%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL535+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 : n018.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 01:10:14 PM UTC 2026
% Result : Theorem 19.31s 2.87s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL535+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 00:39:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 19.31/2.87 % Refutation found
% 19.31/2.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.31/2.87 % SZS output start CNFRefutation for theBenchmark
% 19.31/2.87 fof(f1,axiom,(
% 19.31/2.87 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f2,axiom,(
% 19.31/2.87 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f4,axiom,(
% 19.31/2.87 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f5,axiom,(
% 19.31/2.87 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f7,axiom,(
% 19.31/2.87 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f9,axiom,(
% 19.31/2.87 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f11,axiom,(
% 19.31/2.87 ( or_2<=> (! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f12,axiom,(
% 19.31/2.87 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f15,axiom,(
% 19.31/2.87 ( equivalence_3<=> (! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f21,axiom,(
% 19.31/2.87 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f27,axiom,(
% 19.31/2.87 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f29,axiom,(
% 19.31/2.87 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f32,axiom,(
% 19.31/2.87 op_or ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f33,axiom,(
% 19.31/2.87 op_implies_and ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f35,axiom,(
% 19.31/2.87 modus_ponens ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f37,axiom,(
% 19.31/2.87 implies_1 ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f38,axiom,(
% 19.31/2.87 implies_2 ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f40,axiom,(
% 19.31/2.87 and_1 ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f42,axiom,(
% 19.31/2.87 and_3 ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f44,axiom,(
% 19.31/2.87 or_2 ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f45,axiom,(
% 19.31/2.87 or_3 ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f48,axiom,(
% 19.31/2.87 equivalence_3 ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f49,axiom,(
% 19.31/2.87 substitution_of_equivalents ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f50,axiom,(
% 19.31/2.87 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f55,axiom,(
% 19.31/2.87 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f58,axiom,(
% 19.31/2.87 ( axiom_5<=> (! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f71,axiom,(
% 19.31/2.87 ( axiom_m9<=> (! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f73,axiom,(
% 19.31/2.87 ( op_possibly=> (! [X] : possibly(X) = not(necessarily(not(X))) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f75,axiom,(
% 19.31/2.87 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f77,axiom,(
% 19.31/2.87 op_possibly ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f78,axiom,(
% 19.31/2.87 necessitation ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f80,axiom,(
% 19.31/2.87 axiom_M ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f81,axiom,(
% 19.31/2.87 axiom_5 ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f85,axiom,(
% 19.31/2.87 op_strict_implies ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f88,conjecture,(
% 19.31/2.87 axiom_m9 ),
% 19.31/2.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.31/2.87 fof(f89,negated_conjecture,(
% 19.31/2.87 ~(axiom_m9 )),
% 19.31/2.87 inference(negated_conjecture,[status(cth)],[f88])).
% 19.31/2.87 fof(f90,plain,(
% 19.31/2.87 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 19.31/2.87 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 19.31/2.87 fof(f91,plain,(
% 19.31/2.87 (~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))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f90])).
% 19.31/2.87 fof(f92,plain,(
% 19.31/2.87 (~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))))),
% 19.31/2.87 inference(miniscoping,[status(thm)],[f91])).
% 19.31/2.87 fof(f93,plain,(
% 19.31/2.87 (~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)))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f92])).
% 19.31/2.87 fof(f94,plain,(
% 19.31/2.87 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f93])).
% 19.31/2.87 fof(f98,plain,(
% 19.31/2.87 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 19.31/2.87 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 19.31/2.87 fof(f99,plain,(
% 19.31/2.87 (~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)))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f98])).
% 19.31/2.87 fof(f100,plain,(
% 19.31/2.87 (~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))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f99])).
% 19.31/2.87 fof(f101,plain,(
% 19.31/2.87 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f100])).
% 19.31/2.87 fof(f108,plain,(
% 19.31/2.87 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f4])).
% 19.31/2.87 fof(f109,plain,(
% 19.31/2.87 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|~is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl))))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f108])).
% 19.31/2.87 fof(f110,plain,(
% 19.31/2.87 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f109])).
% 19.31/2.87 fof(f112,plain,(
% 19.31/2.87 (~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)))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f5])).
% 19.31/2.87 fof(f113,plain,(
% 19.31/2.87 (~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))))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f112])).
