%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL519+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 : n006.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 14.41s 2.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL519+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n006.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 00:36:43 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 14.41/2.37 % Refutation found
% 14.41/2.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.41/2.37 % SZS output start CNFRefutation for theBenchmark
% 14.41/2.37 fof(f1,axiom,(
% 14.41/2.37 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f2,axiom,(
% 14.41/2.37 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f16,axiom,(
% 14.41/2.37 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f17,axiom,(
% 14.41/2.37 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f18,axiom,(
% 14.41/2.37 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f23,axiom,(
% 14.41/2.37 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f27,axiom,(
% 14.41/2.37 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f28,axiom,(
% 14.41/2.37 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f29,axiom,(
% 14.41/2.37 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f30,axiom,(
% 14.41/2.37 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f31,axiom,(
% 14.41/2.37 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f32,axiom,(
% 14.41/2.37 op_or ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f33,axiom,(
% 14.41/2.37 op_implies_and ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f34,axiom,(
% 14.41/2.37 op_equiv ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f35,axiom,(
% 14.41/2.37 modus_ponens ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f36,axiom,(
% 14.41/2.37 kn1 ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f37,axiom,(
% 14.41/2.37 kn2 ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f38,axiom,(
% 14.41/2.37 kn3 ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f39,axiom,(
% 14.41/2.37 substitution_of_equivalents ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f40,axiom,(
% 14.41/2.37 op_implies_or ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f41,axiom,(
% 14.41/2.37 op_and ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f43,conjecture,(
% 14.41/2.37 r2 ),
% 14.41/2.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.41/2.37 fof(f44,negated_conjecture,(
% 14.41/2.37 ~(r2 )),
% 14.41/2.37 inference(negated_conjecture,[status(cth)],[f43])).
% 14.41/2.37 fof(f45,plain,(
% 14.41/2.37 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 14.41/2.37 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 14.41/2.37 fof(f46,plain,(
% 14.41/2.37 (~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))))),
% 14.41/2.37 inference(NNF_transformation,[status(thm)],[f45])).
% 14.41/2.37 fof(f47,plain,(
% 14.41/2.37 (~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))))),
% 14.41/2.37 inference(miniscoping,[status(thm)],[f46])).
% 14.41/2.37 fof(f48,plain,(
% 14.41/2.37 (~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)))),
% 14.41/2.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f47])).
% 14.41/2.37 fof(f49,plain,(
% 14.41/2.37 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f48])).
% 14.41/2.37 fof(f53,plain,(
% 14.41/2.37 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 14.41/2.37 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 14.41/2.37 fof(f54,plain,(
% 14.41/2.37 (~substitution_of_equivalents|(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y)))&(substitution_of_equivalents|(?[X,Y]: (is_a_theorem(equiv(X,Y))&~X=Y)))),
% 14.41/2.37 inference(NNF_transformation,[status(thm)],[f53])).
% 14.41/2.37 fof(f55,plain,(
% 14.41/2.37 (~substitution_of_equivalents|(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y)))&(substitution_of_equivalents|(is_a_theorem(equiv(sK2_skl,sK3_skl))&~sK2_skl=sK3_skl))),
% 14.41/2.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f54])).
% 14.41/2.37 fof(f56,plain,(
% 14.41/2.37 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f55])).
% 14.41/2.37 fof(f111,plain,(
% 14.41/2.37 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 14.41/2.37 inference(NNF_transformation,[status(thm)],[f16])).
% 14.41/2.37 fof(f112,plain,(
% 14.41/2.37 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))))),
% 14.41/2.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f111])).
% 14.41/2.37 fof(f113,plain,(
% 14.41/2.37 ![X0]: (~kn1|is_a_theorem(implies(X0,and(X0,X0))))),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f112])).
% 14.41/2.37 fof(f115,plain,(
% 14.41/2.37 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 14.41/2.37 inference(NNF_transformation,[status(thm)],[f17])).
% 14.41/2.37 fof(f116,plain,(
% 14.41/2.37 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl)))),
% 14.41/2.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl]),skolemize(P,sK33_skl),skolemize(Q,sK34_skl)],[f115])).
% 14.41/2.37 fof(f117,plain,(
% 14.41/2.37 ![X0,X1]: (~kn2|is_a_theorem(implies(and(X0,X1),X0)))),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f116])).
