%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL549+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 : 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 01:10:15 PM UTC 2026
% Result : Theorem 9.01s 2.25s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL549+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n018.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 00:40:13 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 9.01/2.25 % Refutation found
% 9.01/2.25 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.01/2.25 % SZS output start CNFRefutation for theBenchmark
% 9.01/2.25 fof(f1,axiom,(
% 9.01/2.25 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f2,axiom,(
% 9.01/2.25 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f4,axiom,(
% 9.01/2.25 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f5,axiom,(
% 9.01/2.25 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f7,axiom,(
% 9.01/2.25 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f9,axiom,(
% 9.01/2.25 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f11,axiom,(
% 9.01/2.25 ( or_2<=> (! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f12,axiom,(
% 9.01/2.25 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f22,axiom,(
% 9.01/2.25 ( r1<=> (! [P] : is_a_theorem(implies(or(P,P),P)) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f27,axiom,(
% 9.01/2.25 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f29,axiom,(
% 9.01/2.25 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f31,axiom,(
% 9.01/2.25 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f32,axiom,(
% 9.01/2.25 op_or ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f33,axiom,(
% 9.01/2.25 op_implies_and ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f34,axiom,(
% 9.01/2.25 op_equiv ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f35,axiom,(
% 9.01/2.25 modus_ponens ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f37,axiom,(
% 9.01/2.25 implies_1 ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f38,axiom,(
% 9.01/2.25 implies_2 ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f40,axiom,(
% 9.01/2.25 and_1 ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f42,axiom,(
% 9.01/2.25 and_3 ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f44,axiom,(
% 9.01/2.25 or_2 ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f45,axiom,(
% 9.01/2.25 or_3 ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f49,axiom,(
% 9.01/2.25 substitution_of_equivalents ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f50,axiom,(
% 9.01/2.25 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f55,axiom,(
% 9.01/2.25 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f56,axiom,(
% 9.01/2.25 ( axiom_4<=> (! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f57,axiom,(
% 9.01/2.25 ( axiom_B<=> (! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f72,axiom,(
% 9.01/2.25 ( axiom_m10<=> (! [X] : is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f73,axiom,(
% 9.01/2.25 ( op_possibly=> (! [X] : possibly(X) = not(necessarily(not(X))) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f75,axiom,(
% 9.01/2.25 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f77,axiom,(
% 9.01/2.25 op_possibly ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f78,axiom,(
% 9.01/2.25 necessitation ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f80,axiom,(
% 9.01/2.25 axiom_M ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f81,axiom,(
% 9.01/2.25 axiom_4 ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f82,axiom,(
% 9.01/2.25 axiom_B ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f86,axiom,(
% 9.01/2.25 op_strict_implies ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f89,conjecture,(
% 9.01/2.25 axiom_m10 ),
% 9.01/2.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.01/2.25 fof(f90,negated_conjecture,(
% 9.01/2.25 ~(axiom_m10 )),
% 9.01/2.25 inference(negated_conjecture,[status(cth)],[f89])).
% 9.01/2.25 fof(f91,plain,(
% 9.01/2.25 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 9.01/2.25 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 9.01/2.25 fof(f92,plain,(
% 9.01/2.25 (~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))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f91])).
% 9.01/2.25 fof(f93,plain,(
% 9.01/2.25 (~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))))),
% 9.01/2.25 inference(miniscoping,[status(thm)],[f92])).
% 9.01/2.25 fof(f94,plain,(
% 9.01/2.25 (~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)))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f93])).
% 9.01/2.25 fof(f95,plain,(
% 9.01/2.25 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f94])).
% 9.01/2.25 fof(f99,plain,(
% 9.01/2.25 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 9.01/2.25 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 9.01/2.25 fof(f100,plain,(
% 9.01/2.25 (~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)))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f99])).
% 9.01/2.25 fof(f101,plain,(
% 9.01/2.25 (~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))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f100])).
% 9.01/2.25 fof(f102,plain,(
% 9.01/2.25 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f101])).
% 9.01/2.25 fof(f109,plain,(
% 9.01/2.25 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f4])).
% 9.01/2.25 fof(f110,plain,(
% 9.01/2.25 (~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))))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f109])).
% 9.01/2.25 fof(f111,plain,(
% 9.01/2.25 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f110])).
% 9.01/2.25 fof(f113,plain,(
% 9.01/2.25 (~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)))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f5])).
% 9.01/2.25 fof(f114,plain,(
% 9.01/2.25 (~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))))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f113])).
% 9.01/2.25 fof(f115,plain,(
% 9.01/2.25 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f114])).
% 9.01/2.25 fof(f121,plain,(
% 9.01/2.25 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f7])).
% 9.01/2.25 fof(f122,plain,(
% 9.01/2.25 (~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)))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f121])).
% 9.01/2.25 fof(f123,plain,(
% 9.01/2.25 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f122])).
% 9.01/2.25 fof(f129,plain,(
% 9.01/2.25 (~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))))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f9])).
% 9.01/2.25 fof(f130,plain,(
% 9.01/2.25 (~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)))))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f129])).
% 9.01/2.25 fof(f131,plain,(
% 9.01/2.25 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f130])).
% 9.01/2.25 fof(f137,plain,(
% 9.01/2.25 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|(?[X,Y]: ~is_a_theorem(implies(Y,or(X,Y)))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f11])).
% 9.01/2.25 fof(f138,plain,(
% 9.01/2.25 (~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))))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f137])).
% 9.01/2.25 fof(f139,plain,(
% 9.01/2.25 ![X0,X1]: (~or_2|is_a_theorem(implies(X0,or(X1,X0))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f138])).
% 9.01/2.25 fof(f141,plain,(
% 9.01/2.25 (~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))))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f12])).
