%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL485+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 01:10:09 PM UTC 2026
% Result : Theorem 107.21s 13.92s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL485+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:36:52 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 107.21/13.92 % Refutation found
% 107.21/13.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 107.21/13.92 % SZS output start CNFRefutation for theBenchmark
% 107.21/13.92 fof(f1,axiom,(
% 107.21/13.92 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f5,axiom,(
% 107.21/13.92 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f19,axiom,(
% 107.21/13.92 ( cn1<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f22,axiom,(
% 107.21/13.92 ( r1<=> (! [P] : is_a_theorem(implies(or(P,P),P)) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f23,axiom,(
% 107.21/13.92 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f24,axiom,(
% 107.21/13.92 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f25,axiom,(
% 107.21/13.92 ( r4<=> (! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f26,axiom,(
% 107.21/13.92 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f27,axiom,(
% 107.21/13.92 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f28,axiom,(
% 107.21/13.92 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f29,axiom,(
% 107.21/13.92 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f30,axiom,(
% 107.21/13.92 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f32,axiom,(
% 107.21/13.92 op_implies_or ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f33,axiom,(
% 107.21/13.92 op_and ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f35,axiom,(
% 107.21/13.92 modus_ponens ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f36,axiom,(
% 107.21/13.92 r1 ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f37,axiom,(
% 107.21/13.92 r2 ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f38,axiom,(
% 107.21/13.92 r3 ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f39,axiom,(
% 107.21/13.92 r4 ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f40,axiom,(
% 107.21/13.92 r5 ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f42,axiom,(
% 107.21/13.92 op_or ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f43,axiom,(
% 107.21/13.92 op_implies_and ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f45,conjecture,(
% 107.21/13.92 implies_2 ),
% 107.21/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 107.21/13.92 fof(f46,negated_conjecture,(
% 107.21/13.92 ~(implies_2 )),
% 107.21/13.92 inference(negated_conjecture,[status(cth)],[f45])).
% 107.21/13.92 fof(f47,plain,(
% 107.21/13.92 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 107.21/13.92 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 107.21/13.92 fof(f48,plain,(
% 107.21/13.92 (~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))))),
% 107.21/13.92 inference(NNF_transformation,[status(thm)],[f47])).
% 107.21/13.92 fof(f49,plain,(
% 107.21/13.92 (~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))))),
% 107.21/13.92 inference(miniscoping,[status(thm)],[f48])).
% 107.21/13.92 fof(f50,plain,(
% 107.21/13.92 (~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)))),
% 107.21/13.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f49])).
% 107.21/13.92 fof(f51,plain,(
% 107.21/13.92 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f50])).
% 107.21/13.92 fof(f69,plain,(
% 107.21/13.92 (~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)))))),
% 107.21/13.92 inference(NNF_transformation,[status(thm)],[f5])).
% 107.21/13.92 fof(f70,plain,(
% 107.21/13.92 (~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))))),
% 107.21/13.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f69])).
% 107.21/13.92 fof(f72,plain,(
% 107.21/13.92 implies_2|~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl)))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f70])).
% 107.21/13.92 fof(f125,plain,(
% 107.21/13.92 (~cn1|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))&(cn1|(?[P,Q,R]: ~is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))),
% 107.21/13.92 inference(NNF_transformation,[status(thm)],[f19])).
% 107.21/13.92 fof(f126,plain,(
% 107.21/13.92 (~cn1|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))&(cn1|~is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl)))))),
% 107.21/13.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl,sK39_skl,sK40_skl]),skolemize(P,sK38_skl),skolemize(Q,sK39_skl),skolemize(R,sK40_skl)],[f125])).
% 107.21/13.92 fof(f127,plain,(
% 107.21/13.92 ![X0,X1,X2]: (~cn1|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f126])).
% 107.21/13.92 fof(f128,plain,(
% 107.21/13.92 cn1|~is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl))))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f126])).
% 107.21/13.92 fof(f137,plain,(
% 107.21/13.92 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|(?[P]: ~is_a_theorem(implies(or(P,P),P))))),
% 107.21/13.92 inference(NNF_transformation,[status(thm)],[f22])).
