X0]: (is_a_theorem(not(not(implies(X0,X0)))))),
% 0.11/0.50 inference(resolution,[status(thm)],[f1046,f276])).
% 0.11/0.51 fof(f1123,plain,(
% 0.11/0.51 ![X0,X1]: (~is_a_theorem(or(not(implies(X0,X0)),X1))|is_a_theorem(X1))),
% 0.11/0.51 inference(resolution,[status(thm)],[f1063,f201])).
% 0.11/0.51 fof(f1131,plain,(
% 0.11/0.51 ![X0,X1]: (~is_a_theorem(implies(implies(X0,X0),X1))|is_a_theorem(X1))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f182,f1123])).
% 0.11/0.51 fof(f1249,plain,(
% 0.11/0.51 ![X0,X1]: (is_a_theorem(or(and(X0,X1),not(and(X1,X0)))))),
% 0.11/0.51 inference(resolution,[status(thm)],[f1131,f676])).
% 0.11/0.51 fof(f1435,plain,(
% 0.11/0.51 ![X0,X1]: (is_a_theorem(or(and(not(X0),X1),implies(X1,X0))))),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f188,f1249])).
% 0.11/0.51 fof(f3174,plain,(
% 0.11/0.51 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),X1),implies(not(X1),X0))))),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f199,f1435])).
% 0.11/0.51 fof(f3186,plain,(
% 0.11/0.51 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),implies(not(X1),X0))))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f198,f3174])).
% 0.11/0.51 fof(f3187,plain,(
% 0.11/0.51 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f198,f3186])).
% 0.11/0.51 fof(f3199,plain,(
% 0.11/0.51 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0)))),
% 0.11/0.51 inference(resolution,[status(thm)],[f3187,f178])).
% 0.11/0.51 fof(f3246,plain,(
% 0.11/0.51 ![X0]: (is_a_theorem(or(and(not(X0),not(not(not(X0)))),X0)))),
% 0.11/0.51 inference(resolution,[status(thm)],[f3199,f251])).
% 0.11/0.51 fof(f3277,plain,(
% 0.11/0.51 ![X0]: (is_a_theorem(implies(implies(not(X0),not(not(X0))),X0)))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f199,f3246])).
% 0.11/0.51 fof(f3278,plain,(
% 0.11/0.51 ![X0]: (is_a_theorem(or(and(not(X0),not(X0)),X0)))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f219,f3277])).
% 0.11/0.51 fof(f3279,plain,(
% 0.11/0.51 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f199,f3278])).
% 0.11/0.51 fof(f3280,plain,(
% 0.11/0.51 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f198,f3279])).
% 0.11/0.51 fof(f3320,plain,(
% 0.11/0.51 $false),
% 0.11/0.51 inference(backward_subsumption_resolution,[status(thm)],[f177,f3280])).
% 0.11/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.31/0.54 % Elapsed time: 0.176807 seconds
% 0.31/0.54 % CPU time: 1.075223 seconds
% 0.31/0.54 % Total memory used: 116.892 MB
% 0.31/0.54 % Net memory used: 116.024 MB
%------------------------------------------------------------------------------