% 9.01/2.25 fof(f142,plain,(
% 9.01/2.25 (~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)))))),
% 9.01/2.25 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)],[f141])).
% 9.01/2.25 fof(f143,plain,(
% 9.01/2.25 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f142])).
% 9.01/2.25 fof(f181,plain,(
% 9.01/2.25 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|(?[P]: ~is_a_theorem(implies(or(P,P),P))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f22])).
% 9.01/2.25 fof(f182,plain,(
% 9.01/2.25 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(P,sK44_skl)],[f181])).
% 9.01/2.25 fof(f183,plain,(
% 9.01/2.25 ![X0]: (~r1|is_a_theorem(implies(or(X0,X0),X0)))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f182])).
% 9.01/2.25 fof(f184,plain,(
% 9.01/2.25 r1|~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f182])).
% 9.01/2.25 fof(f201,plain,(
% 9.01/2.25 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 9.01/2.25 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 9.01/2.25 fof(f202,plain,(
% 9.01/2.25 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f201])).
% 9.01/2.25 fof(f205,plain,(
% 9.01/2.25 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 9.01/2.25 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 9.01/2.25 fof(f206,plain,(
% 9.01/2.25 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f205])).
% 9.01/2.25 fof(f209,plain,(
% 9.01/2.25 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 9.01/2.25 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 9.01/2.25 fof(f210,plain,(
% 9.01/2.25 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f209])).
% 9.01/2.25 fof(f211,plain,(
% 9.01/2.25 op_or),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f32])).
% 9.01/2.25 fof(f212,plain,(
% 9.01/2.25 op_implies_and),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f33])).
% 9.01/2.25 fof(f213,plain,(
% 9.01/2.25 op_equiv),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f34])).
% 9.01/2.25 fof(f214,plain,(
% 9.01/2.25 modus_ponens),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f35])).
% 9.01/2.25 fof(f216,plain,(
% 9.01/2.25 implies_1),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f37])).
% 9.01/2.25 fof(f217,plain,(
% 9.01/2.25 implies_2),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f38])).
% 9.01/2.25 fof(f219,plain,(
% 9.01/2.25 and_1),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f40])).
% 9.01/2.25 fof(f221,plain,(
% 9.01/2.25 and_3),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f42])).
% 9.01/2.25 fof(f223,plain,(
% 9.01/2.25 or_2),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f44])).
% 9.01/2.25 fof(f224,plain,(
% 9.01/2.25 or_3),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f45])).
% 9.01/2.25 fof(f228,plain,(
% 9.01/2.25 substitution_of_equivalents),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f49])).
% 9.01/2.25 fof(f229,plain,(
% 9.01/2.25 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 9.01/2.25 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 9.01/2.25 fof(f230,plain,(
% 9.01/2.25 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f229])).
% 9.01/2.25 fof(f231,plain,(
% 9.01/2.25 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f230])).
% 9.01/2.25 fof(f232,plain,(
% 9.01/2.25 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f231])).
% 9.01/2.25 fof(f260,plain,(
% 9.01/2.25 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f55])).
% 9.01/2.25 fof(f261,plain,(
% 9.01/2.25 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f260])).
% 9.01/2.25 fof(f262,plain,(
% 9.01/2.25 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f261])).
% 9.01/2.25 fof(f264,plain,(
% 9.01/2.25 (~axiom_4|(![X]: is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))&(axiom_4|(?[X]: ~is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f56])).
% 9.01/2.25 fof(f265,plain,(
% 9.01/2.25 (~axiom_4|(![X]: is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))&(axiom_4|~is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl)))))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK65_skl]),skolemize(X,sK65_skl)],[f264])).
% 9.01/2.25 fof(f266,plain,(
% 9.01/2.25 ![X0]: (~axiom_4|is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f265])).
% 9.01/2.25 fof(f268,plain,(
% 9.01/2.25 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|(?[X]: ~is_a_theorem(implies(X,necessarily(possibly(X))))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f57])).
% 9.01/2.25 fof(f269,plain,(
% 9.01/2.25 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|~is_a_theorem(implies(sK66_skl,necessarily(possibly(sK66_skl)))))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl]),skolemize(X,sK66_skl)],[f268])).
% 9.01/2.25 fof(f270,plain,(
% 9.01/2.25 ![X0]: (~axiom_B|is_a_theorem(implies(X0,necessarily(possibly(X0)))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f269])).
% 9.01/2.25 fof(f328,plain,(
% 9.01/2.25 (~axiom_m10|(![X]: is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))))&(axiom_m10|(?[X]: ~is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))))),
% 9.01/2.25 inference(NNF_transformation,[status(thm)],[f72])).
% 9.01/2.25 fof(f329,plain,(
% 9.01/2.25 (~axiom_m10|(![X]: is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))))&(axiom_m10|~is_a_theorem(strict_implies(possibly(sK93_skl),necessarily(possibly(sK93_skl)))))),
% 9.01/2.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK93_skl]),skolemize(X,sK93_skl)],[f328])).
% 9.01/2.25 fof(f331,plain,(
% 9.01/2.25 axiom_m10|~is_a_theorem(strict_implies(possibly(sK93_skl),necessarily(possibly(sK93_skl))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f329])).
% 9.01/2.25 fof(f332,plain,(
% 9.01/2.25 ~op_possibly|(![X]: possibly(X)=not(necessarily(not(X))))),
% 9.01/2.25 inference(pre_NNF_transformation,[status(thm)],[f73])).
% 9.01/2.25 fof(f333,plain,(
% 9.01/2.25 ![X0]: (~op_possibly|possibly(X0)=not(necessarily(not(X0))))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f332])).
% 9.01/2.25 fof(f336,plain,(
% 9.01/2.25 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 9.01/2.25 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 9.01/2.25 fof(f337,plain,(
% 9.01/2.25 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f336])).