% 14.41/2.37 fof(f119,plain,(
% 14.41/2.37 (~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)))))))),
% 14.41/2.37 inference(NNF_transformation,[status(thm)],[f18])).
% 14.41/2.37 fof(f120,plain,(
% 14.41/2.37 (~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))))))),
% 14.41/2.37 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])).
% 14.41/2.37 fof(f121,plain,(
% 14.41/2.37 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))))),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f120])).
% 14.41/2.37 fof(f139,plain,(
% 14.41/2.37 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 14.41/2.37 inference(NNF_transformation,[status(thm)],[f23])).
% 14.41/2.37 fof(f140,plain,(
% 14.41/2.37 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))))),
% 14.41/2.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(P,sK45_skl),skolemize(Q,sK46_skl)],[f139])).
% 14.41/2.37 fof(f142,plain,(
% 14.41/2.37 r2|~is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl)))),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f140])).
% 14.41/2.37 fof(f155,plain,(
% 14.41/2.37 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 14.41/2.37 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 14.41/2.37 fof(f156,plain,(
% 14.41/2.37 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f155])).
% 14.41/2.37 fof(f157,plain,(
% 14.41/2.37 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 14.41/2.37 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 14.41/2.37 fof(f158,plain,(
% 14.41/2.37 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f157])).
% 14.41/2.37 fof(f159,plain,(
% 14.41/2.37 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 14.41/2.37 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 14.41/2.37 fof(f160,plain,(
% 14.41/2.37 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f159])).
% 14.41/2.37 fof(f161,plain,(
% 14.41/2.37 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 14.41/2.37 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 14.41/2.37 fof(f162,plain,(
% 14.41/2.37 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f161])).
% 14.41/2.37 fof(f163,plain,(
% 14.41/2.37 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 14.41/2.37 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 14.41/2.37 fof(f164,plain,(
% 14.41/2.37 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f163])).
% 14.41/2.37 fof(f165,plain,(
% 14.41/2.37 op_or),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f32])).
% 14.41/2.37 fof(f166,plain,(
% 14.41/2.37 op_implies_and),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f33])).
% 14.41/2.37 fof(f167,plain,(
% 14.41/2.37 op_equiv),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f34])).
% 14.41/2.37 fof(f168,plain,(
% 14.41/2.37 modus_ponens),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f35])).
% 14.41/2.37 fof(f169,plain,(
% 14.41/2.37 kn1),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f36])).
% 14.41/2.37 fof(f170,plain,(
% 14.41/2.37 kn2),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f37])).
% 14.41/2.37 fof(f171,plain,(
% 14.41/2.37 kn3),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f38])).
% 14.41/2.37 fof(f172,plain,(
% 14.41/2.37 substitution_of_equivalents),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f39])).
% 14.41/2.37 fof(f173,plain,(
% 14.41/2.37 op_implies_or),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f40])).
% 14.41/2.37 fof(f174,plain,(
% 14.41/2.37 op_and),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f41])).
% 14.41/2.37 fof(f176,plain,(
% 14.41/2.37 ~r2),
% 14.41/2.37 inference(cnf_transformation,[status(thm)],[f44])).
% 14.41/2.37 fof(f177,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f49,f168])).
% 14.41/2.37 fof(f178,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f56,f172])).
% 14.41/2.37 fof(f179,plain,(
% 14.41/2.37 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f113,f169])).
% 14.41/2.37 fof(f180,plain,(
% 14.41/2.37 ![X0]: (~is_a_theorem(X0)|is_a_theorem(and(X0,X0)))),
% 14.41/2.37 inference(resolution,[status(thm)],[f179,f177])).
% 14.41/2.37 fof(f181,plain,(
% 14.41/2.37 ![X0]: (is_a_theorem(and(implies(X0,and(X0,X0)),implies(X0,and(X0,X0)))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f180,f179])).
% 14.41/2.37 fof(f182,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f117,f170])).
% 14.41/2.37 fof(f183,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(X0))),
% 14.41/2.37 inference(resolution,[status(thm)],[f182,f177])).
% 14.41/2.37 fof(f184,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(and(implies(and(X0,X1),X0),implies(and(X0,X1),X0))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f182,f180])).
% 14.41/2.37 fof(f185,plain,(
% 14.41/2.37 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f162,f173])).
% 14.41/2.37 fof(f187,plain,(
% 14.41/2.37 ~is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl)))),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f142,f176])).
