%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL504+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 : n009.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 78.76s 10.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL504+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 : n009.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 00:35:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 78.76/10.36 % Refutation found
% 78.76/10.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 78.76/10.36 % SZS output start CNFRefutation for theBenchmark
% 78.76/10.36 fof(f1,axiom,(
% 78.76/10.36 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f5,axiom,(
% 78.76/10.36 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f16,axiom,(
% 78.76/10.36 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f17,axiom,(
% 78.76/10.36 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f18,axiom,(
% 78.76/10.36 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f27,axiom,(
% 78.76/10.36 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f29,axiom,(
% 78.76/10.36 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f32,axiom,(
% 78.76/10.36 op_or ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f33,axiom,(
% 78.76/10.36 op_implies_and ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f35,axiom,(
% 78.76/10.36 modus_ponens ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f36,axiom,(
% 78.76/10.36 kn1 ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f37,axiom,(
% 78.76/10.36 kn2 ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f38,axiom,(
% 78.76/10.36 kn3 ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f43,conjecture,(
% 78.76/10.36 implies_2 ),
% 78.76/10.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 78.76/10.36 fof(f44,negated_conjecture,(
% 78.76/10.36 ~(implies_2 )),
% 78.76/10.36 inference(negated_conjecture,[status(cth)],[f43])).
% 78.76/10.36 fof(f45,plain,(
% 78.76/10.36 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 78.76/10.36 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 78.76/10.36 fof(f46,plain,(
% 78.76/10.36 (~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))))),
% 78.76/10.36 inference(NNF_transformation,[status(thm)],[f45])).
% 78.76/10.36 fof(f47,plain,(
% 78.76/10.36 (~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))))),
% 78.76/10.36 inference(miniscoping,[status(thm)],[f46])).
% 78.76/10.36 fof(f48,plain,(
% 78.76/10.36 (~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)))),
% 78.76/10.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f47])).
% 78.76/10.36 fof(f49,plain,(
% 78.76/10.36 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f48])).
% 78.76/10.36 fof(f67,plain,(
% 78.76/10.36 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|(?[X,Y]: ~is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))),
% 78.76/10.36 inference(NNF_transformation,[status(thm)],[f5])).
% 78.76/10.36 fof(f68,plain,(
% 78.76/10.36 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl))))),
% 78.76/10.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f67])).
% 78.76/10.36 fof(f70,plain,(
% 78.76/10.36 implies_2|~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl)))),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f68])).
% 78.76/10.36 fof(f111,plain,(
% 78.76/10.36 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 78.76/10.36 inference(NNF_transformation,[status(thm)],[f16])).
% 78.76/10.36 fof(f112,plain,(
% 78.76/10.36 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))))),
% 78.76/10.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f111])).
% 78.76/10.36 fof(f113,plain,(
% 78.76/10.36 ![X0]: (~kn1|is_a_theorem(implies(X0,and(X0,X0))))),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f112])).
% 78.76/10.36 fof(f115,plain,(
% 78.76/10.36 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 78.76/10.36 inference(NNF_transformation,[status(thm)],[f17])).
% 78.76/10.36 fof(f116,plain,(
% 78.76/10.36 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl)))),
% 78.76/10.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl]),skolemize(P,sK33_skl),skolemize(Q,sK34_skl)],[f115])).
% 78.76/10.36 fof(f117,plain,(
% 78.76/10.36 ![X0,X1]: (~kn2|is_a_theorem(implies(and(X0,X1),X0)))),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f116])).
% 78.76/10.36 fof(f119,plain,(
% 78.76/10.36 (~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)))))))),
% 78.76/10.36 inference(NNF_transformation,[status(thm)],[f18])).
% 78.76/10.36 fof(f120,plain,(
% 78.76/10.36 (~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))))))),
% 78.76/10.36 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])).
% 78.76/10.36 fof(f121,plain,(
% 78.76/10.36 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))))),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f120])).
% 78.76/10.36 fof(f155,plain,(
% 78.76/10.36 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 78.76/10.36 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 78.76/10.36 fof(f156,plain,(
% 78.76/10.36 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f155])).
% 78.76/10.36 fof(f159,plain,(
% 78.76/10.36 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 78.76/10.36 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 78.76/10.36 fof(f160,plain,(
% 78.76/10.36 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f159])).
% 78.76/10.36 fof(f165,plain,(
% 78.76/10.36 op_or),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f32])).
% 78.76/10.36 fof(f166,plain,(
% 78.76/10.36 op_implies_and),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f33])).
% 78.76/10.36 fof(f168,plain,(
% 78.76/10.36 modus_ponens),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f35])).
% 78.76/10.36 fof(f169,plain,(
% 78.76/10.36 kn1),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f36])).