% 19.31/2.87 fof(f114,plain,(
% 19.31/2.87 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f113])).
% 19.31/2.87 fof(f120,plain,(
% 19.31/2.87 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f7])).
% 19.31/2.87 fof(f121,plain,(
% 19.31/2.87 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|~is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl)))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f120])).
% 19.31/2.87 fof(f122,plain,(
% 19.31/2.87 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f121])).
% 19.31/2.87 fof(f128,plain,(
% 19.31/2.87 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,and(X,Y))))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f9])).
% 19.31/2.87 fof(f129,plain,(
% 19.31/2.87 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|~is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl)))))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f128])).
% 19.31/2.87 fof(f130,plain,(
% 19.31/2.87 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f129])).
% 19.31/2.87 fof(f136,plain,(
% 19.31/2.87 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|(?[X,Y]: ~is_a_theorem(implies(Y,or(X,Y)))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f11])).
% 19.31/2.87 fof(f137,plain,(
% 19.31/2.87 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|~is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl))))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f136])).
% 19.31/2.87 fof(f138,plain,(
% 19.31/2.87 ![X0,X1]: (~or_2|is_a_theorem(implies(X0,or(X1,X0))))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f137])).
% 19.31/2.87 fof(f140,plain,(
% 19.31/2.87 (~or_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))))&(or_3|(?[X,Y,Z]: ~is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f12])).
% 19.31/2.87 fof(f141,plain,(
% 19.31/2.87 (~or_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))))&(or_3|~is_a_theorem(implies(implies(sK23_skl,sK25_skl),implies(implies(sK24_skl,sK25_skl),implies(or(sK23_skl,sK24_skl),sK25_skl)))))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl]),skolemize(X,sK23_skl),skolemize(Y,sK24_skl),skolemize(Z,sK25_skl)],[f140])).
% 19.31/2.87 fof(f142,plain,(
% 19.31/2.87 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f141])).
% 19.31/2.87 fof(f152,plain,(
% 19.31/2.87 (~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))))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f15])).
% 19.31/2.87 fof(f153,plain,(
% 19.31/2.87 (~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)))))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(X,sK30_skl),skolemize(Y,sK31_skl)],[f152])).
% 19.31/2.87 fof(f154,plain,(
% 19.31/2.87 ![X0,X1]: (~equivalence_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f153])).
% 19.31/2.87 fof(f176,plain,(
% 19.31/2.87 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f21])).
% 19.31/2.87 fof(f177,plain,(
% 19.31/2.87 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f176])).
% 19.31/2.87 fof(f178,plain,(
% 19.31/2.87 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f177])).
% 19.31/2.87 fof(f179,plain,(
% 19.31/2.87 cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f177])).
% 19.31/2.87 fof(f200,plain,(
% 19.31/2.87 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 19.31/2.87 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 19.31/2.87 fof(f201,plain,(
% 19.31/2.87 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f200])).
% 19.31/2.87 fof(f204,plain,(
% 19.31/2.87 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 19.31/2.87 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 19.31/2.87 fof(f205,plain,(
% 19.31/2.87 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f204])).
% 19.31/2.87 fof(f210,plain,(
% 19.31/2.87 op_or),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f32])).
% 19.31/2.87 fof(f211,plain,(
% 19.31/2.87 op_implies_and),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f33])).
% 19.31/2.87 fof(f213,plain,(
% 19.31/2.87 modus_ponens),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f35])).
% 19.31/2.87 fof(f215,plain,(
% 19.31/2.87 implies_1),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f37])).
% 19.31/2.87 fof(f216,plain,(
% 19.31/2.87 implies_2),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f38])).
% 19.31/2.87 fof(f218,plain,(
% 19.31/2.87 and_1),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f40])).
% 19.31/2.87 fof(f220,plain,(
% 19.31/2.87 and_3),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f42])).
% 19.31/2.87 fof(f222,plain,(
% 19.31/2.87 or_2),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f44])).
% 19.31/2.87 fof(f223,plain,(
% 19.31/2.87 or_3),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f45])).
% 19.31/2.87 fof(f226,plain,(
% 19.31/2.87 equivalence_3),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f48])).
% 19.31/2.87 fof(f227,plain,(
% 19.31/2.87 substitution_of_equivalents),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f49])).
