%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL533+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 : n002.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 01:10:13 PM UTC 2026
% Result : Theorem 21.28s 18.16s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL533+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
% 0.11/15.39 % Computer : n002.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Mon Sep 21 00:40:33 UTC 2026
% 0.15/15.40 % CPUTime :
% 0.15/15.41 % Drodi V4.1.1
% 21.28/18.16 % Refutation found
% 21.28/18.16 % SZS status Theorem for theBenchmark: Theorem is valid
% 21.28/18.16 % SZS output start CNFRefutation for theBenchmark
% 21.28/18.16 fof(f1,axiom,(
% 21.28/18.16 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f2,axiom,(
% 21.28/18.16 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f3,axiom,(
% 21.28/18.16 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f4,axiom,(
% 21.28/18.16 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f5,axiom,(
% 21.28/18.16 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f8,axiom,(
% 21.28/18.16 ( and_2<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f9,axiom,(
% 21.28/18.16 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f11,axiom,(
% 21.28/18.16 ( or_2<=> (! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f12,axiom,(
% 21.28/18.16 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f21,axiom,(
% 21.28/18.16 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f27,axiom,(
% 21.28/18.16 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f29,axiom,(
% 21.28/18.16 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f31,axiom,(
% 21.28/18.16 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f32,axiom,(
% 21.28/18.16 op_or ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f33,axiom,(
% 21.28/18.16 op_implies_and ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f34,axiom,(
% 21.28/18.16 op_equiv ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f35,axiom,(
% 21.28/18.16 modus_ponens ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f36,axiom,(
% 21.28/18.16 modus_tollens ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f37,axiom,(
% 21.28/18.16 implies_1 ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f38,axiom,(
% 21.28/18.16 implies_2 ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f41,axiom,(
% 21.28/18.16 and_2 ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f42,axiom,(
% 21.28/18.16 and_3 ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f44,axiom,(
% 21.28/18.16 or_2 ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f45,axiom,(
% 21.28/18.16 or_3 ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f49,axiom,(
% 21.28/18.16 substitution_of_equivalents ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f50,axiom,(
% 21.28/18.16 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f54,axiom,(
% 21.28/18.16 ( axiom_K<=> (! [X,Y] : is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y)))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f55,axiom,(
% 21.28/18.16 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f68,axiom,(
% 21.28/18.16 ( axiom_m6<=> (! [X] : is_a_theorem(strict_implies(X,possibly(X))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f73,axiom,(
% 21.28/18.16 ( op_possibly=> (! [X] : possibly(X) = not(necessarily(not(X))) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f75,axiom,(
% 21.28/18.16 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f77,axiom,(
% 21.28/18.16 op_possibly ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f78,axiom,(
% 21.28/18.16 necessitation ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f79,axiom,(
% 21.28/18.16 axiom_K ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f80,axiom,(
% 21.28/18.16 axiom_M ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f85,axiom,(
% 21.28/18.16 op_strict_implies ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f88,conjecture,(
% 21.28/18.16 axiom_m6 ),
% 21.28/18.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.28/18.16 fof(f89,negated_conjecture,(
% 21.28/18.16 ~(axiom_m6 )),
% 21.28/18.16 inference(negated_conjecture,[status(cth)],[f88])).
% 21.28/18.16 fof(f90,plain,(
% 21.28/18.16 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 21.28/18.16 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 21.28/18.16 fof(f91,plain,(
% 21.28/18.16 (~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))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f90])).
% 21.28/18.16 fof(f92,plain,(
% 21.28/18.16 (~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))))),
% 21.28/18.16 inference(miniscoping,[status(thm)],[f91])).
% 21.28/18.16 fof(f93,plain,(
% 21.28/18.16 (~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)))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f92])).
% 21.28/18.16 fof(f94,plain,(
% 21.28/18.16 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f93])).
% 21.28/18.16 fof(f98,plain,(
% 21.28/18.16 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 21.28/18.16 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 21.28/18.16 fof(f99,plain,(
% 21.28/18.16 (~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)))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f98])).
% 21.28/18.16 fof(f100,plain,(
% 21.28/18.16 (~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))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f99])).
% 21.28/18.16 fof(f101,plain,(
% 21.28/18.16 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f100])).
% 21.28/18.16 fof(f104,plain,(
% 21.28/18.16 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|(?[X,Y]: ~is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f3])).
% 21.28/18.16 fof(f105,plain,(
% 21.28/18.16 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|~is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl))))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f104])).