% 78.76/10.36 fof(f170,plain,(
% 78.76/10.36 kn2),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f37])).
% 78.76/10.36 fof(f171,plain,(
% 78.76/10.36 kn3),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f38])).
% 78.76/10.36 fof(f176,plain,(
% 78.76/10.36 ~implies_2),
% 78.76/10.36 inference(cnf_transformation,[status(thm)],[f44])).
% 78.76/10.36 fof(f177,plain,(
% 78.76/10.36 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 78.76/10.36 inference(forward_subsumption_resolution,[status(thm)],[f49,f168])).
% 78.76/10.36 fof(f179,plain,(
% 78.76/10.36 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 78.76/10.36 inference(forward_subsumption_resolution,[status(thm)],[f113,f169])).
% 78.76/10.36 fof(f182,plain,(
% 78.76/10.36 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 78.76/10.36 inference(forward_subsumption_resolution,[status(thm)],[f117,f170])).
% 78.76/10.36 fof(f186,plain,(
% 78.76/10.36 ~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl)))),
% 78.76/10.36 inference(forward_subsumption_resolution,[status(thm)],[f70,f176])).
% 78.76/10.36 fof(f187,plain,(
% 78.76/10.36 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 78.76/10.36 inference(forward_subsumption_resolution,[status(thm)],[f160,f166])).
% 78.76/10.36 fof(f188,plain,(
% 78.76/10.36 ![X0,X1,X2]: (implies(X0,and(X1,not(X2)))=not(and(X0,implies(X1,X2))))),
% 78.76/10.36 inference(paramodulation,[status(thm)],[f187,f187])).
% 78.76/10.36 fof(f189,plain,(
% 78.76/10.36 ![X0,X1]: (~op_or|or(X0,X1)=implies(not(X0),X1))),
% 78.76/10.36 inference(forward_demodulation,[status(thm)],[f187,f156])).
% 78.76/10.36 fof(f196,plain,(
% 78.76/10.36 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 78.76/10.36 inference(forward_subsumption_resolution,[status(thm)],[f189,f165])).
% 78.76/10.36 fof(f197,plain,(
% 78.76/10.36 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 78.76/10.36 inference(paramodulation,[status(thm)],[f187,f196])).
% 78.76/10.36 fof(f198,plain,(
% 78.76/10.36 ![X0]: (is_a_theorem(or(X0,and(not(X0),not(X0)))))),
% 78.76/10.36 inference(paramodulation,[status(thm)],[f196,f179])).
% 78.76/10.36 fof(f199,plain,(
% 78.76/10.36 ![X0,X1]: (~is_a_theorem(not(X0))|~is_a_theorem(or(X0,X1))|is_a_theorem(X1))),
% 78.76/10.36 inference(paramodulation,[status(thm)],[f196,f177])).
% 78.76/10.36 fof(f254,plain,(
% 78.76/10.36 ![X0]: (is_a_theorem(not(and(not(X0),implies(not(X0),X0)))))),
% 78.76/10.36 inference(paramodulation,[status(thm)],[f188,f179])).
% 78.76/10.36 fof(f268,plain,(
% 78.76/10.36 ![X0]: (is_a_theorem(not(and(not(X0),or(X0,X0)))))),
% 78.76/10.36 inference(forward_demodulation,[status(thm)],[f196,f254])).
% 78.76/10.36 fof(f270,plain,(
% 78.76/10.36 ![X0,X1]: (~is_a_theorem(or(and(not(X0),or(X0,X0)),X1))|is_a_theorem(X1))),
% 78.76/10.36 inference(resolution,[status(thm)],[f268,f199])).
% 78.76/10.36 fof(f341,plain,(
% 78.76/10.36 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))))),
% 78.76/10.36 inference(forward_demodulation,[status(thm)],[f196,f121])).
% 78.76/10.36 fof(f342,plain,(
% 78.76/10.36 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))))),
% 78.76/10.36 inference(forward_subsumption_resolution,[status(thm)],[f341,f171])).
% 78.76/10.36 fof(f345,plain,(
% 78.76/10.36 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0)))))))),
% 78.76/10.36 inference(paramodulation,[status(thm)],[f196,f342])).
% 78.76/10.36 fof(f355,plain,(
% 78.76/10.36 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))))),
% 78.76/10.36 inference(forward_demodulation,[status(thm)],[f187,f345])).
% 78.76/10.36 fof(f358,plain,(
% 78.76/10.36 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(and(X1,X2),implies(X2,X0))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f355,f177])).
% 78.76/10.36 fof(f361,plain,(
% 78.76/10.36 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0)))))),
% 78.76/10.36 inference(paramodulation,[status(thm)],[f197,f355])).