% 9.01/2.25 fof(f340,plain,(
% 9.01/2.25 op_possibly),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f77])).
% 9.01/2.25 fof(f341,plain,(
% 9.01/2.25 necessitation),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f78])).
% 9.01/2.25 fof(f343,plain,(
% 9.01/2.25 axiom_M),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f80])).
% 9.01/2.25 fof(f344,plain,(
% 9.01/2.25 axiom_4),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f81])).
% 9.01/2.25 fof(f345,plain,(
% 9.01/2.25 axiom_B),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f82])).
% 9.01/2.25 fof(f349,plain,(
% 9.01/2.25 op_strict_implies),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f86])).
% 9.01/2.25 fof(f352,plain,(
% 9.01/2.25 ~axiom_m10),
% 9.01/2.25 inference(cnf_transformation,[status(thm)],[f90])).
% 9.01/2.25 fof(f353,definition,(
% 9.01/2.25 sQ0_spl <=> (modus_ponens)),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f355,plain,(
% 9.01/2.25 ~modus_ponens|sQ0_spl),
% 9.01/2.25 inference(component_clause,[status(thm)],[f353])).
% 9.01/2.25 fof(f356,definition,(
% 9.01/2.25 ![X0,X1]: (sQ1_spl <=> (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f357,plain,(
% 9.01/2.25 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~sQ1_spl)),
% 9.01/2.25 inference(component_clause,[status(thm)],[f356])).
% 9.01/2.25 fof(f359,plain,(
% 9.01/2.25 ~sQ0_spl|sQ1_spl),
% 9.01/2.25 inference(split_clause,[status(thm)],[f95,f353,f356])).
% 9.01/2.25 fof(f372,definition,(
% 9.01/2.25 sQ5_spl <=> (substitution_of_equivalents)),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f374,plain,(
% 9.01/2.25 ~substitution_of_equivalents|sQ5_spl),
% 9.01/2.25 inference(component_clause,[status(thm)],[f372])).
% 9.01/2.25 fof(f375,definition,(
% 9.01/2.25 ![X0,X1]: (sQ6_spl <=> (~is_a_theorem(equiv(X0,X1))|X0=X1))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f376,plain,(
% 9.01/2.25 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~sQ6_spl)),
% 9.01/2.25 inference(component_clause,[status(thm)],[f375])).
% 9.01/2.25 fof(f378,plain,(
% 9.01/2.25 ~sQ5_spl|sQ6_spl),
% 9.01/2.25 inference(split_clause,[status(thm)],[f102,f372,f375])).
% 9.01/2.25 fof(f398,definition,(
% 9.01/2.25 sQ12_spl <=> (implies_1)),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f400,plain,(
% 9.01/2.25 ~implies_1|sQ12_spl),
% 9.01/2.25 inference(component_clause,[status(thm)],[f398])).
% 9.01/2.25 fof(f401,definition,(
% 9.01/2.25 ![X0,X1]: (sQ13_spl <=> (is_a_theorem(implies(X0,implies(X1,X0)))))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f402,plain,(
% 9.01/2.25 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~sQ13_spl)),
% 9.01/2.25 inference(component_clause,[status(thm)],[f401])).
% 9.01/2.25 fof(f404,plain,(
% 9.01/2.25 ~sQ12_spl|sQ13_spl),
% 9.01/2.25 inference(split_clause,[status(thm)],[f111,f398,f401])).
% 9.01/2.25 fof(f409,definition,(
% 9.01/2.25 sQ15_spl <=> (implies_2)),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f411,plain,(
% 9.01/2.25 ~implies_2|sQ15_spl),
% 9.01/2.25 inference(component_clause,[status(thm)],[f409])).
% 9.01/2.25 fof(f412,definition,(
% 9.01/2.25 ![X0,X1]: (sQ16_spl <=> (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f413,plain,(
% 9.01/2.25 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))|~sQ16_spl)),
% 9.01/2.25 inference(component_clause,[status(thm)],[f412])).
% 9.01/2.25 fof(f415,plain,(
% 9.01/2.25 ~sQ15_spl|sQ16_spl),
% 9.01/2.25 inference(split_clause,[status(thm)],[f115,f409,f412])).
% 9.01/2.25 fof(f431,definition,(
% 9.01/2.25 sQ21_spl <=> (and_1)),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f433,plain,(
% 9.01/2.25 ~and_1|sQ21_spl),
% 9.01/2.25 inference(component_clause,[status(thm)],[f431])).
% 9.01/2.25 fof(f434,definition,(
% 9.01/2.25 ![X0,X1]: (sQ22_spl <=> (is_a_theorem(implies(and(X0,X1),X0))))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f435,plain,(
% 9.01/2.25 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~sQ22_spl)),
% 9.01/2.25 inference(component_clause,[status(thm)],[f434])).
% 9.01/2.25 fof(f437,plain,(
% 9.01/2.25 ~sQ21_spl|sQ22_spl),
% 9.01/2.25 inference(split_clause,[status(thm)],[f123,f431,f434])).
% 9.01/2.25 fof(f453,definition,(
% 9.01/2.25 sQ27_spl <=> (and_3)),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f455,plain,(
% 9.01/2.25 ~and_3|sQ27_spl),
% 9.01/2.25 inference(component_clause,[status(thm)],[f453])).
% 9.01/2.25 fof(f456,definition,(
% 9.01/2.25 ![X0,X1]: (sQ28_spl <=> (is_a_theorem(implies(X0,implies(X1,and(X0,X1))))))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f457,plain,(
% 9.01/2.25 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1))))|~sQ28_spl)),
% 9.01/2.25 inference(component_clause,[status(thm)],[f456])).