% 14.41/2.37 fof(f188,plain,(
% 14.41/2.37 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f160,f166])).
% 14.41/2.37 fof(f191,plain,(
% 14.41/2.37 ![X0,X1]: (~op_or|or(X0,X1)=implies(not(X0),X1))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f188,f156])).
% 14.41/2.37 fof(f198,plain,(
% 14.41/2.37 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f191,f165])).
% 14.41/2.37 fof(f199,plain,(
% 14.41/2.37 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f188,f198])).
% 14.41/2.37 fof(f201,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(not(X0))|~is_a_theorem(or(X0,X1))|is_a_theorem(X1))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f198,f177])).
% 14.41/2.37 fof(f209,plain,(
% 14.41/2.37 ![X0,X1]: (~op_and|and(X0,X1)=not(implies(X0,not(X1))))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f185,f158])).
% 14.41/2.37 fof(f210,plain,(
% 14.41/2.37 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1))))),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f209,f174])).
% 14.41/2.37 fof(f211,plain,(
% 14.41/2.37 ![X0,X1]: (and(not(X0),X1)=not(or(X0,not(X1))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f198,f210])).
% 14.41/2.37 fof(f219,plain,(
% 14.41/2.37 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(and(X0,X1),X2))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f210,f185])).
% 14.41/2.37 fof(f222,plain,(
% 14.41/2.37 ![X0,X1]: (and(not(not(X0)),X1)=not(implies(X0,not(X1))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f185,f211])).
% 14.41/2.37 fof(f233,plain,(
% 14.41/2.37 ![X0,X1]: (and(not(not(X0)),X1)=and(X0,X1))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f210,f222])).
% 14.41/2.37 fof(f241,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(not(not(X0))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f233,f183])).
% 14.41/2.37 fof(f272,plain,(
% 14.41/2.37 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f164,f167])).
% 14.41/2.37 fof(f274,plain,(
% 14.41/2.37 ![X0,X1]: (equiv(X0,not(X1))=and(implies(X0,not(X1)),or(X1,X0)))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f198,f272])).
% 14.41/2.37 fof(f276,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|is_a_theorem(not(not(implies(X0,X1)))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f272,f241])).
% 14.41/2.37 fof(f278,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f272,f182])).
% 14.41/2.37 fof(f279,plain,(
% 14.41/2.37 ![X0]: (is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f272,f179])).
% 14.41/2.37 fof(f283,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f198,f278])).
% 14.41/2.37 fof(f284,plain,(
% 14.41/2.37 ![X0]: (~is_a_theorem(implies(X0,X0))|is_a_theorem(equiv(X0,X0)))),
% 14.41/2.37 inference(resolution,[status(thm)],[f279,f177])).
% 14.41/2.37 fof(f295,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(equiv(not(not(X0)),X1),implies(X0,X1))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f185,f283])).
% 14.41/2.37 fof(f394,plain,(
% 14.41/2.37 ![X0,X1,X2]: (and(implies(X0,not(X1)),X2)=not(or(and(X0,X1),not(X2))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f219,f210])).
% 14.41/2.37 fof(f405,plain,(
% 14.41/2.37 ![X0,X1,X2]: (and(implies(X0,not(X1)),X2)=and(not(and(X0,X1)),X2))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f211,f394])).
% 14.41/2.37 fof(f417,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(equiv(not(not(X0)),X1))|is_a_theorem(implies(X0,X1)))),
% 14.41/2.37 inference(resolution,[status(thm)],[f295,f177])).
% 14.41/2.37 fof(f605,plain,(
% 14.41/2.37 ![X0]: (is_a_theorem(not(not(implies(X0,and(X0,X0))))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f181,f241])).
% 14.41/2.37 fof(f638,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(or(not(implies(X0,and(X0,X0))),X1))|is_a_theorem(X1))),
% 14.41/2.37 inference(resolution,[status(thm)],[f605,f201])).
% 14.41/2.37 fof(f647,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(implies(implies(X0,and(X0,X0)),X1))|is_a_theorem(X1))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f185,f638])).
% 14.41/2.37 fof(f695,plain,(
% 14.41/2.37 ![X0,X1,X2]: (~kn3|is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f198,f121])).
% 14.41/2.37 fof(f696,plain,(
% 14.41/2.37 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))))),
% 14.41/2.37 inference(forward_subsumption_resolution,[status(thm)],[f695,f171])).