% 21.28/18.16 fof(f106,plain,(
% 21.28/18.16 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f105])).
% 21.28/18.16 fof(f108,plain,(
% 21.28/18.16 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f4])).
% 21.28/18.16 fof(f109,plain,(
% 21.28/18.16 (~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))))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f108])).
% 21.28/18.16 fof(f110,plain,(
% 21.28/18.16 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f109])).
% 21.28/18.16 fof(f112,plain,(
% 21.28/18.16 (~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)))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f5])).
% 21.28/18.16 fof(f113,plain,(
% 21.28/18.16 (~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))))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f112])).
% 21.28/18.16 fof(f114,plain,(
% 21.28/18.16 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f113])).
% 21.28/18.16 fof(f124,plain,(
% 21.28/18.16 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),Y))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f8])).
% 21.28/18.16 fof(f125,plain,(
% 21.28/18.16 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|~is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl)))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(X,sK15_skl),skolemize(Y,sK16_skl)],[f124])).
% 21.28/18.16 fof(f126,plain,(
% 21.28/18.16 ![X0,X1]: (~and_2|is_a_theorem(implies(and(X0,X1),X1)))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f125])).
% 21.28/18.16 fof(f128,plain,(
% 21.28/18.16 (~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))))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f9])).
% 21.28/18.16 fof(f129,plain,(
% 21.28/18.16 (~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)))))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f128])).
% 21.28/18.16 fof(f130,plain,(
% 21.28/18.16 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f129])).
% 21.28/18.16 fof(f136,plain,(
% 21.28/18.16 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|(?[X,Y]: ~is_a_theorem(implies(Y,or(X,Y)))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f11])).
% 21.28/18.16 fof(f137,plain,(
% 21.28/18.16 (~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))))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f136])).
% 21.28/18.16 fof(f138,plain,(
% 21.28/18.16 ![X0,X1]: (~or_2|is_a_theorem(implies(X0,or(X1,X0))))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f137])).
% 21.28/18.16 fof(f140,plain,(
% 21.28/18.16 (~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))))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f12])).
% 21.28/18.16 fof(f141,plain,(
% 21.28/18.16 (~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)))))),
% 21.28/18.16 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])).
% 21.28/18.16 fof(f142,plain,(
% 21.28/18.16 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f141])).
% 21.28/18.16 fof(f176,plain,(
% 21.28/18.16 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f21])).
% 21.28/18.16 fof(f177,plain,(
% 21.28/18.16 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f176])).
% 21.28/18.16 fof(f178,plain,(
% 21.28/18.16 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f177])).
% 21.28/18.16 fof(f179,plain,(
% 21.28/18.16 cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f177])).
% 21.28/18.16 fof(f200,plain,(
% 21.28/18.16 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 21.28/18.16 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 21.28/18.16 fof(f201,plain,(
% 21.28/18.16 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f200])).
% 21.28/18.16 fof(f204,plain,(
% 21.28/18.16 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 21.28/18.16 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 21.28/18.16 fof(f205,plain,(
% 21.28/18.16 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f204])).
% 21.28/18.16 fof(f208,plain,(
% 21.28/18.16 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 21.28/18.16 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 21.28/18.16 fof(f209,plain,(
% 21.28/18.16 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f208])).
% 21.28/18.16 fof(f210,plain,(
% 21.28/18.16 op_or),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f32])).
% 21.28/18.16 fof(f211,plain,(
% 21.28/18.16 op_implies_and),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f33])).
% 21.28/18.16 fof(f212,plain,(
% 21.28/18.16 op_equiv),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f34])).
% 21.28/18.16 fof(f213,plain,(
% 21.28/18.16 modus_ponens),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f35])).
% 21.28/18.16 fof(f214,plain,(
% 21.28/18.16 modus_tollens),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f36])).
% 21.28/18.16 fof(f215,plain,(
% 21.28/18.16 implies_1),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f37])).
% 21.28/18.16 fof(f216,plain,(
% 21.28/18.16 implies_2),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f38])).
% 21.28/18.16 fof(f219,plain,(
% 21.28/18.16 and_2),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f41])).
% 21.28/18.16 fof(f220,plain,(
% 21.28/18.16 and_3),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f42])).
% 21.28/18.16 fof(f222,plain,(
% 21.28/18.16 or_2),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f44])).
% 21.28/18.16 fof(f223,plain,(
% 21.28/18.16 or_3),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f45])).