% 9.01/2.25 fof(f459,plain,(
% 9.01/2.25 ~sQ27_spl|sQ28_spl),
% 9.01/2.25 inference(split_clause,[status(thm)],[f131,f453,f456])).
% 9.01/2.25 fof(f475,definition,(
% 9.01/2.25 sQ33_spl <=> (or_2)),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f477,plain,(
% 9.01/2.25 ~or_2|sQ33_spl),
% 9.01/2.25 inference(component_clause,[status(thm)],[f475])).
% 9.01/2.25 fof(f478,definition,(
% 9.01/2.25 ![X0,X1]: (sQ34_spl <=> (is_a_theorem(implies(X0,or(X1,X0)))))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f479,plain,(
% 9.01/2.25 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~sQ34_spl)),
% 9.01/2.25 inference(component_clause,[status(thm)],[f478])).
% 9.01/2.25 fof(f481,plain,(
% 9.01/2.25 ~sQ33_spl|sQ34_spl),
% 9.01/2.25 inference(split_clause,[status(thm)],[f139,f475,f478])).
% 9.01/2.25 fof(f486,definition,(
% 9.01/2.25 sQ36_spl <=> (or_3)),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f488,plain,(
% 9.01/2.25 ~or_3|sQ36_spl),
% 9.01/2.25 inference(component_clause,[status(thm)],[f486])).
% 9.01/2.25 fof(f489,definition,(
% 9.01/2.25 ![X0,X1,X2]: (sQ37_spl <=> (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f490,plain,(
% 9.01/2.25 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))|~sQ37_spl)),
% 9.01/2.25 inference(component_clause,[status(thm)],[f489])).
% 9.01/2.25 fof(f492,plain,(
% 9.01/2.25 ~sQ36_spl|sQ37_spl),
% 9.01/2.25 inference(split_clause,[status(thm)],[f143,f486,f489])).
% 9.01/2.25 fof(f533,definition,(
% 9.01/2.25 ![X0]: (sQ49_spl <=> (is_a_theorem(implies(X0,and(X0,X0)))))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f534,plain,(
% 9.01/2.25 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~sQ49_spl)),
% 9.01/2.25 inference(component_clause,[status(thm)],[f533])).
% 9.01/2.25 fof(f590,definition,(
% 9.01/2.25 sQ64_spl <=> (r1)),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f593,definition,(
% 9.01/2.25 ![X0]: (sQ65_spl <=> (is_a_theorem(implies(or(X0,X0),X0))))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f594,plain,(
% 9.01/2.25 ![X0]: (is_a_theorem(implies(or(X0,X0),X0))|~sQ65_spl)),
% 9.01/2.25 inference(component_clause,[status(thm)],[f593])).
% 9.01/2.25 fof(f596,plain,(
% 9.01/2.25 ~sQ64_spl|sQ65_spl),
% 9.01/2.25 inference(split_clause,[status(thm)],[f183,f590,f593])).
% 9.01/2.25 fof(f597,definition,(
% 9.01/2.25 sQ66_spl <=> (is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)))),
% 9.01/2.25 introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition])).
% 9.01/2.25 fof(f599,plain,(
% 9.01/2.25 ~is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))|sQ66_spl),
% 9.01/2.25 inference(component_clause,[status(thm)],[f597])).
% 9.01/2.25 fof(f600,plain,(
% 9.01/2.26 sQ64_spl|~sQ66_spl),
% 9.01/2.26 inference(split_clause,[status(thm)],[f184,f590,f597])).
% 9.01/2.26 fof(f642,definition,(
% 9.01/2.26 sQ78_spl <=> (op_or)),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f644,plain,(
% 9.01/2.26 ~op_or|sQ78_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f642])).
% 9.01/2.26 fof(f645,definition,(
% 9.01/2.26 ![X0,X1]: (sQ79_spl <=> (or(X0,X1)=not(and(not(X0),not(X1)))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f646,plain,(
% 9.01/2.26 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~sQ79_spl)),
% 9.01/2.26 inference(component_clause,[status(thm)],[f645])).
% 9.01/2.26 fof(f648,plain,(
% 9.01/2.26 ~sQ78_spl|sQ79_spl),
% 9.01/2.26 inference(split_clause,[status(thm)],[f202,f642,f645])).
% 9.01/2.26 fof(f656,definition,(
% 9.01/2.26 sQ82_spl <=> (op_implies_and)),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f658,plain,(
% 9.01/2.26 ~op_implies_and|sQ82_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f656])).
% 9.01/2.26 fof(f659,definition,(
% 9.01/2.26 ![X0,X1]: (sQ83_spl <=> (implies(X0,X1)=not(and(X0,not(X1)))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f660,plain,(
% 9.01/2.26 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~sQ83_spl)),
% 9.01/2.26 inference(component_clause,[status(thm)],[f659])).
% 9.01/2.26 fof(f662,plain,(
% 9.01/2.26 ~sQ82_spl|sQ83_spl),
% 9.01/2.26 inference(split_clause,[status(thm)],[f206,f656,f659])).
% 9.01/2.26 fof(f670,definition,(
% 9.01/2.26 sQ86_spl <=> (op_equiv)),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f672,plain,(
% 9.01/2.26 ~op_equiv|sQ86_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f670])).
% 9.01/2.26 fof(f673,definition,(
% 9.01/2.26 ![X0,X1]: (sQ87_spl <=> (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f674,plain,(
% 9.01/2.26 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~sQ87_spl)),
% 9.01/2.26 inference(component_clause,[status(thm)],[f673])).
% 9.01/2.26 fof(f676,plain,(
% 9.01/2.26 ~sQ86_spl|sQ87_spl),
% 9.01/2.26 inference(split_clause,[status(thm)],[f210,f670,f673])).
% 9.01/2.26 fof(f677,definition,(
% 9.01/2.26 sQ88_spl <=> (necessitation)),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f679,plain,(
% 9.01/2.26 ~necessitation|sQ88_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f677])).