% 19.31/2.87 fof(f228,plain,(
% 19.31/2.87 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 19.31/2.87 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 19.31/2.87 fof(f229,plain,(
% 19.31/2.87 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f228])).
% 19.31/2.87 fof(f230,plain,(
% 19.31/2.87 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f229])).
% 19.31/2.87 fof(f231,plain,(
% 19.31/2.87 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f230])).
% 19.31/2.87 fof(f259,plain,(
% 19.31/2.87 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f55])).
% 19.31/2.87 fof(f260,plain,(
% 19.31/2.87 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f259])).
% 19.31/2.87 fof(f261,plain,(
% 19.31/2.87 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f260])).
% 19.31/2.87 fof(f271,plain,(
% 19.31/2.87 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|(?[X]: ~is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f58])).
% 19.31/2.87 fof(f272,plain,(
% 19.31/2.87 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|~is_a_theorem(implies(possibly(sK67_skl),necessarily(possibly(sK67_skl)))))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK67_skl]),skolemize(X,sK67_skl)],[f271])).
% 19.31/2.87 fof(f273,plain,(
% 19.31/2.87 ![X0]: (~axiom_5|is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f272])).
% 19.31/2.87 fof(f323,plain,(
% 19.31/2.87 (~axiom_m9|(![X]: is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))))&(axiom_m9|(?[X]: ~is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))))),
% 19.31/2.87 inference(NNF_transformation,[status(thm)],[f71])).
% 19.31/2.87 fof(f324,plain,(
% 19.31/2.87 (~axiom_m9|(![X]: is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))))&(axiom_m9|~is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl))))),
% 19.31/2.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK92_skl]),skolemize(X,sK92_skl)],[f323])).
% 19.31/2.87 fof(f326,plain,(
% 19.31/2.87 axiom_m9|~is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl)))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f324])).
% 19.31/2.87 fof(f331,plain,(
% 19.31/2.87 ~op_possibly|(![X]: possibly(X)=not(necessarily(not(X))))),
% 19.31/2.87 inference(pre_NNF_transformation,[status(thm)],[f73])).
% 19.31/2.87 fof(f332,plain,(
% 19.31/2.87 ![X0]: (~op_possibly|possibly(X0)=not(necessarily(not(X0))))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f331])).
% 19.31/2.87 fof(f335,plain,(
% 19.31/2.87 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 19.31/2.87 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 19.31/2.87 fof(f336,plain,(
% 19.31/2.87 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f335])).
% 19.31/2.87 fof(f339,plain,(
% 19.31/2.87 op_possibly),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f77])).
% 19.31/2.87 fof(f340,plain,(
% 19.31/2.87 necessitation),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f78])).
% 19.31/2.87 fof(f342,plain,(
% 19.31/2.87 axiom_M),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f80])).
% 19.31/2.87 fof(f343,plain,(
% 19.31/2.87 axiom_5),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f81])).
% 19.31/2.87 fof(f347,plain,(
% 19.31/2.87 op_strict_implies),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f85])).
% 19.31/2.87 fof(f350,plain,(
% 19.31/2.87 ~axiom_m9),
% 19.31/2.87 inference(cnf_transformation,[status(thm)],[f89])).
% 19.31/2.87 fof(f351,plain,(
% 19.31/2.87 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 19.31/2.87 inference(backward_subsumption_resolution,[status(thm)],[f94,f213])).
% 19.31/2.87 fof(f354,plain,(
% 19.31/2.87 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 19.31/2.87 inference(backward_subsumption_resolution,[status(thm)],[f110,f215])).
% 19.31/2.87 fof(f355,plain,(
% 19.31/2.87 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 19.31/2.87 inference(backward_subsumption_resolution,[status(thm)],[f114,f216])).
% 19.31/2.87 fof(f357,plain,(
% 19.31/2.87 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 19.31/2.87 inference(backward_subsumption_resolution,[status(thm)],[f122,f218])).
% 19.31/2.87 fof(f359,plain,(
% 19.31/2.87 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f130,f220])).
% 19.31/2.87 fof(f361,plain,(
% 19.31/2.87 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 19.31/2.87 inference(backward_subsumption_resolution,[status(thm)],[f138,f222])).
% 19.31/2.87 fof(f362,plain,(
% 19.31/2.87 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f142,f223])).
% 19.31/2.87 fof(f365,plain,(
% 19.31/2.87 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f154,f226])).