% 21.28/18.16 fof(f227,plain,(
% 21.28/18.16 substitution_of_equivalents),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f49])).
% 21.28/18.16 fof(f228,plain,(
% 21.28/18.16 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 21.28/18.16 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 21.28/18.16 fof(f229,plain,(
% 21.28/18.16 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f228])).
% 21.28/18.16 fof(f230,plain,(
% 21.28/18.16 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f229])).
% 21.28/18.16 fof(f231,plain,(
% 21.28/18.16 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f230])).
% 21.28/18.16 fof(f255,plain,(
% 21.28/18.16 (~axiom_K|(![X,Y]: is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))))&(axiom_K|(?[X,Y]: ~is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f54])).
% 21.28/18.16 fof(f256,plain,(
% 21.28/18.16 (~axiom_K|(![X,Y]: is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))))&(axiom_K|~is_a_theorem(implies(necessarily(implies(sK62_skl,sK63_skl)),implies(necessarily(sK62_skl),necessarily(sK63_skl)))))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK62_skl,sK63_skl]),skolemize(X,sK62_skl),skolemize(Y,sK63_skl)],[f255])).
% 21.28/18.16 fof(f257,plain,(
% 21.28/18.16 ![X0,X1]: (~axiom_K|is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f256])).
% 21.28/18.16 fof(f259,plain,(
% 21.28/18.16 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f55])).
% 21.28/18.16 fof(f260,plain,(
% 21.28/18.16 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f259])).
% 21.28/18.16 fof(f261,plain,(
% 21.28/18.16 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f260])).
% 21.28/18.16 fof(f311,plain,(
% 21.28/18.16 (~axiom_m6|(![X]: is_a_theorem(strict_implies(X,possibly(X)))))&(axiom_m6|(?[X]: ~is_a_theorem(strict_implies(X,possibly(X)))))),
% 21.28/18.16 inference(NNF_transformation,[status(thm)],[f68])).
% 21.28/18.16 fof(f312,plain,(
% 21.28/18.16 (~axiom_m6|(![X]: is_a_theorem(strict_implies(X,possibly(X)))))&(axiom_m6|~is_a_theorem(strict_implies(sK87_skl,possibly(sK87_skl))))),
% 21.28/18.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK87_skl]),skolemize(X,sK87_skl)],[f311])).
% 21.28/18.16 fof(f314,plain,(
% 21.28/18.16 axiom_m6|~is_a_theorem(strict_implies(sK87_skl,possibly(sK87_skl)))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f312])).
% 21.28/18.16 fof(f331,plain,(
% 21.28/18.16 ~op_possibly|(![X]: possibly(X)=not(necessarily(not(X))))),
% 21.28/18.16 inference(pre_NNF_transformation,[status(thm)],[f73])).
% 21.28/18.16 fof(f332,plain,(
% 21.28/18.16 ![X0]: (~op_possibly|possibly(X0)=not(necessarily(not(X0))))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f331])).
% 21.28/18.16 fof(f335,plain,(
% 21.28/18.16 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 21.28/18.16 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 21.28/18.16 fof(f336,plain,(
% 21.28/18.16 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f335])).
% 21.28/18.16 fof(f339,plain,(
% 21.28/18.16 op_possibly),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f77])).
% 21.28/18.16 fof(f340,plain,(
% 21.28/18.16 necessitation),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f78])).
% 21.28/18.16 fof(f341,plain,(
% 21.28/18.16 axiom_K),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f79])).
% 21.28/18.16 fof(f342,plain,(
% 21.28/18.16 axiom_M),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f80])).
% 21.28/18.16 fof(f347,plain,(
% 21.28/18.16 op_strict_implies),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f85])).
% 21.28/18.16 fof(f350,plain,(
% 21.28/18.16 ~axiom_m6),
% 21.28/18.16 inference(cnf_transformation,[status(thm)],[f89])).
% 21.28/18.16 fof(f351,plain,(
% 21.28/18.16 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f201,f210])).
% 21.28/18.16 fof(f352,plain,(
% 21.28/18.16 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f205,f211])).
% 21.28/18.16 fof(f353,plain,(
% 21.28/18.16 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f209,f212])).
% 21.28/18.16 fof(f354,plain,(
% 21.28/18.16 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f94,f213])).
% 21.28/18.16 fof(f355,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f106,f214])).
% 21.28/18.16 fof(f356,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f110,f215])).
% 21.28/18.16 fof(f357,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f114,f216])).
% 21.28/18.16 fof(f360,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1)))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f126,f219])).
