%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL495+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 : n011.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 01:10:10 PM UTC 2026
% Result : Theorem 73.04s 24.95s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL495+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.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
% 0.16/15.68 % CPULimit : 300
% 0.16/15.68 % WCLimit : 300
% 0.16/15.68 % DateTime : Mon Sep 21 00:36:55 UTC 2026
% 0.16/15.69 % CPUTime :
% 0.58/15.71 % Drodi V4.1.1
% 73.04/24.95 % Refutation found
% 73.04/24.95 % SZS status Theorem for theBenchmark: Theorem is valid
% 73.04/24.95 % SZS output start CNFRefutation for theBenchmark
% 73.04/24.95 fof(f1,axiom,(
% 73.04/24.95 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f2,axiom,(
% 73.04/24.95 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f15,axiom,(
% 73.04/24.95 ( equivalence_3<=> (! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f19,axiom,(
% 73.04/24.95 ( cn1<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f22,axiom,(
% 73.04/24.95 ( r1<=> (! [P] : is_a_theorem(implies(or(P,P),P)) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f23,axiom,(
% 73.04/24.95 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f24,axiom,(
% 73.04/24.95 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f25,axiom,(
% 73.04/24.95 ( r4<=> (! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f26,axiom,(
% 73.04/24.95 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f27,axiom,(
% 73.04/24.95 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f28,axiom,(
% 73.04/24.95 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f29,axiom,(
% 73.04/24.95 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f30,axiom,(
% 73.04/24.95 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f31,axiom,(
% 73.04/24.95 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f32,axiom,(
% 73.04/24.95 op_implies_or ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f33,axiom,(
% 73.04/24.95 op_and ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f34,axiom,(
% 73.04/24.95 op_equiv ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f35,axiom,(
% 73.04/24.95 modus_ponens ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f36,axiom,(
% 73.04/24.95 r1 ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f37,axiom,(
% 73.04/24.95 r2 ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f38,axiom,(
% 73.04/24.95 r3 ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f39,axiom,(
% 73.04/24.95 r4 ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f40,axiom,(
% 73.04/24.95 r5 ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f41,axiom,(
% 73.04/24.95 substitution_of_equivalents ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f42,axiom,(
% 73.04/24.95 op_or ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f43,axiom,(
% 73.04/24.95 op_implies_and ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f45,conjecture,(
% 73.04/24.95 equivalence_3 ),
% 73.04/24.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 73.04/24.95 fof(f46,negated_conjecture,(
% 73.04/24.95 ~(equivalence_3 )),
% 73.04/24.95 inference(negated_conjecture,[status(cth)],[f45])).
% 73.04/24.95 fof(f47,plain,(
% 73.04/24.95 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 73.04/24.95 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 73.04/24.95 fof(f48,plain,(
% 73.04/24.95 (~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))))),
% 73.04/24.95 inference(NNF_transformation,[status(thm)],[f47])).
% 73.04/24.95 fof(f49,plain,(
% 73.04/24.95 (~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))))),
% 73.04/24.95 inference(miniscoping,[status(thm)],[f48])).
% 73.04/24.95 fof(f50,plain,(
% 73.04/24.95 (~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)))),
% 73.04/24.95 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f49])).
% 73.04/24.95 fof(f51,plain,(
% 73.04/24.95 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f50])).
% 73.04/24.95 fof(f55,plain,(
% 73.04/24.95 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 73.04/24.95 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 73.04/24.95 fof(f56,plain,(
% 73.04/24.95 (~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)))),
% 73.04/24.95 inference(NNF_transformation,[status(thm)],[f55])).
% 73.04/24.95 fof(f57,plain,(
% 73.04/24.95 (~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))),
% 73.04/24.95 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f56])).
% 73.04/24.95 fof(f58,plain,(
% 73.04/24.95 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f57])).
% 73.04/24.95 fof(f109,plain,(
% 73.04/24.95 (~equivalence_3|(![X,Y]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))))&(equivalence_3|(?[X,Y]: ~is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))))),
% 73.04/24.95 inference(NNF_transformation,[status(thm)],[f15])).
% 73.04/24.95 fof(f110,plain,(
% 73.04/24.95 (~equivalence_3|(![X,Y]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))))&(equivalence_3|~is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl)))))),
% 73.04/24.95 inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(X,sK30_skl),skolemize(Y,sK31_skl)],[f109])).