% 9.01/2.26 fof(f680,definition,(
% 9.01/2.26 ![X0]: (sQ89_spl <=> (~is_a_theorem(X0)|is_a_theorem(necessarily(X0))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f681,plain,(
% 9.01/2.26 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0))|~sQ89_spl)),
% 9.01/2.26 inference(component_clause,[status(thm)],[f680])).
% 9.01/2.26 fof(f683,plain,(
% 9.01/2.26 ~sQ88_spl|sQ89_spl),
% 9.01/2.26 inference(split_clause,[status(thm)],[f232,f677,f680])).
% 9.01/2.26 fof(f714,definition,(
% 9.01/2.26 ![X0,X1]: (sQ98_spl <=> (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f715,plain,(
% 9.01/2.26 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))|~sQ98_spl)),
% 9.01/2.26 inference(component_clause,[status(thm)],[f714])).
% 9.01/2.26 fof(f756,definition,(
% 9.01/2.26 sQ109_spl <=> (axiom_M)),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f758,plain,(
% 9.01/2.26 ~axiom_M|sQ109_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f756])).
% 9.01/2.26 fof(f759,definition,(
% 9.01/2.26 ![X0]: (sQ110_spl <=> (is_a_theorem(implies(necessarily(X0),X0))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f760,plain,(
% 9.01/2.26 ![X0]: (is_a_theorem(implies(necessarily(X0),X0))|~sQ110_spl)),
% 9.01/2.26 inference(component_clause,[status(thm)],[f759])).
% 9.01/2.26 fof(f762,plain,(
% 9.01/2.26 ~sQ109_spl|sQ110_spl),
% 9.01/2.26 inference(split_clause,[status(thm)],[f262,f756,f759])).
% 9.01/2.26 fof(f767,definition,(
% 9.01/2.26 sQ112_spl <=> (axiom_4)),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f769,plain,(
% 9.01/2.26 ~axiom_4|sQ112_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f767])).
% 9.01/2.26 fof(f770,definition,(
% 9.01/2.26 ![X0]: (sQ113_spl <=> (is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f771,plain,(
% 9.01/2.26 ![X0]: (is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))|~sQ113_spl)),
% 9.01/2.26 inference(component_clause,[status(thm)],[f770])).
% 9.01/2.26 fof(f773,plain,(
% 9.01/2.26 ~sQ112_spl|sQ113_spl),
% 9.01/2.26 inference(split_clause,[status(thm)],[f266,f767,f770])).
% 9.01/2.26 fof(f778,definition,(
% 9.01/2.26 sQ115_spl <=> (axiom_B)),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f780,plain,(
% 9.01/2.26 ~axiom_B|sQ115_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f778])).
% 9.01/2.26 fof(f781,definition,(
% 9.01/2.26 ![X0]: (sQ116_spl <=> (is_a_theorem(implies(X0,necessarily(possibly(X0))))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f782,plain,(
% 9.01/2.26 ![X0]: (is_a_theorem(implies(X0,necessarily(possibly(X0))))|~sQ116_spl)),
% 9.01/2.26 inference(component_clause,[status(thm)],[f781])).
% 9.01/2.26 fof(f784,plain,(
% 9.01/2.26 ~sQ115_spl|sQ116_spl),
% 9.01/2.26 inference(split_clause,[status(thm)],[f270,f778,f781])).
% 9.01/2.26 fof(f943,definition,(
% 9.01/2.26 sQ160_spl <=> (axiom_m10)),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f944,plain,(
% 9.01/2.26 axiom_m10|~sQ160_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f943])).
% 9.01/2.26 fof(f946,definition,(
% 9.01/2.26 ![X0]: (sQ161_spl <=> (is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f947,plain,(
% 9.01/2.26 ![X0]: (is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))|~sQ161_spl)),
% 9.01/2.26 inference(component_clause,[status(thm)],[f946])).
% 9.01/2.26 fof(f950,definition,(
% 9.01/2.26 sQ162_spl <=> (is_a_theorem(strict_implies(possibly(sK93_skl),necessarily(possibly(sK93_skl)))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f952,plain,(
% 9.01/2.26 ~is_a_theorem(strict_implies(possibly(sK93_skl),necessarily(possibly(sK93_skl))))|sQ162_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f950])).
% 9.01/2.26 fof(f953,plain,(
% 9.01/2.26 sQ160_spl|~sQ162_spl),
% 9.01/2.26 inference(split_clause,[status(thm)],[f331,f943,f950])).
% 9.01/2.26 fof(f954,definition,(
% 9.01/2.26 sQ163_spl <=> (op_possibly)),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f956,plain,(
% 9.01/2.26 ~op_possibly|sQ163_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f954])).
% 9.01/2.26 fof(f957,definition,(
% 9.01/2.26 ![X0]: (sQ164_spl <=> (possibly(X0)=not(necessarily(not(X0)))))),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f958,plain,(
% 9.01/2.26 ![X0]: (possibly(X0)=not(necessarily(not(X0)))|~sQ164_spl)),
% 9.01/2.26 inference(component_clause,[status(thm)],[f957])).
% 9.01/2.26 fof(f960,plain,(
% 9.01/2.26 ~sQ163_spl|sQ164_spl),
% 9.01/2.26 inference(split_clause,[status(thm)],[f333,f954,f957])).
% 9.01/2.26 fof(f968,definition,(
% 9.01/2.26 sQ167_spl <=> (op_strict_implies)),
% 9.01/2.26 introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition])).
% 9.01/2.26 fof(f970,plain,(
% 9.01/2.26 ~op_strict_implies|sQ167_spl),
% 9.01/2.26 inference(component_clause,[status(thm)],[f968])).