% 21.28/18.16 fof(f361,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f130,f220])).
% 21.28/18.16 fof(f363,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f138,f222])).
% 21.28/18.16 fof(f364,plain,(
% 21.28/18.16 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f142,f223])).
% 21.28/18.16 fof(f368,plain,(
% 21.28/18.16 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f101,f227])).
% 21.28/18.16 fof(f369,plain,(
% 21.28/18.16 ![X0]: (possibly(X0)=not(necessarily(not(X0))))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f332,f339])).
% 21.28/18.16 fof(f370,plain,(
% 21.28/18.16 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f231,f340])).
% 21.28/18.16 fof(f371,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f257,f341])).
% 21.28/18.16 fof(f372,plain,(
% 21.28/18.16 ![X0]: (is_a_theorem(implies(necessarily(X0),X0)))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f261,f342])).
% 21.28/18.16 fof(f374,plain,(
% 21.28/18.16 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f336,f347])).
% 21.28/18.16 fof(f376,plain,(
% 21.28/18.16 ~is_a_theorem(strict_implies(sK87_skl,possibly(sK87_skl)))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f314,f350])).
% 21.28/18.16 fof(f377,plain,(
% 21.28/18.16 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 21.28/18.16 inference(backward_demodulation,[status(thm)],[f352,f351])).
% 21.28/18.16 fof(f382,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(strict_implies(X0,X1),implies(necessarily(X0),necessarily(X1)))))),
% 21.28/18.16 inference(backward_demodulation,[status(thm)],[f374,f371])).
% 21.28/18.16 fof(f384,plain,(
% 21.28/18.16 cn3|~is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl))),
% 21.28/18.16 inference(backward_demodulation,[status(thm)],[f377,f179])).
% 21.28/18.16 fof(f388,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 21.28/18.16 inference(backward_demodulation,[status(thm)],[f377,f355])).
% 21.28/18.16 fof(f389,plain,(
% 21.28/18.16 ![X0]: (~cn3|is_a_theorem(implies(or(X0,X0),X0)))),
% 21.28/18.16 inference(backward_demodulation,[status(thm)],[f377,f178])).
% 21.28/18.16 fof(f398,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))))),
% 21.28/18.16 inference(paramodulation,[status(thm)],[f374,f372])).
% 21.28/18.16 fof(f399,plain,(
% 21.28/18.16 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1)))),
% 21.28/18.16 inference(paramodulation,[status(thm)],[f374,f370])).
% 21.28/18.16 fof(f400,plain,(
% 21.28/18.16 ![X0,X1]: (or(necessarily(not(X0)),X1)=implies(possibly(X0),X1))),
% 21.28/18.16 inference(paramodulation,[status(thm)],[f369,f377])).
% 21.28/18.16 fof(f404,plain,(
% 21.28/18.16 ![X0,X1]: (strict_implies(not(X0),X1)=necessarily(or(X0,X1)))),
% 21.28/18.16 inference(paramodulation,[status(thm)],[f377,f374])).
% 21.28/18.16 fof(f413,plain,(
% 21.28/18.16 ![X0,X1,X2]: (implies(X0,and(X1,not(X2)))=not(and(X0,implies(X1,X2))))),
% 21.28/18.16 inference(paramodulation,[status(thm)],[f352,f352])).
% 21.28/18.16 fof(f414,plain,(
% 21.28/18.16 ![X0,X1]: (implies(X0,necessarily(not(X1)))=not(and(X0,possibly(X1))))),
% 21.28/18.16 inference(paramodulation,[status(thm)],[f369,f352])).
% 21.28/18.16 fof(f447,plain,(
% 21.28/18.16 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,and(X0,X1))))),
% 21.28/18.16 inference(resolution,[status(thm)],[f361,f354])).
% 21.28/18.16 fof(f500,plain,(
% 21.28/18.16 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1)))),
% 21.28/18.16 inference(resolution,[status(thm)],[f447,f354])).
% 21.28/18.16 fof(f543,plain,(
% 21.28/18.16 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1)))),
% 21.28/18.16 inference(paramodulation,[status(thm)],[f353,f500])).
% 21.28/18.16 fof(f586,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(strict_implies(or(X0,not(X1)),implies(X1,X0))))),
% 21.28/18.16 inference(resolution,[status(thm)],[f388,f399])).
% 21.28/18.16 fof(f622,plain,(
% 21.28/18.16 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 21.28/18.16 inference(resolution,[status(thm)],[f357,f354])).