% 73.04/24.95 fof(f112,plain,(
% 73.04/24.95 equivalence_3|~is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl))))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f110])).
% 73.04/24.95 fof(f125,plain,(
% 73.04/24.95 (~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))))))),
% 73.04/24.95 inference(NNF_transformation,[status(thm)],[f19])).
% 73.04/24.95 fof(f126,plain,(
% 73.04/24.95 (~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)))))),
% 73.04/24.95 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])).
% 73.04/24.95 fof(f127,plain,(
% 73.04/24.95 ![X0,X1,X2]: (~cn1|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f126])).
% 73.04/24.95 fof(f128,plain,(
% 73.04/24.95 cn1|~is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl))))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f126])).
% 73.04/24.95 fof(f137,plain,(
% 73.04/24.95 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|(?[P]: ~is_a_theorem(implies(or(P,P),P))))),
% 73.04/24.95 inference(NNF_transformation,[status(thm)],[f22])).
% 73.04/24.95 fof(f138,plain,(
% 73.04/24.95 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)))),
% 73.04/24.95 inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(P,sK44_skl)],[f137])).
% 73.04/24.95 fof(f139,plain,(
% 73.04/24.95 ![X0]: (~r1|is_a_theorem(implies(or(X0,X0),X0)))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f138])).
% 73.04/24.95 fof(f141,plain,(
% 73.04/24.95 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 73.04/24.95 inference(NNF_transformation,[status(thm)],[f23])).
% 73.04/24.95 fof(f142,plain,(
% 73.04/24.95 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))))),
% 73.04/24.95 inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(P,sK45_skl),skolemize(Q,sK46_skl)],[f141])).
% 73.04/24.95 fof(f143,plain,(
% 73.04/24.95 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f142])).
% 73.04/24.95 fof(f145,plain,(
% 73.04/24.95 (~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)))))),
% 73.04/24.95 inference(NNF_transformation,[status(thm)],[f24])).
% 73.04/24.95 fof(f146,plain,(
% 73.04/24.95 (~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))))),
% 73.04/24.95 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f145])).
% 73.04/24.95 fof(f147,plain,(
% 73.04/24.95 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f146])).
% 73.04/24.95 fof(f149,plain,(
% 73.04/24.95 (~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))))))),
% 73.04/24.95 inference(NNF_transformation,[status(thm)],[f25])).
% 73.04/24.95 fof(f150,plain,(
% 73.04/24.95 (~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)))))),
% 73.04/24.95 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])).
% 73.04/24.95 fof(f151,plain,(
% 73.04/24.95 ![X0,X1,X2]: (~r4|is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f150])).
% 73.04/24.95 fof(f153,plain,(
% 73.04/24.95 (~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))))))),
% 73.04/24.95 inference(NNF_transformation,[status(thm)],[f26])).
% 73.04/24.95 fof(f154,plain,(
% 73.04/24.95 (~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)))))),
% 73.04/24.95 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])).
% 73.04/24.95 fof(f155,plain,(
% 73.04/24.95 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f154])).
% 73.04/24.95 fof(f157,plain,(
% 73.04/24.95 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 73.04/24.95 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 73.04/24.95 fof(f158,plain,(
% 73.04/24.95 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f157])).
% 73.04/24.95 fof(f159,plain,(
% 73.04/24.95 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 73.04/24.95 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 73.04/24.95 fof(f160,plain,(
% 73.04/24.95 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f159])).
% 73.04/24.95 fof(f161,plain,(
% 73.04/24.95 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 73.04/24.95 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 73.04/24.95 fof(f162,plain,(
% 73.04/24.95 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f161])).
% 73.04/24.95 fof(f163,plain,(
% 73.04/24.95 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 73.04/24.95 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 73.04/24.95 fof(f164,plain,(
% 73.04/24.95 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f163])).
% 73.04/24.95 fof(f165,plain,(
% 73.04/24.95 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 73.04/24.95 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 73.04/24.95 fof(f166,plain,(
% 73.04/24.95 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f165])).
% 73.04/24.95 fof(f167,plain,(
% 73.04/24.95 op_implies_or),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f32])).
% 73.04/24.95 fof(f168,plain,(
% 73.04/24.95 op_and),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f33])).