% 78.76/10.36 fof(f368,plain,(
% 78.76/10.36 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))))),
% 78.76/10.36 inference(forward_demodulation,[status(thm)],[f196,f361])).
% 78.76/10.36 fof(f374,plain,(
% 78.76/10.36 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(implies(implies(X1,X2),or(X2,X0))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f368,f177])).
% 78.76/10.36 fof(f384,plain,(
% 78.76/10.36 ![X0,X1]: (is_a_theorem(implies(implies(and(not(X0),not(X0)),X1),or(X1,X0))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f374,f198])).
% 78.76/10.36 fof(f411,plain,(
% 78.76/10.36 ![X0,X1]: (~is_a_theorem(implies(and(not(X0),not(X0)),X1))|is_a_theorem(or(X1,X0)))),
% 78.76/10.36 inference(resolution,[status(thm)],[f384,f177])).
% 78.76/10.36 fof(f423,plain,(
% 78.76/10.36 ![X0]: (is_a_theorem(or(not(X0),X0)))),
% 78.76/10.36 inference(resolution,[status(thm)],[f411,f182])).
% 78.76/10.36 fof(f432,plain,(
% 78.76/10.36 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f423,f374])).
% 78.76/10.36 fof(f433,plain,(
% 78.76/10.36 ![X0,X1]: (is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f423,f358])).
% 78.76/10.36 fof(f436,plain,(
% 78.76/10.36 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(X1,not(X0))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f432,f177])).
% 78.76/10.36 fof(f446,plain,(
% 78.76/10.36 ![X0]: (is_a_theorem(implies(or(X0,X0),not(not(X0)))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f433,f270])).
% 78.76/10.36 fof(f458,plain,(
% 78.76/10.36 ![X0]: (~is_a_theorem(or(X0,X0))|is_a_theorem(not(not(X0))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f446,f177])).
% 78.76/10.36 fof(f489,plain,(
% 78.76/10.36 ![X0,X1]: (is_a_theorem(or(X0,not(and(X0,X1)))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f436,f182])).
% 78.76/10.36 fof(f495,plain,(
% 78.76/10.36 ![X0,X1,X2]: (is_a_theorem(implies(implies(not(and(X0,X1)),X2),or(X2,X0))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f489,f374])).
% 78.76/10.36 fof(f499,plain,(
% 78.76/10.36 ![X0,X1]: (is_a_theorem(or(X0,implies(X0,X1))))),
% 78.76/10.36 inference(paramodulation,[status(thm)],[f187,f489])).
% 78.76/10.36 fof(f503,plain,(
% 78.76/10.36 ![X0,X1,X2]: (is_a_theorem(implies(or(and(X0,X1),X2),or(X2,X0))))),
% 78.76/10.36 inference(forward_demodulation,[status(thm)],[f196,f495])).
% 78.76/10.36 fof(f506,plain,(
% 78.76/10.36 ![X0,X1,X2]: (is_a_theorem(or(and(implies(X0,X1),X2),implies(X2,X0))))),
% 78.76/10.36 inference(resolution,[status(thm)],[f499,f358])).
% 78.76/10.36 fof(f566,plain,(
% 78.76/10.36 ![X0,X1,X2]: (~is_a_theorem(or(and(X0,X1),X2))|is_a_theorem(or(X2,X0)))),
% 78.76/10.36 inference(resolution,[status(thm)],[f503,f177])).
% 78.76/10.36 fof(f603,plain,(
% 78.76/10.36 ![X0,X1,X2]: (is_a_theorem(or(implies(X0,X1),implies(X1,X2))))),
% 68.80/10.49 inference(resolution,[status(thm)],[f566,f506])).
% 68.80/10.49 fof(f626,plain,(
% 68.80/10.49 ![X0]: (is_a_theorem(not(not(implies(X0,X0)))))),
% 68.80/10.49 inference(resolution,[status(thm)],[f603,f458])).
% 68.80/10.49 fof(f634,plain,(
% 68.80/10.49 ![X0,X1]: (~is_a_theorem(or(not(implies(X0,X0)),X1))|is_a_theorem(X1))),
% 68.80/10.49 inference(resolution,[status(thm)],[f626,f199])).
% 68.80/10.49 fof(f673,plain,(
% 68.80/10.49 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 68.80/10.49 inference(resolution,[status(thm)],[f634,f423])).
% 68.80/10.49 fof(f681,plain,(
% 68.80/10.49 ![X0]: (is_a_theorem(or(and(not(X0),not(X0)),X0)))),
% 68.80/10.49 inference(resolution,[status(thm)],[f673,f411])).