% 21.28/18.16 fof(f722,plain,(
% 21.28/18.16 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(necessarily(X0),necessarily(X1))))),
% 21.28/18.16 inference(resolution,[status(thm)],[f382,f354])).
% 21.28/18.16 fof(f1072,plain,(
% 21.28/18.16 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))))),
% 21.28/18.16 inference(resolution,[status(thm)],[f622,f364])).
% 21.28/18.16 fof(f1074,plain,(
% 21.28/18.16 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 21.28/18.16 inference(resolution,[status(thm)],[f622,f361])).
% 21.28/18.16 fof(f1075,plain,(
% 21.28/18.16 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 21.28/18.16 inference(resolution,[status(thm)],[f622,f356])).
% 21.28/18.16 fof(f1318,plain,(
% 21.28/18.16 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1)))),
% 21.28/18.16 inference(resolution,[status(thm)],[f1072,f354])).
% 21.28/18.16 fof(f1420,plain,(
% 21.28/18.16 ~is_a_theorem(implies(sK43_skl,sK43_skl))|cn3),
% 21.28/18.16 inference(resolution,[status(thm)],[f1318,f384])).
% 21.28/18.16 fof(f1429,plain,(
% 21.28/18.16 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 21.28/18.16 inference(backward_subsumption_resolution,[status(thm)],[f389,f1430])).
% 21.28/18.16 fof(f1430,plain,(
% 21.28/18.16 cn3),
% 21.28/18.16 inference(forward_subsumption_resolution,[status(thm)],[f1420,f1075])).
% 21.28/18.16 fof(f1619,plain,(
% 21.28/18.16 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(necessarily(X0))|is_a_theorem(necessarily(X1)))),
% 21.28/18.21 inference(resolution,[status(thm)],[f722,f354])).
% 21.28/18.21 fof(f1815,plain,(
% 21.28/18.21 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(necessarily(X1))|~is_a_theorem(X0))),
% 21.28/18.21 inference(resolution,[status(thm)],[f1619,f370])).
% 21.28/18.21 fof(f1823,plain,(
% 21.28/18.21 ![X0,X1]: (is_a_theorem(necessarily(implies(X0,X1)))|~is_a_theorem(or(X1,not(X0))))),
% 21.28/18.21 inference(resolution,[status(thm)],[f1815,f586])).
% 21.28/18.21 fof(f1861,plain,(
% 21.28/18.21 ![X0,X1]: (is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(or(X1,not(X0))))),
% 21.28/18.21 inference(forward_demodulation,[status(thm)],[f374,f1823])).
% 21.28/18.21 fof(f6723,plain,(
% 21.28/18.21 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|is_a_theorem(equiv(X0,or(X0,X0))))),
% 21.28/18.21 inference(resolution,[status(thm)],[f543,f1429])).
% 21.28/18.21 fof(f6775,plain,(
% 21.28/18.21 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|is_a_theorem(equiv(and(X0,X0),X0)))),
% 21.28/18.21 inference(resolution,[status(thm)],[f543,f1074])).
% 21.28/18.21 fof(f6797,plain,(
% 21.28/18.21 ![X0]: (is_a_theorem(equiv(X0,or(X0,X0))))),
% 21.28/18.21 inference(forward_subsumption_resolution,[status(thm)],[f6723,f363])).
% 21.28/18.21 fof(f6816,plain,(
% 21.28/18.21 ![X0]: (is_a_theorem(equiv(and(X0,X0),X0)))),
% 21.28/18.21 inference(forward_subsumption_resolution,[status(thm)],[f6775,f360])).
% 21.28/18.21 fof(f6824,plain,(
% 21.28/18.21 ![X0]: (X0=or(X0,X0))),
% 21.28/18.21 inference(resolution,[status(thm)],[f6797,f368])).
% 21.28/18.21 fof(f6913,plain,(
% 21.28/18.21 ![X0]: (necessarily(not(X0))=implies(possibly(X0),necessarily(not(X0))))),
% 21.28/18.21 inference(paramodulation,[status(thm)],[f400,f6824])).
% 21.28/18.21 fof(f6975,plain,(
% 21.28/18.21 ![X0]: (strict_implies(not(X0),X0)=necessarily(X0))),
% 21.28/18.21 inference(paramodulation,[status(thm)],[f6824,f404])).