% 73.04/24.95 fof(f169,plain,(
% 73.04/24.95 op_equiv),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f34])).
% 73.04/24.95 fof(f170,plain,(
% 73.04/24.95 modus_ponens),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f35])).
% 73.04/24.95 fof(f171,plain,(
% 73.04/24.95 r1),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f36])).
% 73.04/24.95 fof(f172,plain,(
% 73.04/24.95 r2),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f37])).
% 73.04/24.95 fof(f173,plain,(
% 73.04/24.95 r3),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f38])).
% 73.04/24.95 fof(f174,plain,(
% 73.04/24.95 r4),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f39])).
% 73.04/24.95 fof(f175,plain,(
% 73.04/24.95 r5),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f40])).
% 73.04/24.95 fof(f176,plain,(
% 73.04/24.95 substitution_of_equivalents),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f41])).
% 73.04/24.95 fof(f177,plain,(
% 73.04/24.95 op_or),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f42])).
% 73.04/24.95 fof(f178,plain,(
% 73.04/24.95 op_implies_and),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f43])).
% 73.04/24.95 fof(f180,plain,(
% 73.04/24.95 ~equivalence_3),
% 73.04/24.95 inference(cnf_transformation,[status(thm)],[f46])).
% 73.04/24.95 fof(f181,plain,(
% 73.04/24.95 ~is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl))))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f112,f180])).
% 73.04/24.95 fof(f182,plain,(
% 73.04/24.95 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 73.04/24.95 inference(backward_subsumption_resolution,[status(thm)],[f51,f170])).
% 73.04/24.95 fof(f184,plain,(
% 73.04/24.95 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 73.04/24.95 inference(backward_subsumption_resolution,[status(thm)],[f58,f176])).
% 73.04/24.95 fof(f185,plain,(
% 73.04/24.95 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f139,f171])).
% 73.04/24.95 fof(f187,plain,(
% 73.04/24.95 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f143,f172])).
% 73.04/24.95 fof(f188,plain,(
% 73.04/24.95 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f164,f167])).
% 73.04/24.95 fof(f189,plain,(
% 73.04/24.95 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f188,f187])).
% 73.04/24.95 fof(f190,plain,(
% 73.04/24.95 ![X0]: (is_a_theorem(implies(implies(X0,not(X0)),not(X0))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f188,f185])).
% 73.04/24.95 fof(f192,plain,(
% 73.04/24.95 ![X0]: (~is_a_theorem(or(X0,X0))|is_a_theorem(X0))),
% 73.04/24.95 inference(resolution,[status(thm)],[f182,f185])).
% 73.04/24.95 fof(f195,plain,(
% 73.04/24.95 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f147,f173])).
% 73.04/24.95 fof(f196,plain,(
% 73.04/24.95 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0)))),
% 73.04/24.95 inference(resolution,[status(thm)],[f195,f182])).
% 73.04/24.95 fof(f198,plain,(
% 73.04/24.95 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f188,f195])).
% 73.04/24.95 fof(f199,plain,(
% 73.04/24.95 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f151,f174])).
% 73.04/24.95 fof(f200,plain,(
% 73.04/24.95 ![X0,X1,X2]: (~is_a_theorem(or(X0,or(X1,X2)))|is_a_theorem(or(X1,or(X0,X2))))),
% 73.04/24.95 inference(resolution,[status(thm)],[f199,f182])).
% 73.04/24.95 fof(f210,plain,(
% 73.04/24.95 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f155,f175])).
% 73.04/24.95 fof(f211,plain,(
% 73.04/24.95 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X2,X0),or(X2,X1))))),
% 73.04/24.95 inference(resolution,[status(thm)],[f210,f182])).
% 73.04/24.95 fof(f212,plain,(
% 73.04/24.95 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f188,f210])).
% 73.04/24.95 fof(f214,plain,(
% 73.04/24.95 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))))),
% 73.04/24.95 inference(forward_demodulation,[status(thm)],[f188,f212])).
% 73.04/24.95 fof(f225,plain,(
% 73.04/24.95 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f158,f177])).
% 73.04/24.95 fof(f229,plain,(
% 73.04/24.95 ![X0,X1]: (~op_and|and(X0,X1)=not(implies(X0,not(X1))))),
% 73.04/24.95 inference(forward_demodulation,[status(thm)],[f188,f160])).