% 9.01/2.26 fof(f971,definition,(
% 9.01/2.26 ![X0,X1]: (sQ168_spl <=> (strict_implies(X0,X1)=necessarily(implies(X0,X1))))),
% 13.13/2.26 introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition])).
% 13.13/2.26 fof(f972,plain,(
% 13.13/2.26 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1))|~sQ168_spl)),
% 13.13/2.26 inference(component_clause,[status(thm)],[f971])).
% 13.13/2.26 fof(f974,plain,(
% 13.13/2.26 ~sQ167_spl|sQ168_spl),
% 13.13/2.26 inference(split_clause,[status(thm)],[f337,f968,f971])).
% 13.13/2.26 fof(f984,plain,(
% 13.13/2.26 $false|sQ0_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f355,f214])).
% 13.13/2.26 fof(f985,plain,(
% 13.13/2.26 sQ0_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f984])).
% 13.13/2.26 fof(f986,plain,(
% 13.13/2.26 $false|sQ88_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f679,f341])).
% 13.13/2.26 fof(f987,plain,(
% 13.13/2.26 sQ88_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f986])).
% 13.13/2.26 fof(f988,plain,(
% 13.13/2.26 $false|sQ5_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f374,f228])).
% 13.13/2.26 fof(f989,plain,(
% 13.13/2.26 sQ5_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f988])).
% 13.13/2.26 fof(f990,plain,(
% 13.13/2.26 $false|sQ167_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f970,f349])).
% 13.13/2.26 fof(f991,plain,(
% 13.13/2.26 sQ167_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f990])).
% 13.13/2.26 fof(f992,plain,(
% 13.13/2.26 $false|sQ163_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f956,f340])).
% 13.13/2.26 fof(f993,plain,(
% 13.13/2.26 sQ163_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f992])).
% 13.13/2.26 fof(f994,plain,(
% 13.13/2.26 $false|sQ86_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f672,f213])).
% 13.13/2.26 fof(f995,plain,(
% 13.13/2.26 sQ86_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f994])).
% 13.13/2.26 fof(f996,plain,(
% 13.13/2.26 $false|sQ82_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f658,f212])).
% 13.13/2.26 fof(f997,plain,(
% 13.13/2.26 sQ82_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f996])).
% 13.13/2.26 fof(f998,plain,(
% 13.13/2.26 $false|sQ78_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f644,f211])).
% 13.13/2.26 fof(f999,plain,(
% 13.13/2.26 sQ78_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f998])).
% 13.13/2.26 fof(f1000,plain,(
% 13.13/2.26 $false|~sQ161_spl|sQ162_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f952,f947])).
% 13.13/2.26 fof(f1001,plain,(
% 13.13/2.26 ~sQ161_spl|sQ162_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f1000])).
% 13.13/2.26 fof(f1014,plain,(
% 13.13/2.26 $false|sQ109_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f758,f343])).
% 13.13/2.26 fof(f1015,plain,(
% 13.13/2.26 sQ109_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f1014])).
% 13.13/2.26 fof(f1017,plain,(
% 13.13/2.26 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1))|~sQ89_spl|~sQ168_spl)),
% 13.13/2.26 inference(paramodulation,[status(thm)],[f972,f681])).
% 13.13/2.26 fof(f1033,plain,(
% 13.13/2.26 $false|sQ115_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f780,f345])).
% 13.13/2.26 fof(f1034,plain,(
% 13.13/2.26 sQ115_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f1033])).
% 13.13/2.26 fof(f1037,plain,(
% 13.13/2.26 $false|sQ33_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f477,f223])).
% 13.13/2.26 fof(f1038,plain,(
% 13.13/2.26 sQ33_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f1037])).
% 13.13/2.26 fof(f1045,plain,(
% 13.13/2.26 $false|sQ21_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f433,f219])).
% 13.13/2.26 fof(f1046,plain,(
% 13.13/2.26 sQ21_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f1045])).
% 13.13/2.26 fof(f1059,plain,(
% 13.13/2.26 $false|sQ12_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f400,f216])).
% 13.13/2.26 fof(f1060,plain,(
% 13.13/2.26 sQ12_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f1059])).
% 13.13/2.26 fof(f1073,plain,(
% 13.13/2.26 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,and(X0,X1)))|~sQ1_spl|~sQ28_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f357,f457])).
% 13.13/2.26 fof(f1143,plain,(
% 13.13/2.26 ![X0,X1]: (possibly(and(X0,not(X1)))=not(necessarily(implies(X0,X1)))|~sQ164_spl|~sQ83_spl)),
% 13.13/2.26 inference(paramodulation,[status(thm)],[f660,f958])).
% 13.13/2.26 fof(f1144,plain,(
% 13.13/2.26 ![X0,X1]: (possibly(and(X0,not(X1)))=not(strict_implies(X0,X1))|~sQ168_spl|~sQ164_spl|~sQ83_spl)),
% 13.13/2.26 inference(forward_demodulation,[status(thm)],[f972,f1143])).
% 13.13/2.26 fof(f1151,plain,(
% 13.13/2.26 ![X0]: (is_a_theorem(strict_implies(X0,necessarily(possibly(X0))))|~sQ89_spl|~sQ168_spl|~sQ116_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f1017,f782])).
% 13.13/2.26 fof(f1158,plain,(
% 13.13/2.26 $false|sQ112_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f769,f344])).
% 13.13/2.26 fof(f1159,plain,(
% 13.13/2.26 sQ112_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f1158])).
% 13.13/2.26 fof(f1314,plain,(
% 13.13/2.26 $false|sQ36_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f488,f224])).
% 13.13/2.26 fof(f1315,plain,(
% 13.13/2.26 sQ36_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f1314])).
% 13.13/2.26 fof(f1354,plain,(
% 13.13/2.26 $false|sQ15_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f411,f217])).