% 21.28/18.21 fof(f7014,plain,(
% 21.28/18.21 ![X0]: (necessarily(not(X0))=not(and(possibly(X0),possibly(X0))))),
% 21.28/18.21 inference(forward_demodulation,[status(thm)],[f414,f6913])).
% 21.28/18.21 fof(f7044,plain,(
% 21.28/18.21 ![X0]: (and(X0,X0)=X0)),
% 21.28/18.21 inference(resolution,[status(thm)],[f6816,f368])).
% 21.28/18.21 fof(f7102,plain,(
% 21.28/18.21 ![X0]: (necessarily(not(X0))=not(possibly(X0)))),
% 21.28/18.21 inference(backward_demodulation,[status(thm)],[f7044,f7014])).
% 21.28/18.21 fof(f7276,plain,(
% 21.28/18.21 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,implies(not(X1),X1))))),
% 21.28/18.21 inference(paramodulation,[status(thm)],[f7044,f413])).
% 21.28/18.21 fof(f7281,plain,(
% 21.28/18.21 ![X0]: (implies(not(X0),X0)=not(not(X0)))),
% 21.28/18.21 inference(paramodulation,[status(thm)],[f7044,f352])).
% 21.28/18.21 fof(f7543,plain,(
% 21.28/18.21 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,or(X1,X1))))),
% 21.28/18.21 inference(forward_demodulation,[status(thm)],[f377,f7276])).
% 21.28/18.21 fof(f7675,plain,(
% 21.28/18.21 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,X1)))),
% 21.28/18.21 inference(forward_demodulation,[status(thm)],[f6824,f7543])).
% 21.28/18.21 fof(f7680,plain,(
% 21.28/18.21 ![X0]: (or(X0,X0)=not(not(X0)))),
% 21.28/18.21 inference(forward_demodulation,[status(thm)],[f377,f7281])).
% 21.28/18.21 fof(f7696,plain,(
% 21.28/18.21 ![X0]: (X0=not(not(X0)))),
% 21.28/18.21 inference(forward_demodulation,[status(thm)],[f6824,f7680])).
% 21.28/18.21 fof(f8381,plain,(
% 21.28/18.21 ![X0]: (strict_implies(X0,not(X0))=necessarily(not(X0)))),
% 21.28/18.21 inference(paramodulation,[status(thm)],[f7696,f6975])).
% 21.28/18.21 fof(f8635,plain,(
% 21.28/18.21 ![X0,X1]: (or(possibly(X0),X1)=implies(necessarily(not(X0)),X1))),
% 21.28/18.21 inference(paramodulation,[status(thm)],[f7102,f377])).
% 21.28/18.21 fof(f9389,plain,(
% 21.28/18.21 ![X0]: (is_a_theorem(implies(necessarily(not(X0)),implies(X0,not(X0)))))),
% 21.28/18.21 inference(paramodulation,[status(thm)],[f8381,f398])).
% 21.28/18.21 fof(f9499,plain,(
% 21.28/18.21 ![X0]: (is_a_theorem(or(possibly(X0),implies(X0,not(X0)))))),
% 21.28/18.21 inference(forward_demodulation,[status(thm)],[f8635,f9389])).
% 21.28/18.21 fof(f9500,plain,(
% 21.28/18.21 ![X0]: (is_a_theorem(or(possibly(X0),not(and(X0,X0)))))),
% 21.28/18.21 inference(forward_demodulation,[status(thm)],[f7675,f9499])).
% 21.28/18.21 fof(f9501,plain,(
% 21.28/18.21 ![X0]: (is_a_theorem(or(possibly(X0),not(X0))))),
% 21.28/18.21 inference(forward_demodulation,[status(thm)],[f7044,f9500])).
% 21.28/18.21 fof(f9502,plain,(
% 21.28/18.21 ![X0]: (is_a_theorem(strict_implies(X0,possibly(X0))))),
% 21.28/18.21 inference(resolution,[status(thm)],[f9501,f1861])).
% 21.28/18.21 fof(f9515,plain,(
% 21.28/18.21 $false),
% 21.28/18.21 inference(backward_subsumption_resolution,[status(thm)],[f376,f9502])).
% 21.28/18.21 % SZS output end CNFRefutation for theBenchmark.p
% 5.57/18.25 % Elapsed time: 2.832720 seconds
% 5.57/18.25 % CPU time: 22.193750 seconds
% 5.57/18.25 % Total memory used: 397.975 MB
% 5.57/18.25 % Net memory used: 378.429 MB
%------------------------------------------------------------------------------