% 73.04/24.95 fof(f230,plain,(
% 73.04/24.95 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1))))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f229,f168])).
% 73.04/24.95 fof(f235,plain,(
% 73.04/24.95 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(and(X0,X1),X2))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f230,f188])).
% 73.04/24.95 fof(f236,plain,(
% 73.04/24.95 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 73.04/24.95 inference(backward_demodulation,[status(thm)],[f237,f225])).
% 73.04/24.95 fof(f237,plain,(
% 73.04/24.95 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f162,f178])).
% 73.04/24.95 fof(f251,plain,(
% 73.04/24.95 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f237,f236])).
% 73.04/24.95 fof(f252,plain,(
% 73.04/24.95 ![X0,X1]: (and(not(X0),X1)=not(or(X0,not(X1))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f236,f230])).
% 73.04/24.95 fof(f253,plain,(
% 73.04/24.95 ![X0,X1]: (is_a_theorem(or(X0,implies(X1,not(X0)))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f236,f189])).
% 73.04/24.95 fof(f254,plain,(
% 73.04/24.95 ![X0,X1]: (is_a_theorem(or(X0,or(X1,not(X0)))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f236,f187])).
% 73.04/24.95 fof(f259,plain,(
% 73.04/24.95 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f166,f169])).
% 73.04/24.95 fof(f261,plain,(
% 73.04/24.95 ![X0,X1]: (equiv(X0,not(X1))=and(implies(X0,not(X1)),or(X1,X0)))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f236,f259])).
% 73.04/24.95 fof(f285,plain,(
% 73.04/24.95 ![X0,X1]: (~is_a_theorem(or(X0,not(X1)))|is_a_theorem(implies(X1,X0)))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f188,f196])).
% 73.04/24.95 fof(f313,plain,(
% 73.04/24.95 ![X0,X1]: (~is_a_theorem(or(X0,or(or(X0,X1),X1)))|is_a_theorem(or(X0,X1)))),
% 73.04/24.95 inference(resolution,[status(thm)],[f200,f192])).
% 73.04/24.95 fof(f315,plain,(
% 73.04/24.95 ![X0,X1,X2]: (~is_a_theorem(or(X0,or(not(X1),X2)))|is_a_theorem(implies(X1,or(X0,X2))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f188,f200])).
% 73.04/24.95 fof(f317,plain,(
% 73.04/24.95 ![X0,X1,X2]: (~is_a_theorem(or(X0,implies(X1,X2)))|is_a_theorem(implies(X1,or(X0,X2))))),
% 73.04/24.95 inference(forward_demodulation,[status(thm)],[f188,f315])).
% 73.04/24.95 fof(f339,plain,(
% 73.04/24.95 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(or(X2,X0))|is_a_theorem(or(X2,X1)))),
% 73.04/24.95 inference(resolution,[status(thm)],[f211,f182])).
% 73.04/24.95 fof(f635,plain,(
% 73.04/24.95 ![X0]: (is_a_theorem(or(and(X0,X0),not(X0))))),
% 73.04/24.95 inference(backward_demodulation,[status(thm)],[f235,f190])).
% 73.04/24.95 fof(f649,plain,(
% 73.04/24.95 ![X0,X1,X2]: (and(implies(X0,not(X1)),X2)=not(or(and(X0,X1),not(X2))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f235,f230])).
% 73.04/24.95 fof(f1252,plain,(
% 73.04/24.95 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 73.04/24.95 inference(resolution,[status(thm)],[f285,f635])).
% 73.04/24.95 fof(f1343,plain,(
% 73.04/24.95 ![X0]: (is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f259,f1252])).
% 73.04/24.95 fof(f1461,plain,(
% 73.04/24.95 ![X0]: (is_a_theorem(or(X0,not(X0))))),
% 73.04/24.95 inference(resolution,[status(thm)],[f313,f254])).
% 73.04/24.95 fof(f1502,plain,(
% 73.04/24.95 ![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))))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f251,f317])).
% 73.04/24.95 fof(f1510,plain,(
% 73.04/24.95 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(X0,X1),implies(X2,X3)))|is_a_theorem(implies(X2,implies(implies(X0,X1),X3))))),
% 73.04/24.95 inference(forward_demodulation,[status(thm)],[f251,f1502])).