% 107.21/13.92 fof(f138,plain,(
% 107.21/13.92 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)))),
% 107.21/13.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(P,sK44_skl)],[f137])).
% 107.21/13.92 fof(f139,plain,(
% 107.21/13.92 ![X0]: (~r1|is_a_theorem(implies(or(X0,X0),X0)))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f138])).
% 107.21/13.92 fof(f141,plain,(
% 107.21/13.92 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 107.21/13.92 inference(NNF_transformation,[status(thm)],[f23])).
% 107.21/13.92 fof(f142,plain,(
% 107.21/13.92 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))))),
% 107.21/13.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(P,sK45_skl),skolemize(Q,sK46_skl)],[f141])).
% 107.21/13.92 fof(f143,plain,(
% 107.21/13.92 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f142])).
% 107.21/13.92 fof(f145,plain,(
% 107.21/13.92 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|(?[P,Q]: ~is_a_theorem(implies(or(P,Q),or(Q,P)))))),
% 107.21/13.92 inference(NNF_transformation,[status(thm)],[f24])).
% 107.21/13.92 fof(f146,plain,(
% 107.21/13.92 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))))),
% 107.21/13.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f145])).
% 107.21/13.92 fof(f147,plain,(
% 107.21/13.92 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f146])).
% 107.21/13.92 fof(f149,plain,(
% 107.21/13.92 (~r4|(![P,Q,R]: is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))&(r4|(?[P,Q,R]: ~is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))),
% 107.21/13.92 inference(NNF_transformation,[status(thm)],[f25])).
% 107.21/13.92 fof(f150,plain,(
% 107.21/13.92 (~r4|(![P,Q,R]: is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))&(r4|~is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl)))))),
% 107.21/13.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK49_skl,sK50_skl,sK51_skl]),skolemize(P,sK49_skl),skolemize(Q,sK50_skl),skolemize(R,sK51_skl)],[f149])).
% 107.21/13.92 fof(f151,plain,(
% 107.21/13.92 ![X0,X1,X2]: (~r4|is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f150])).
% 107.21/13.92 fof(f153,plain,(
% 107.21/13.92 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|(?[P,Q,R]: ~is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))),
% 107.21/13.92 inference(NNF_transformation,[status(thm)],[f26])).
% 107.21/13.92 fof(f154,plain,(
% 107.21/13.92 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|~is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl)))))),
% 107.21/13.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl]),skolemize(P,sK52_skl),skolemize(Q,sK53_skl),skolemize(R,sK54_skl)],[f153])).
% 107.21/13.92 fof(f155,plain,(
% 107.21/13.92 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f154])).
% 107.21/13.92 fof(f157,plain,(
% 107.21/13.92 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 107.21/13.92 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 107.21/13.92 fof(f158,plain,(
% 107.21/13.92 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f157])).
% 107.21/13.92 fof(f159,plain,(
% 107.21/13.92 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 107.21/13.92 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 107.21/13.92 fof(f160,plain,(
% 107.21/13.92 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f159])).
% 107.21/13.92 fof(f161,plain,(
% 107.21/13.92 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 107.21/13.92 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 107.21/13.92 fof(f162,plain,(
% 107.21/13.92 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f161])).
% 107.21/13.92 fof(f163,plain,(
% 107.21/13.92 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 107.21/13.92 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 107.21/13.92 fof(f164,plain,(
% 107.21/13.92 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f163])).
% 107.21/13.92 fof(f167,plain,(
% 107.21/13.92 op_implies_or),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f32])).
% 107.21/13.92 fof(f168,plain,(
% 107.21/13.92 op_and),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f33])).
% 107.21/13.92 fof(f170,plain,(
% 107.21/13.92 modus_ponens),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f35])).
% 107.21/13.92 fof(f171,plain,(
% 107.21/13.92 r1),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f36])).
% 107.21/13.92 fof(f172,plain,(
% 107.21/13.92 r2),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f37])).