% 68.80/10.49 fof(f682,plain,(
% 68.80/10.49 ![X0]: (is_a_theorem(or(X0,not(X0))))),
% 68.80/10.49 inference(resolution,[status(thm)],[f673,f436])).
% 68.80/10.49 fof(f687,plain,(
% 68.80/10.49 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 68.80/10.49 inference(forward_demodulation,[status(thm)],[f197,f681])).
% 68.80/10.49 fof(f688,plain,(
% 68.80/10.49 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 68.80/10.49 inference(forward_demodulation,[status(thm)],[f196,f687])).
% 68.80/10.49 fof(f696,plain,(
% 68.80/10.49 ![X0,X1]: (is_a_theorem(or(not(and(X0,X1)),X0)))),
% 68.80/10.49 inference(resolution,[status(thm)],[f682,f566])).
% 68.80/10.49 fof(f697,plain,(
% 68.80/10.49 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),X1),or(X1,X0))))),
% 68.80/10.49 inference(resolution,[status(thm)],[f682,f374])).
% 68.80/10.49 fof(f702,plain,(
% 68.80/10.49 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 68.80/10.49 inference(forward_demodulation,[status(thm)],[f196,f697])).
% 68.80/10.49 fof(f713,plain,(
% 68.80/10.49 ![X0]: (is_a_theorem(or(X0,not(or(X0,X0)))))),
% 68.80/10.49 inference(resolution,[status(thm)],[f688,f436])).
% 68.80/10.49 fof(f729,plain,(
% 68.80/10.49 ![X0,X1]: (is_a_theorem(or(implies(X0,X1),X0)))),
% 68.80/10.49 inference(paramodulation,[status(thm)],[f187,f696])).
% 68.80/10.49 fof(f734,plain,(
% 68.80/10.49 ![X0,X1,X2]: (is_a_theorem(or(and(X0,X1),implies(X1,implies(X0,X2)))))),
% 68.80/10.49 inference(resolution,[status(thm)],[f729,f358])).
% 68.80/10.49 fof(f750,plain,(
% 68.80/10.49 ![X0,X1]: (is_a_theorem(implies(implies(not(or(X0,X0)),X1),or(X1,X0))))),
% 68.80/10.49 inference(resolution,[status(thm)],[f713,f374])).
% 68.80/10.49 fof(f755,plain,(
% 68.80/10.49 ![X0,X1]: (is_a_theorem(implies(or(or(X0,X0),X1),or(X1,X0))))),
% 68.80/10.49 inference(forward_demodulation,[status(thm)],[f196,f750])).
% 68.80/10.49 fof(f772,plain,(
% 68.80/10.49 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0)))),
% 68.80/10.49 inference(resolution,[status(thm)],[f702,f177])).
% 68.80/10.49 fof(f3379,plain,(
% 68.80/10.49 ![X0,X1,X2]: (is_a_theorem(or(implies(X0,implies(X1,X2)),and(X1,X0))))),
% 68.80/10.49 inference(resolution,[status(thm)],[f734,f772])).
% 68.80/10.49 fof(f3400,plain,(
% 68.80/10.49 ![X0,X1]: (~is_a_theorem(or(or(X0,X0),X1))|is_a_theorem(or(X1,X0)))),
% 68.80/10.49 inference(resolution,[status(thm)],[f755,f177])).
% 68.80/10.49 fof(f4369,plain,(
% 68.80/10.49 ![X0,X1,X2]: (is_a_theorem(or(or(X0,implies(X1,X2)),and(X1,not(X0)))))),
% 68.80/10.49 inference(paramodulation,[status(thm)],[f196,f3379])).
% 68.80/10.49 fof(f119781,plain,(
% 68.80/10.49 ![X0,X1]: (is_a_theorem(or(and(X0,not(implies(X0,X1))),implies(X0,X1))))),
% 68.80/10.49 inference(resolution,[status(thm)],[f4369,f3400])).
% 68.80/10.49 fof(f119817,plain,(
% 68.80/10.49 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 68.80/10.49 inference(forward_demodulation,[status(thm)],[f197,f119781])).
% 68.80/10.49 fof(f119830,plain,(
% 68.80/10.49 $false),
% 68.80/10.49 inference(backward_subsumption_resolution,[status(thm)],[f186,f119817])).
% 68.80/10.49 % SZS output end CNFRefutation for theBenchmark.p
% 49.80/10.58 % Elapsed time: 10.203669 seconds
% 49.80/10.58 % CPU time: 80.365544 seconds
% 49.80/10.58 % Total memory used: 1.337 GB
% 49.80/10.58 % Net memory used: 1.306 GB
%------------------------------------------------------------------------------