% 73.04/24.95 fof(f1576,plain,(
% 73.04/24.95 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 73.04/24.95 inference(resolution,[status(thm)],[f1461,f285])).
% 73.04/24.95 fof(f1608,plain,(
% 73.04/24.95 ![X0,X1,X2,X3]: (~is_a_theorem(implies(X0,implies(X1,X2)))|~is_a_theorem(or(X3,X0))|is_a_theorem(implies(X1,or(X3,X2))))),
% 73.04/24.95 inference(resolution,[status(thm)],[f339,f317])).
% 73.04/24.95 fof(f2259,plain,(
% 73.04/24.95 ![X0]: (~is_a_theorem(implies(X0,X0))|is_a_theorem(equiv(X0,X0)))),
% 73.04/24.95 inference(resolution,[status(thm)],[f1343,f182])).
% 73.04/24.95 fof(f2267,plain,(
% 73.04/24.95 ![X0]: (is_a_theorem(equiv(X0,X0)))),
% 73.04/24.95 inference(forward_subsumption_resolution,[status(thm)],[f2259,f1576])).
% 73.04/24.95 fof(f12387,plain,(
% 73.04/24.95 ![X0,X1]: (equiv(X0,not(X1))=and(not(and(X0,X1)),or(X1,X0)))),
% 73.04/24.95 inference(backward_demodulation,[status(thm)],[f12392,f261])).
% 73.04/24.95 fof(f12392,plain,(
% 73.04/24.95 ![X0,X1,X2]: (and(implies(X0,not(X1)),X2)=and(not(and(X0,X1)),X2))),
% 73.04/24.95 inference(forward_demodulation,[status(thm)],[f252,f649])).
% 73.04/24.95 fof(f12604,plain,(
% 73.04/24.95 ![X0,X1]: (equiv(X0,not(not(X1)))=and(implies(X0,X1),or(not(X1),X0)))),
% 73.04/24.95 inference(paramodulation,[status(thm)],[f237,f12387])).
% 73.04/24.95 fof(f12680,plain,(
% 73.04/24.95 ![X0,X1]: (equiv(X0,not(not(X1)))=and(implies(X0,X1),implies(X1,X0)))),
% 73.04/24.95 inference(forward_demodulation,[status(thm)],[f188,f12604])).
% 73.04/25.05 fof(f12681,plain,(
% 73.04/25.05 ![X0,X1]: (equiv(X0,not(not(X1)))=equiv(X0,X1))),
% 73.04/25.05 inference(forward_demodulation,[status(thm)],[f259,f12680])).
% 73.04/25.05 fof(f20133,plain,(
% 73.04/25.05 ![X0]: (is_a_theorem(equiv(not(not(X0)),X0)))),
% 73.04/25.05 inference(paramodulation,[status(thm)],[f12681,f2267])).
% 73.04/25.05 fof(f20149,plain,(
% 73.04/25.05 ![X0]: (not(not(X0))=X0)),
% 73.04/25.05 inference(resolution,[status(thm)],[f20133,f184])).
% 73.04/25.05 fof(f21383,plain,(
% 73.04/25.05 ![X0,X1]: (not(and(X0,X1))=implies(X0,not(X1)))),
% 73.04/25.05 inference(paramodulation,[status(thm)],[f230,f20149])).
% 73.04/25.05 fof(f28934,plain,(
% 73.04/25.05 ![X0,X1]: (is_a_theorem(or(X0,not(and(X1,X0)))))),
% 73.04/25.05 inference(backward_demodulation,[status(thm)],[f21383,f253])).
% 73.04/25.05 fof(f28949,plain,(
% 73.04/25.05 ![X0]: (is_a_theorem(not(and(or(not(X0),not(X0)),X0))))),
% 73.04/25.05 inference(paramodulation,[status(thm)],[f21383,f185])).
% 73.04/25.05 fof(f29046,plain,(
% 73.04/25.05 ![X0]: (is_a_theorem(not(and(implies(X0,not(X0)),X0))))),
% 73.04/25.05 inference(forward_demodulation,[status(thm)],[f188,f28949])).
% 73.04/25.05 fof(f29047,plain,(
% 73.04/25.05 ![X0]: (is_a_theorem(not(and(not(and(X0,X0)),X0))))),
% 73.04/25.05 inference(forward_demodulation,[status(thm)],[f21383,f29046])).