% 107.21/13.92 fof(f173,plain,(
% 107.21/13.92 r3),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f38])).
% 107.21/13.92 fof(f174,plain,(
% 107.21/13.92 r4),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f39])).
% 107.21/13.92 fof(f175,plain,(
% 107.21/13.92 r5),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f40])).
% 107.21/13.92 fof(f177,plain,(
% 107.21/13.92 op_or),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f42])).
% 107.21/13.92 fof(f178,plain,(
% 107.21/13.92 op_implies_and),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f43])).
% 107.21/13.92 fof(f180,plain,(
% 107.21/13.92 ~implies_2),
% 107.21/13.92 inference(cnf_transformation,[status(thm)],[f46])).
% 107.21/13.92 fof(f181,plain,(
% 107.21/13.92 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 107.21/13.92 inference(backward_subsumption_resolution,[status(thm)],[f51,f170])).
% 107.21/13.92 fof(f183,plain,(
% 107.21/13.92 ~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl)))),
% 107.21/13.92 inference(forward_subsumption_resolution,[status(thm)],[f72,f180])).
% 107.21/13.92 fof(f185,plain,(
% 107.21/13.92 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 107.21/13.92 inference(forward_subsumption_resolution,[status(thm)],[f139,f171])).
% 107.21/13.92 fof(f187,plain,(
% 107.21/13.92 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 107.21/13.92 inference(forward_subsumption_resolution,[status(thm)],[f143,f172])).
% 107.21/13.92 fof(f188,plain,(
% 107.21/13.92 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 107.21/13.92 inference(forward_subsumption_resolution,[status(thm)],[f164,f167])).
% 107.21/13.92 fof(f189,plain,(
% 107.21/13.92 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f188,f187])).
% 107.21/13.92 fof(f195,plain,(
% 107.21/13.92 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 107.21/13.92 inference(forward_subsumption_resolution,[status(thm)],[f147,f173])).
% 107.21/13.92 fof(f196,plain,(
% 107.21/13.92 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0)))),
% 107.21/13.92 inference(resolution,[status(thm)],[f195,f181])).
% 107.21/13.92 fof(f197,plain,(
% 107.21/13.92 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f188,f195])).
% 107.21/13.92 fof(f199,plain,(
% 107.21/13.92 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 107.21/13.92 inference(forward_subsumption_resolution,[status(thm)],[f151,f174])).
% 107.21/13.92 fof(f200,plain,(
% 107.21/13.92 ![X0,X1,X2]: (~is_a_theorem(or(X0,or(X1,X2)))|is_a_theorem(or(X1,or(X0,X2))))),
% 107.21/13.92 inference(resolution,[status(thm)],[f199,f181])).
% 107.21/13.92 fof(f210,plain,(
% 107.21/13.92 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 107.21/13.92 inference(forward_subsumption_resolution,[status(thm)],[f155,f175])).
% 107.21/13.92 fof(f211,plain,(
% 107.21/13.92 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X2,X0),or(X2,X1))))),
% 107.21/13.92 inference(resolution,[status(thm)],[f210,f181])).
% 107.21/13.92 fof(f212,plain,(
% 107.21/13.92 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f188,f210])).
% 107.21/13.92 fof(f214,plain,(
% 107.21/13.92 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))))),
% 107.21/13.92 inference(forward_demodulation,[status(thm)],[f188,f212])).
% 107.21/13.92 fof(f225,plain,(
% 107.21/13.92 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 107.21/13.92 inference(forward_subsumption_resolution,[status(thm)],[f158,f177])).
% 107.21/13.92 fof(f229,plain,(
% 107.21/13.92 ![X0,X1]: (~op_and|and(X0,X1)=not(implies(X0,not(X1))))),
% 107.21/13.92 inference(forward_demodulation,[status(thm)],[f188,f160])).
% 107.21/13.92 fof(f230,plain,(
% 107.21/13.92 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1))))),
% 107.21/13.92 inference(forward_subsumption_resolution,[status(thm)],[f229,f168])).