% 13.13/2.26 fof(f1355,plain,(
% 13.13/2.26 sQ15_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f1354])).
% 13.13/2.26 fof(f1387,plain,(
% 13.13/2.26 $false|sQ27_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f455,f221])).
% 13.13/2.26 fof(f1388,plain,(
% 13.13/2.26 sQ27_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f1387])).
% 13.13/2.26 fof(f1447,plain,(
% 13.13/2.26 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1))|~sQ98_spl|~sQ87_spl)),
% 13.13/2.26 inference(paramodulation,[status(thm)],[f674,f715])).
% 13.13/2.26 fof(f1469,plain,(
% 13.13/2.26 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~sQ83_spl|~sQ79_spl)),
% 13.13/2.26 inference(forward_demodulation,[status(thm)],[f660,f646])).
% 13.13/2.26 fof(f1489,plain,(
% 13.13/2.26 ![X0,X1]: (strict_implies(not(X0),X1)=necessarily(or(X0,X1))|~sQ168_spl|~sQ83_spl|~sQ79_spl)),
% 13.13/2.26 inference(paramodulation,[status(thm)],[f1469,f972])).
% 13.13/2.26 fof(f1609,plain,(
% 13.13/2.26 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))|~sQ28_spl|~sQ1_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f1073,f357])).
% 13.13/2.26 fof(f1997,plain,(
% 13.13/2.26 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1))|~sQ16_spl|~sQ1_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f413,f357])).
% 13.13/2.26 fof(f2987,plain,(
% 13.13/2.26 sQ98_spl|~sQ28_spl|~sQ1_spl),
% 13.13/2.26 inference(split_clause,[status(thm)],[f1609,f714,f456,f356])).
% 13.13/2.26 fof(f3961,plain,(
% 13.13/2.26 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1)))|~sQ16_spl|~sQ1_spl|~sQ37_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f1997,f490])).
% 13.13/2.26 fof(f3963,plain,(
% 13.13/2.26 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~sQ16_spl|~sQ1_spl|~sQ28_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f1997,f457])).
% 13.13/2.26 fof(f3964,plain,(
% 13.13/2.26 ![X0]: (is_a_theorem(implies(X0,X0))|~sQ16_spl|~sQ1_spl|~sQ13_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f1997,f402])).
% 13.13/2.26 fof(f3969,plain,(
% 13.13/2.26 sQ49_spl|~sQ16_spl|~sQ1_spl|~sQ28_spl),
% 13.13/2.26 inference(split_clause,[status(thm)],[f3963,f533,f412,f356,f456])).
% 13.13/2.26 fof(f4208,plain,(
% 13.13/2.26 $false|~sQ160_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f944,f352])).
% 13.13/2.26 fof(f4209,plain,(
% 13.13/2.26 ~sQ160_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f4208])).
% 13.13/2.26 fof(f4392,plain,(
% 13.13/2.26 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1))|~sQ16_spl|~sQ37_spl|~sQ1_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f3961,f357])).
% 13.13/2.26 fof(f4499,plain,(
% 13.13/2.26 ~is_a_theorem(implies(sK44_skl,sK44_skl))|~sQ16_spl|~sQ37_spl|~sQ1_spl|sQ66_spl),
% 13.13/2.26 inference(resolution,[status(thm)],[f4392,f599])).
% 13.13/2.26 fof(f4506,plain,(
% 13.13/2.26 $false|~sQ13_spl|~sQ16_spl|~sQ37_spl|~sQ1_spl|sQ66_spl),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f4499,f3964])).
% 13.13/2.26 fof(f4507,plain,(
% 13.13/2.26 ~sQ13_spl|~sQ16_spl|~sQ37_spl|~sQ1_spl|sQ66_spl),
% 13.13/2.26 inference(contradiction_clause,[status(thm)],[f4506])).
% 13.13/2.26 fof(f6949,plain,(
% 13.13/2.26 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|is_a_theorem(equiv(X0,or(X0,X0)))|~sQ98_spl|~sQ87_spl|~sQ65_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f1447,f594])).
% 13.13/2.26 fof(f6953,plain,(
% 13.13/2.26 ![X0]: (~is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0)))|is_a_theorem(equiv(necessarily(necessarily(X0)),necessarily(X0)))|~sQ98_spl|~sQ87_spl|~sQ113_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f1447,f771])).
% 13.13/2.26 fof(f6957,plain,(
% 13.13/2.26 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|is_a_theorem(equiv(and(X0,X0),X0))|~sQ98_spl|~sQ87_spl|~sQ49_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f1447,f534])).
% 13.13/2.26 fof(f6977,plain,(
% 13.13/2.26 ![X0]: (is_a_theorem(equiv(X0,or(X0,X0)))|~sQ34_spl|~sQ98_spl|~sQ87_spl|~sQ65_spl)),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f6949,f479])).
% 13.13/2.26 fof(f6980,plain,(
% 13.13/2.26 ![X0]: (is_a_theorem(equiv(necessarily(necessarily(X0)),necessarily(X0)))|~sQ110_spl|~sQ98_spl|~sQ87_spl|~sQ113_spl)),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f6953,f760])).
% 13.13/2.26 fof(f6982,plain,(
% 13.13/2.26 ![X0]: (is_a_theorem(equiv(and(X0,X0),X0))|~sQ22_spl|~sQ98_spl|~sQ87_spl|~sQ49_spl)),
% 13.13/2.26 inference(forward_subsumption_resolution,[status(thm)],[f6957,f435])).
% 13.13/2.26 fof(f7052,plain,(
% 13.13/2.26 ![X0]: (necessarily(necessarily(X0))=necessarily(X0)|~sQ110_spl|~sQ98_spl|~sQ87_spl|~sQ113_spl|~sQ6_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f6980,f376])).