% 73.04/25.05 fof(f75526,plain,(
% 73.04/25.05 ~is_a_theorem(implies(implies(sK39_skl,sK40_skl),implies(implies(sK38_skl,sK39_skl),implies(sK38_skl,sK40_skl))))|cn1),
% 73.04/25.05 inference(resolution,[status(thm)],[f1510,f128])).
% 73.04/25.05 fof(f75551,plain,(
% 73.04/25.05 cn1),
% 73.04/25.05 inference(forward_subsumption_resolution,[status(thm)],[f75526,f214])).
% 73.04/25.05 fof(f75722,plain,(
% 73.04/25.05 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 73.04/25.05 inference(backward_subsumption_resolution,[status(thm)],[f127,f75551])).
% 73.04/25.05 fof(f75727,plain,(
% 73.04/25.05 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X2),implies(X0,X2))))),
% 73.04/25.05 inference(resolution,[status(thm)],[f75722,f182])).
% 73.04/25.05 fof(f75778,plain,(
% 73.04/25.05 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(X0,X2)))),
% 73.04/25.05 inference(resolution,[status(thm)],[f75727,f182])).
% 73.04/25.05 fof(f76024,plain,(
% 73.04/25.05 ![X0]: (~is_a_theorem(implies(implies(sK30_skl,sK31_skl),X0))|~is_a_theorem(implies(X0,implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl)))))),
% 73.04/25.05 inference(resolution,[status(thm)],[f75778,f181])).
% 73.04/25.05 fof(f76428,plain,(
% 73.04/25.05 ~is_a_theorem(implies(implies(sK30_skl,sK31_skl),or(equiv(sK30_skl,sK31_skl),not(implies(sK31_skl,sK30_skl)))))),
% 73.04/25.05 inference(resolution,[status(thm)],[f76024,f198])).
% 73.04/25.05 fof(f77915,plain,(
% 73.04/25.05 ![X0]: (~is_a_theorem(implies(X0,implies(implies(sK30_skl,sK31_skl),not(implies(sK31_skl,sK30_skl)))))|~is_a_theorem(or(equiv(sK30_skl,sK31_skl),X0)))),
% 73.04/25.05 inference(resolution,[status(thm)],[f1608,f76428])).
% 73.04/25.05 fof(f77947,plain,(
% 73.04/25.05 ![X0]: (~is_a_theorem(implies(X0,not(and(implies(sK30_skl,sK31_skl),implies(sK31_skl,sK30_skl)))))|~is_a_theorem(or(equiv(sK30_skl,sK31_skl),X0)))),
% 73.04/25.05 inference(forward_demodulation,[status(thm)],[f21383,f77915])).
% 73.04/25.05 fof(f77948,plain,(
% 73.04/25.05 ![X0]: (~is_a_theorem(not(and(X0,and(implies(sK30_skl,sK31_skl),implies(sK31_skl,sK30_skl)))))|~is_a_theorem(or(equiv(sK30_skl,sK31_skl),X0)))),
% 73.04/25.05 inference(forward_demodulation,[status(thm)],[f21383,f77947])).
% 73.04/25.05 fof(f77949,plain,(
% 73.04/25.05 ![X0]: (~is_a_theorem(not(and(X0,equiv(sK30_skl,sK31_skl))))|~is_a_theorem(or(equiv(sK30_skl,sK31_skl),X0)))),
% 73.04/25.05 inference(forward_demodulation,[status(thm)],[f259,f77948])).
% 73.04/25.05 fof(f81142,plain,(
% 73.04/25.05 ~is_a_theorem(or(equiv(sK30_skl,sK31_skl),not(and(equiv(sK30_skl,sK31_skl),equiv(sK30_skl,sK31_skl)))))),
% 73.04/25.05 inference(resolution,[status(thm)],[f77949,f29047])).
% 73.04/25.05 fof(f81147,plain,(
% 73.04/25.05 $false),
% 73.04/25.05 inference(forward_subsumption_resolution,[status(thm)],[f81142,f28934])).
% 73.04/25.05 % SZS output end CNFRefutation for theBenchmark.p
% 11.10/25.09 % Elapsed time: 9.388003 seconds
% 11.10/25.09 % CPU time: 73.843774 seconds
% 11.10/25.09 % Total memory used: 823.839 MB
% 11.10/25.09 % Net memory used: 794.113 MB
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