% 14.41/2.37 fof(f697,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(or(and(and(X0,X0),X1),not(and(X1,X0)))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f696,f647])).
% 14.41/2.37 fof(f705,plain,(
% 14.41/2.37 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0)))))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f198,f696])).
% 14.41/2.37 fof(f712,plain,(
% 14.41/2.37 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f188,f705])).
% 14.41/2.37 fof(f789,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(not(not(implies(and(X0,X1),X0)))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f184,f241])).
% 14.41/2.37 fof(f810,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(not(and(and(not(X0),X1),X0))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f210,f789])).
% 14.41/2.37 fof(f820,plain,(
% 14.41/2.37 ![X0,X1,X2]: (~is_a_theorem(or(and(and(not(X0),X1),X0),X2))|is_a_theorem(X2))),
% 14.41/2.37 inference(resolution,[status(thm)],[f810,f201])).
% 14.41/2.37 fof(f906,plain,(
% 14.41/2.37 ![X0]: (is_a_theorem(not(and(X0,not(X0)))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f820,f697])).
% 14.41/2.37 fof(f914,plain,(
% 14.41/2.37 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f188,f906])).
% 14.41/2.37 fof(f917,plain,(
% 14.41/2.37 ![X0]: (is_a_theorem(equiv(X0,X0)))),
% 14.41/2.37 inference(backward_subsumption_resolution,[status(thm)],[f284,f914])).
% 14.41/2.37 fof(f929,plain,(
% 14.41/2.37 ![X0]: (is_a_theorem(implies(X0,not(not(X0)))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f917,f417])).
% 14.41/2.37 fof(f933,plain,(
% 14.41/2.37 ![X0]: (is_a_theorem(not(not(implies(X0,X0)))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f917,f276])).
% 14.41/2.37 fof(f960,plain,(
% 14.41/2.37 ![X0]: (~is_a_theorem(X0)|is_a_theorem(not(not(X0))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f929,f177])).
% 14.41/2.37 fof(f990,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(or(not(implies(X0,X0)),X1))|is_a_theorem(X1))),
% 14.41/2.37 inference(resolution,[status(thm)],[f933,f201])).
% 14.41/2.37 fof(f998,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(implies(implies(X0,X0),X1))|is_a_theorem(X1))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f185,f990])).
% 14.41/2.37 fof(f1107,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(or(and(X0,X1),not(and(X1,X0)))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f998,f696])).
% 14.41/2.37 fof(f1263,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(or(and(X0,X1),not(and(X1,not(not(X0)))))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f233,f1107])).
% 14.41/2.37 fof(f1264,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(or(and(not(X0),X1),implies(X1,X0))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f188,f1107])).
% 14.41/2.37 fof(f1272,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f188,f1263])).
% 14.41/2.37 fof(f1541,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(X0,not(and(not(X0),X1)))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f1272,f820])).
% 14.41/2.37 fof(f1547,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(not(X1),not(X0)))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f199,f1272])).
% 14.41/2.37 fof(f1556,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f198,f1547])).
% 14.41/2.37 fof(f1573,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(X0,implies(not(X0),X1))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f188,f1541])).
% 14.41/2.37 fof(f1586,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1))))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f198,f1573])).
% 14.41/2.37 fof(f1606,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(or(X0,or(not(X0),X1))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f198,f1586])).
% 14.41/2.37 fof(f1612,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(or(X0,implies(X0,X1))))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f185,f1606])).
% 14.41/2.37 fof(f1820,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(not(not(or(X0,implies(X0,X1))))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f1612,f960])).
% 14.41/2.37 fof(f2582,plain,(
% 14.41/2.37 ![X0,X1,X2]: (~is_a_theorem(or(not(or(X0,implies(X0,X1))),X2))|is_a_theorem(X2))),
% 14.41/2.37 inference(resolution,[status(thm)],[f1820,f201])).
% 14.41/2.37 fof(f2598,plain,(
% 14.41/2.37 ![X0,X1,X2]: (~is_a_theorem(implies(or(X0,implies(X0,X1)),X2))|is_a_theorem(X2))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f185,f2582])).
% 14.41/2.37 fof(f2639,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),X1),implies(not(X1),X0))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f199,f1264])).
% 14.41/2.37 fof(f2651,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),implies(not(X1),X0))))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f198,f2639])).