% 19.31/2.87 fof(f366,plain,(
% 19.31/2.87 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 19.31/2.87 inference(backward_subsumption_resolution,[status(thm)],[f101,f227])).
% 19.31/2.87 fof(f368,plain,(
% 19.31/2.87 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f201,f210])).
% 19.31/2.87 fof(f373,plain,(
% 19.31/2.87 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 19.31/2.87 inference(backward_demodulation,[status(thm)],[f374,f368])).
% 19.31/2.87 fof(f374,plain,(
% 19.31/2.87 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f205,f211])).
% 19.31/2.87 fof(f381,plain,(
% 19.31/2.87 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f231,f340])).
% 19.31/2.87 fof(f384,plain,(
% 19.31/2.87 ![X0]: (is_a_theorem(implies(necessarily(X0),X0)))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f261,f342])).
% 19.31/2.87 fof(f387,plain,(
% 19.31/2.87 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f273,f343])).
% 19.31/2.87 fof(f389,plain,(
% 19.31/2.87 cn3|~is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl))),
% 19.31/2.87 inference(backward_demodulation,[status(thm)],[f373,f179])).
% 19.31/2.87 fof(f394,plain,(
% 19.31/2.87 ![X0]: (~cn3|is_a_theorem(implies(or(X0,X0),X0)))),
% 19.31/2.87 inference(backward_demodulation,[status(thm)],[f373,f178])).
% 19.31/2.87 fof(f421,plain,(
% 19.31/2.87 ~is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl)))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f326,f350])).
% 19.31/2.87 fof(f422,plain,(
% 19.31/2.87 ![X0]: (possibly(X0)=not(necessarily(not(X0))))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f332,f339])).
% 19.31/2.87 fof(f423,plain,(
% 19.31/2.87 ![X0]: (possibly(necessarily(not(X0)))=not(necessarily(possibly(X0))))),
% 19.31/2.87 inference(paramodulation,[status(thm)],[f422,f422])).
% 19.31/2.87 fof(f433,plain,(
% 19.31/2.87 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f336,f347])).
% 19.31/2.87 fof(f436,plain,(
% 19.31/2.87 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1)))),
% 19.31/2.87 inference(paramodulation,[status(thm)],[f433,f381])).
% 19.31/2.87 fof(f450,plain,(
% 19.31/2.87 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))))),
% 19.31/2.87 inference(resolution,[status(thm)],[f351,f365])).
% 19.31/2.87 fof(f458,plain,(
% 19.31/2.87 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 19.31/2.87 inference(resolution,[status(thm)],[f355,f351])).
% 19.31/2.87 fof(f1043,plain,(
% 19.31/2.87 ~is_a_theorem(implies(possibly(possibly(sK92_skl)),possibly(sK92_skl)))),
% 19.31/2.87 inference(resolution,[status(thm)],[f436,f421])).
% 19.31/2.87 fof(f1076,plain,(
% 19.31/2.87 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1)))),
% 19.31/2.87 inference(resolution,[status(thm)],[f450,f351])).
% 19.31/2.87 fof(f1134,plain,(
% 19.31/2.87 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))))),
% 19.31/2.87 inference(resolution,[status(thm)],[f458,f362])).
% 19.31/2.87 fof(f1137,plain,(
% 19.31/2.87 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 19.31/2.87 inference(resolution,[status(thm)],[f458,f359])).
% 19.31/2.87 fof(f1138,plain,(
% 19.31/2.87 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 19.31/2.87 inference(resolution,[status(thm)],[f458,f354])).
% 19.31/2.87 fof(f7464,plain,(
% 19.31/2.87 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1)))),
% 19.31/2.87 inference(resolution,[status(thm)],[f1134,f351])).
% 19.31/2.87 fof(f8391,plain,(
% 19.31/2.87 ~is_a_theorem(implies(sK43_skl,sK43_skl))|cn3),
% 19.31/2.87 inference(resolution,[status(thm)],[f7464,f389])).
% 19.31/2.87 fof(f8403,plain,(
% 19.31/2.87 cn3),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f8391,f1138])).
% 19.31/2.87 fof(f8414,plain,(
% 19.31/2.87 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 19.31/2.87 inference(backward_subsumption_resolution,[status(thm)],[f394,f8403])).