% 107.21/13.92 fof(f234,plain,(
% 107.21/13.92 ![X0,X1,X2]: (or(implies(X0,not(X1)),X2)=not(and(and(X0,X1),not(X2))))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f230,f225])).
% 107.21/13.92 fof(f235,plain,(
% 107.21/13.92 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(and(X0,X1),X2))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f230,f188])).
% 107.21/13.92 fof(f236,plain,(
% 107.21/13.92 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 107.21/13.92 inference(backward_demodulation,[status(thm)],[f237,f225])).
% 107.21/13.92 fof(f237,plain,(
% 107.21/13.92 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 107.21/13.92 inference(forward_subsumption_resolution,[status(thm)],[f162,f178])).
% 107.21/13.92 fof(f241,plain,(
% 107.21/13.92 ![X0,X1,X2]: (implies(and(X0,not(X1)),X2)=or(implies(X0,X1),X2))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f237,f188])).
% 107.21/13.92 fof(f251,plain,(
% 107.21/13.92 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f237,f236])).
% 107.21/13.92 fof(f253,plain,(
% 107.21/13.92 ![X0,X1]: (is_a_theorem(or(X0,implies(X1,not(X0)))))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f236,f189])).
% 107.21/13.92 fof(f289,plain,(
% 107.21/13.92 ![X0,X1]: (is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f188,f197])).
% 107.21/13.92 fof(f315,plain,(
% 107.21/13.92 ![X0,X1,X2]: (~is_a_theorem(or(X0,or(not(X1),X2)))|is_a_theorem(implies(X1,or(X0,X2))))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f188,f200])).
% 107.21/13.92 fof(f317,plain,(
% 107.21/13.92 ![X0,X1,X2]: (~is_a_theorem(or(X0,implies(X1,X2)))|is_a_theorem(implies(X1,or(X0,X2))))),
% 107.21/13.92 inference(forward_demodulation,[status(thm)],[f188,f315])).
% 107.21/13.92 fof(f339,plain,(
% 107.21/13.92 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(or(X2,X0))|is_a_theorem(or(X2,X1)))),
% 107.21/13.92 inference(resolution,[status(thm)],[f211,f181])).
% 107.21/13.92 fof(f576,plain,(
% 107.21/13.92 ![X0,X1,X2]: (or(implies(X0,not(X1)),X2)=implies(and(X0,X1),X2))),
% 107.21/13.92 inference(forward_demodulation,[status(thm)],[f237,f234])).
% 107.21/13.92 fof(f605,plain,(
% 107.21/13.92 ![X0,X1,X2]: (~is_a_theorem(or(X0,implies(X1,not(X2))))|is_a_theorem(implies(and(X1,X2),X0)))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f576,f196])).
% 107.21/13.92 fof(f1309,plain,(
% 107.21/13.92 ![X0,X1]: (is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))))),
% 107.21/13.92 inference(forward_demodulation,[status(thm)],[f235,f289])).
% 107.21/13.92 fof(f1502,plain,(
% 107.21/13.92 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(X0,X1),implies(X2,X3)))|is_a_theorem(implies(X2,or(and(X0,not(X1)),X3))))),
% 107.21/13.92 inference(paramodulation,[status(thm)],[f251,f317])).
% 107.21/13.92 fof(f1510,plain,(
% 107.21/13.92 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(X0,X1),implies(X2,X3)))|is_a_theorem(implies(X2,implies(implies(X0,X1),X3))))),
% 107.21/13.92 inference(forward_demodulation,[status(thm)],[f251,f1502])).
% 71.57/14.08 fof(f9454,plain,(
% 71.57/14.08 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),and(X1,X0))))),
% 71.57/14.08 inference(resolution,[status(thm)],[f605,f1309])).
% 71.57/14.08 fof(f9456,plain,(
% 71.57/14.08 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1)))),
% 71.57/14.08 inference(resolution,[status(thm)],[f605,f253])).