% 14.41/2.37 fof(f2652,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f198,f2651])).
% 14.41/2.37 fof(f2676,plain,(
% 14.41/2.37 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f185,f2652])).
% 14.41/2.37 fof(f5384,plain,(
% 14.41/2.37 ![X0,X1]: (~is_a_theorem(or(X0,not(X1)))|is_a_theorem(implies(X1,X0)))),
% 14.41/2.37 inference(resolution,[status(thm)],[f2676,f177])).
% 14.41/2.37 fof(f10038,plain,(
% 14.41/2.37 ![X0,X1,X2]: (is_a_theorem(or(and(implies(X0,X1),X2),implies(X2,X0))))),
% 14.41/2.37 inference(resolution,[status(thm)],[f2598,f712])).
% 14.41/2.37 fof(f12460,plain,(
% 14.41/2.37 ![X0,X1]: (equiv(X0,not(X1))=and(not(and(X0,X1)),or(X1,X0)))),
% 14.41/2.37 inference(backward_demodulation,[status(thm)],[f405,f274])).
% 14.41/2.37 fof(f13145,plain,(
% 14.41/2.37 ![X0,X1]: (equiv(X0,not(not(X1)))=and(implies(X0,X1),or(not(X1),X0)))),
% 14.41/2.37 inference(paramodulation,[status(thm)],[f188,f12460])).
% 14.41/2.37 fof(f13224,plain,(
% 14.41/2.37 ![X0,X1]: (equiv(X0,not(not(X1)))=and(implies(X0,X1),implies(X1,X0)))),
% 14.41/2.37 inference(forward_demodulation,[status(thm)],[f185,f13145])).
% 14.41/2.37 fof(f13225,plain,(
% 14.41/2.37 ![X0,X1]: (equiv(X0,not(not(X1)))=equiv(X0,X1))),
% 14.41/2.39 inference(forward_demodulation,[status(thm)],[f272,f13224])).
% 14.41/2.39 fof(f13349,plain,(
% 14.41/2.39 ![X0]: (is_a_theorem(equiv(not(not(X0)),X0)))),
% 14.41/2.39 inference(paramodulation,[status(thm)],[f13225,f917])).
% 14.41/2.39 fof(f13415,plain,(
% 14.41/2.39 ![X0]: (not(not(X0))=X0)),
% 14.41/2.39 inference(resolution,[status(thm)],[f13349,f178])).
% 14.41/2.39 fof(f18804,plain,(
% 14.41/2.39 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X2),X0))))),
% 14.41/2.39 inference(paramodulation,[status(thm)],[f199,f10038])).
% 14.41/2.39 fof(f18831,plain,(
% 14.41/2.39 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(X0,X1),X2),or(X2,X0))))),
% 14.41/2.39 inference(forward_demodulation,[status(thm)],[f198,f18804])).
% 14.41/2.39 fof(f28806,plain,(
% 14.41/2.39 ![X0,X1,X2]: (~is_a_theorem(implies(implies(X0,X1),X2))|is_a_theorem(or(X2,X0)))),
% 14.41/2.39 inference(resolution,[status(thm)],[f18831,f177])).
% 14.41/2.39 fof(f33921,plain,(
% 14.41/2.39 ![X0,X1]: (is_a_theorem(or(or(X0,not(X1)),X1)))),
% 14.41/2.39 inference(resolution,[status(thm)],[f28806,f1556])).
% 14.41/2.39 fof(f34046,plain,(
% 14.41/2.39 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,not(not(X0))))))),
% 14.41/2.39 inference(resolution,[status(thm)],[f33921,f5384])).
% 14.41/2.39 fof(f34075,plain,(
% 14.41/2.39 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 14.41/2.39 inference(forward_demodulation,[status(thm)],[f13415,f34046])).
% 14.41/2.39 fof(f34087,plain,(
% 14.41/2.39 $false),
% 14.41/2.39 inference(backward_subsumption_resolution,[status(thm)],[f187,f34075])).
% 14.41/2.39 % SZS output end CNFRefutation for theBenchmark.p
% 2.97/2.42 % Elapsed time: 1.967369 seconds
% 2.97/2.42 % CPU time: 15.203039 seconds
% 2.97/2.42 % Total memory used: 335.069 MB
% 2.97/2.42 % Net memory used: 324.842 MB
%------------------------------------------------------------------------------