% 19.31/2.87 fof(f8901,plain,(
% 19.31/2.87 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|X0=X1)),
% 19.31/2.87 inference(resolution,[status(thm)],[f1076,f366])).
% 19.31/2.87 fof(f9760,plain,(
% 19.31/2.87 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|X0=or(X0,X0))),
% 19.31/2.87 inference(resolution,[status(thm)],[f8901,f8414])).
% 19.31/2.87 fof(f9762,plain,(
% 19.31/2.87 ![X0]: (~is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0)))|necessarily(possibly(X0))=possibly(X0))),
% 19.31/2.87 inference(resolution,[status(thm)],[f8901,f387])).
% 19.31/2.87 fof(f9849,plain,(
% 19.31/2.87 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|and(X0,X0)=X0)),
% 19.31/2.87 inference(resolution,[status(thm)],[f8901,f1137])).
% 19.31/2.87 fof(f9874,plain,(
% 19.31/2.87 ![X0]: (X0=or(X0,X0))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f9760,f361])).
% 19.31/2.87 fof(f9875,plain,(
% 19.31/2.87 ![X0]: (necessarily(possibly(X0))=possibly(X0))),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f9762,f384])).
% 19.31/2.87 fof(f9922,plain,(
% 19.31/2.87 ![X0]: (and(X0,X0)=X0)),
% 19.31/2.87 inference(forward_subsumption_resolution,[status(thm)],[f9849,f357])).
% 19.31/2.87 fof(f10513,plain,(
% 19.31/2.87 ![X0]: (implies(not(X0),X0)=not(not(X0)))),
% 19.31/2.87 inference(paramodulation,[status(thm)],[f9922,f374])).
% 19.31/2.87 fof(f10680,plain,(
% 19.31/2.87 ![X0]: (or(X0,X0)=not(not(X0)))),
% 19.31/2.87 inference(forward_demodulation,[status(thm)],[f373,f10513])).
% 19.31/2.87 fof(f10681,plain,(
% 19.31/2.87 ![X0]: (X0=not(not(X0)))),
% 19.31/2.87 inference(forward_demodulation,[status(thm)],[f9874,f10680])).
% 19.31/2.87 fof(f11215,plain,(
% 19.31/2.87 ![X0]: (possibly(necessarily(not(X0)))=not(possibly(X0)))),
% 19.31/2.87 inference(backward_demodulation,[status(thm)],[f9875,f423])).
% 19.31/2.87 fof(f11262,plain,(
% 19.31/2.87 ![X0]: (possibly(necessarily(possibly(X0)))=not(possibly(necessarily(not(X0)))))),
% 19.31/2.87 inference(paramodulation,[status(thm)],[f422,f11215])).
% 19.31/2.87 fof(f11337,plain,(
% 19.31/2.87 ![X0]: (possibly(possibly(X0))=not(possibly(necessarily(not(X0)))))),
% 19.31/2.87 inference(forward_demodulation,[status(thm)],[f9875,f11262])).
% 19.31/2.87 fof(f11338,plain,(
% 19.31/2.87 ![X0]: (possibly(possibly(X0))=not(not(possibly(X0))))),
% 19.31/2.87 inference(forward_demodulation,[status(thm)],[f11215,f11337])).
% 19.31/2.87 fof(f11339,plain,(
% 19.31/2.87 ![X0]: (possibly(possibly(X0))=possibly(X0))),
% 19.31/2.87 inference(forward_demodulation,[status(thm)],[f10681,f11338])).
% 19.31/2.87 fof(f13327,plain,(
% 19.31/2.90 ~is_a_theorem(implies(possibly(sK92_skl),possibly(sK92_skl)))),
% 19.31/2.90 inference(backward_demodulation,[status(thm)],[f11339,f1043])).
% 19.31/2.90 fof(f13405,plain,(
% 19.31/2.90 $false),
% 19.31/2.90 inference(forward_subsumption_resolution,[status(thm)],[f13327,f1138])).
% 19.31/2.90 % SZS output end CNFRefutation for theBenchmark.p
% 19.31/2.92 % Elapsed time: 2.555555 seconds
% 19.31/2.92 % CPU time: 19.999624 seconds
% 19.31/2.92 % Total memory used: 337.424 MB
% 19.31/2.92 % Net memory used: 324.448 MB
%------------------------------------------------------------------------------