% 71.57/14.08 fof(f20692,plain,(
% 71.57/14.08 ![X0,X1]: (is_a_theorem(or(implies(X0,X1),and(not(X1),X0))))),
% 71.57/14.08 inference(paramodulation,[status(thm)],[f241,f9454])).
% 71.57/14.08 fof(f72254,plain,(
% 71.57/14.08 ~is_a_theorem(implies(implies(sK39_skl,sK40_skl),implies(implies(sK38_skl,sK39_skl),implies(sK38_skl,sK40_skl))))|cn1),
% 71.57/14.08 inference(resolution,[status(thm)],[f1510,f128])).
% 71.57/14.08 fof(f72270,plain,(
% 71.57/14.08 cn1),
% 71.57/14.08 inference(forward_subsumption_resolution,[status(thm)],[f72254,f214])).
% 71.57/14.08 fof(f72653,plain,(
% 71.57/14.08 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 71.57/14.08 inference(backward_subsumption_resolution,[status(thm)],[f127,f72270])).
% 71.57/14.08 fof(f72656,plain,(
% 71.57/14.08 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X2),implies(X0,X2))))),
% 71.57/14.08 inference(resolution,[status(thm)],[f72653,f181])).
% 71.57/14.08 fof(f72704,plain,(
% 71.57/14.08 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(X0,X2)))),
% 71.57/14.08 inference(resolution,[status(thm)],[f72656,f181])).
% 71.57/14.08 fof(f72713,plain,(
% 71.57/14.08 ![X0,X1,X2]: (~is_a_theorem(implies(not(X0),X1))|is_a_theorem(implies(implies(X1,X2),or(X0,X2))))),
% 71.57/14.08 inference(paramodulation,[status(thm)],[f236,f72656])).
% 71.57/14.08 fof(f72723,plain,(
% 71.57/14.08 ![X0,X1,X2]: (~is_a_theorem(or(X0,X1))|is_a_theorem(implies(implies(X1,X2),or(X0,X2))))),
% 71.57/14.08 inference(forward_demodulation,[status(thm)],[f236,f72713])).
% 71.57/14.08 fof(f73085,plain,(
% 71.57/14.08 ![X0]: (~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),X0))|~is_a_theorem(implies(X0,implies(sK8_skl,sK9_skl))))),
% 71.57/14.08 inference(resolution,[status(thm)],[f72704,f183])).
% 71.57/14.08 fof(f73477,plain,(
% 71.57/14.08 ~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),or(implies(sK8_skl,sK9_skl),implies(sK8_skl,sK9_skl))))),
% 71.57/14.08 inference(resolution,[status(thm)],[f73085,f185])).
% 71.57/14.08 fof(f73866,plain,(
% 71.57/14.08 ~is_a_theorem(or(implies(sK8_skl,sK9_skl),sK8_skl))),
% 71.57/14.08 inference(resolution,[status(thm)],[f73477,f72723])).
% 71.57/14.08 fof(f73876,plain,(
% 71.57/14.08 ![X0]: (~is_a_theorem(implies(X0,sK8_skl))|~is_a_theorem(or(implies(sK8_skl,sK9_skl),X0)))),
% 71.57/14.08 inference(resolution,[status(thm)],[f73866,f339])).
% 71.57/14.08 fof(f78323,plain,(
% 71.57/14.08 ![X0]: (~is_a_theorem(or(implies(sK8_skl,sK9_skl),and(X0,sK8_skl))))),
% 71.57/14.08 inference(resolution,[status(thm)],[f73876,f9456])).
% 71.57/14.08 fof(f164746,plain,(
% 71.57/14.08 $false),
% 71.57/14.08 inference(resolution,[status(thm)],[f78323,f20692])).
% 71.57/14.08 % SZS output end CNFRefutation for theBenchmark.p
% 14.84/14.16 % Elapsed time: 13.758887 seconds
% 14.84/14.16 % CPU time: 108.614643 seconds
% 14.84/14.16 % Total memory used: 1.320 GB
% 14.84/14.16 % Net memory used: 1.271 GB
%------------------------------------------------------------------------------