% 13.13/2.26 fof(f7197,plain,(
% 13.13/2.26 ![X0]: (X0=or(X0,X0)|~sQ34_spl|~sQ98_spl|~sQ87_spl|~sQ65_spl|~sQ6_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f6977,f376])).
% 13.13/2.26 fof(f7280,plain,(
% 13.13/2.26 ![X0]: (and(X0,X0)=X0|~sQ22_spl|~sQ98_spl|~sQ87_spl|~sQ49_spl|~sQ6_spl)),
% 13.13/2.26 inference(resolution,[status(thm)],[f6982,f376])).
% 13.13/2.26 fof(f7304,plain,(
% 13.13/2.26 ![X0]: (possibly(not(X0))=not(strict_implies(not(X0),X0))|~sQ168_spl|~sQ164_spl|~sQ83_spl|~sQ22_spl|~sQ98_spl|~sQ87_spl|~sQ49_spl|~sQ6_spl)),
% 13.13/2.26 inference(paramodulation,[status(thm)],[f7280,f1144])).
% 13.13/2.26 fof(f7330,plain,(
% 13.13/2.26 ![X0]: (possibly(not(X0))=not(necessarily(or(X0,X0)))|~sQ79_spl|~sQ168_spl|~sQ164_spl|~sQ83_spl|~sQ22_spl|~sQ98_spl|~sQ87_spl|~sQ49_spl|~sQ6_spl)),
% 13.13/2.27 inference(forward_demodulation,[status(thm)],[f1489,f7304])).
% 13.13/2.27 fof(f7331,plain,(
% 13.13/2.27 ![X0]: (possibly(not(X0))=not(necessarily(X0))|~sQ34_spl|~sQ65_spl|~sQ79_spl|~sQ168_spl|~sQ164_spl|~sQ83_spl|~sQ22_spl|~sQ98_spl|~sQ87_spl|~sQ49_spl|~sQ6_spl)),
% 13.13/2.27 inference(forward_demodulation,[status(thm)],[f7197,f7330])).
% 13.13/2.27 fof(f8580,plain,(
% 13.13/2.27 ![X0]: (possibly(possibly(X0))=not(necessarily(necessarily(not(X0))))|~sQ34_spl|~sQ65_spl|~sQ79_spl|~sQ168_spl|~sQ83_spl|~sQ22_spl|~sQ98_spl|~sQ87_spl|~sQ49_spl|~sQ6_spl|~sQ164_spl)),
% 13.13/2.27 inference(paramodulation,[status(thm)],[f958,f7331])).
% 13.13/2.27 fof(f8606,plain,(
% 13.13/2.27 ![X0]: (possibly(possibly(X0))=not(necessarily(not(X0)))|~sQ110_spl|~sQ113_spl|~sQ34_spl|~sQ65_spl|~sQ79_spl|~sQ168_spl|~sQ83_spl|~sQ22_spl|~sQ98_spl|~sQ87_spl|~sQ49_spl|~sQ6_spl|~sQ164_spl)),
% 13.13/2.27 inference(forward_demodulation,[status(thm)],[f7052,f8580])).
% 13.13/2.27 fof(f8607,plain,(
% 13.13/2.27 ![X0]: (possibly(possibly(X0))=possibly(X0)|~sQ110_spl|~sQ113_spl|~sQ34_spl|~sQ65_spl|~sQ79_spl|~sQ168_spl|~sQ83_spl|~sQ22_spl|~sQ98_spl|~sQ87_spl|~sQ49_spl|~sQ6_spl|~sQ164_spl)),
% 13.13/2.27 inference(forward_demodulation,[status(thm)],[f958,f8606])).
% 13.13/2.27 fof(f8653,plain,(
% 13.13/2.27 ![X0]: (is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))|~sQ89_spl|~sQ116_spl|~sQ110_spl|~sQ113_spl|~sQ34_spl|~sQ65_spl|~sQ79_spl|~sQ168_spl|~sQ83_spl|~sQ22_spl|~sQ98_spl|~sQ87_spl|~sQ49_spl|~sQ6_spl|~sQ164_spl)),
% 13.13/2.27 inference(paramodulation,[status(thm)],[f8607,f1151])).
% 13.13/2.27 fof(f8684,plain,(
% 13.13/2.27 sQ161_spl|~sQ89_spl|~sQ116_spl|~sQ110_spl|~sQ113_spl|~sQ34_spl|~sQ65_spl|~sQ79_spl|~sQ168_spl|~sQ83_spl|~sQ22_spl|~sQ98_spl|~sQ87_spl|~sQ49_spl|~sQ6_spl|~sQ164_spl),
% 13.13/2.27 inference(split_clause,[status(thm)],[f8653,f946,f680,f781,f759,f770,f478,f593,f645,f971,f659,f434,f714,f673,f533,f375,f957])).
% 13.13/2.27 fof(f8692,plain,(
% 13.13/2.27 $false),
% 13.13/2.27 inference(sat_refutation,[status(thm)],[f359,f378,f404,f415,f437,f459,f481,f492,f596,f600,f648,f662,f676,f683,f762,f773,f784,f953,f960,f974,f985,f987,f989,f991,f993,f995,f997,f999,f1001,f1015,f1034,f1038,f1046,f1060,f1159,f1315,f1355,f1388,f2987,f3969,f4209,f4507,f8684])).
% 13.13/2.27 % SZS output end CNFRefutation for theBenchmark.p
% 0.48/2.33 % Elapsed time: 1.856477 seconds
% 0.48/2.33 % CPU time: 14.145840 seconds
% 0.48/2.33 % Total memory used: 251.741 MB
% 0.48/2.33 % Net memory used: 242.111 MB
%------------------------------------------------------------------------------