TSTP Solution File: LCL535+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL535+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:19:33 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL535+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:43:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.19/0.59 % Refutation found
% 0.19/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.59 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.59 fof(f1,axiom,(
% 0.19/0.59 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f2,axiom,(
% 0.19/0.59 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f3,axiom,(
% 0.19/0.59 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f4,axiom,(
% 0.19/0.59 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f5,axiom,(
% 0.19/0.59 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f6,axiom,(
% 0.19/0.59 ( implies_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f7,axiom,(
% 0.19/0.59 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f8,axiom,(
% 0.19/0.59 ( and_2<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f9,axiom,(
% 0.19/0.59 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f10,axiom,(
% 0.19/0.59 ( or_1<=> (! [X,Y] : is_a_theorem(implies(X,or(X,Y))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f11,axiom,(
% 0.19/0.59 ( or_2<=> (! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f12,axiom,(
% 0.19/0.59 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f16,axiom,(
% 0.19/0.59 ( kn1<=> (! [P] : is_a_theorem(implies(P,and(P,P))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f17,axiom,(
% 0.19/0.59 ( kn2<=> (! [P,Q] : is_a_theorem(implies(and(P,Q),P)) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f19,axiom,(
% 0.19/0.59 ( cn1<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f20,axiom,(
% 0.19/0.59 ( cn2<=> (! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f21,axiom,(
% 0.19/0.59 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f22,axiom,(
% 0.19/0.59 ( r1<=> (! [P] : is_a_theorem(implies(or(P,P),P)) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f23,axiom,(
% 0.19/0.59 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f27,axiom,(
% 0.19/0.59 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f29,axiom,(
% 0.19/0.59 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f31,axiom,(
% 0.19/0.59 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f32,axiom,(
% 0.19/0.59 op_or ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f33,axiom,(
% 0.19/0.59 op_implies_and ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f34,axiom,(
% 0.19/0.59 op_equiv ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f35,axiom,(
% 0.19/0.59 modus_ponens ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f36,axiom,(
% 0.19/0.59 modus_tollens ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f37,axiom,(
% 0.19/0.59 implies_1 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f38,axiom,(
% 0.19/0.59 implies_2 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f39,axiom,(
% 0.19/0.59 implies_3 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f40,axiom,(
% 0.19/0.59 and_1 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f41,axiom,(
% 0.19/0.59 and_2 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f42,axiom,(
% 0.19/0.59 and_3 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f43,axiom,(
% 0.19/0.59 or_1 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f44,axiom,(
% 0.19/0.59 or_2 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f45,axiom,(
% 0.19/0.59 or_3 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f46,axiom,(
% 0.19/0.59 equivalence_1 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f47,axiom,(
% 0.19/0.59 equivalence_2 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f48,axiom,(
% 0.19/0.59 equivalence_3 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f49,axiom,(
% 0.19/0.59 substitution_of_equivalents ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f50,axiom,(
% 0.19/0.59 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f52,axiom,(
% 0.19/0.59 ( adjunction<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(Y) )=> is_a_theorem(and(X,Y)) ) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f54,axiom,(
% 0.19/0.59 ( axiom_K<=> (! [X,Y] : is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y)))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f55,axiom,(
% 0.19/0.59 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f58,axiom,(
% 0.19/0.59 ( axiom_5<=> (! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f64,axiom,(
% 0.19/0.59 ( axiom_m2<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f66,axiom,(
% 0.19/0.59 ( axiom_m4<=> (! [X] : is_a_theorem(strict_implies(X,and(X,X))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f71,axiom,(
% 0.19/0.59 ( axiom_m9<=> (! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f72,axiom,(
% 0.19/0.59 ( axiom_m10<=> (! [X] : is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f73,axiom,(
% 0.19/0.59 ( op_possibly=> (! [X] : possibly(X) = not(necessarily(not(X))) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f75,axiom,(
% 0.19/0.59 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f76,axiom,(
% 0.19/0.59 ( op_strict_equiv=> (! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) )) ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f77,axiom,(
% 0.19/0.59 op_possibly ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f78,axiom,(
% 0.19/0.59 necessitation ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f79,axiom,(
% 0.19/0.59 axiom_K ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f80,axiom,(
% 0.19/0.59 axiom_M ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f81,axiom,(
% 0.19/0.59 axiom_5 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f85,axiom,(
% 0.19/0.59 op_strict_implies ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f87,axiom,(
% 0.19/0.59 op_strict_equiv ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f88,conjecture,(
% 0.19/0.59 axiom_m9 ),
% 0.19/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.59 fof(f89,negated_conjecture,(
% 0.19/0.59 ~(axiom_m9 )),
% 0.19/0.59 inference(negated_conjecture,[status(cth)],[f88])).
% 0.19/0.59 fof(f90,plain,(
% 0.19/0.59 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.19/0.59 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.19/0.59 fof(f91,plain,(
% 0.19/0.59 (~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))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f90])).
% 0.19/0.59 fof(f92,plain,(
% 0.19/0.59 (~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))))),
% 0.19/0.59 inference(miniscoping,[status(esa)],[f91])).
% 0.19/0.59 fof(f93,plain,(
% 0.19/0.59 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|((is_a_theorem(sk0_1)&is_a_theorem(implies(sk0_1,sk0_0)))&~is_a_theorem(sk0_0)))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f92])).
% 0.19/0.59 fof(f94,plain,(
% 0.19/0.59 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f93])).
% 0.19/0.59 fof(f98,plain,(
% 0.19/0.59 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 0.19/0.59 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.19/0.59 fof(f99,plain,(
% 0.19/0.59 (~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)))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f98])).
% 0.19/0.59 fof(f100,plain,(
% 0.19/0.59 (~substitution_of_equivalents|(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y)))&(substitution_of_equivalents|(is_a_theorem(equiv(sk0_2,sk0_3))&~sk0_2=sk0_3))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f99])).
% 0.19/0.59 fof(f101,plain,(
% 0.19/0.59 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f100])).
% 0.19/0.59 fof(f104,plain,(
% 0.19/0.59 (~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)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f3])).
% 0.19/0.59 fof(f105,plain,(
% 0.19/0.59 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|~is_a_theorem(implies(implies(not(sk0_5),not(sk0_4)),implies(sk0_4,sk0_5))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f104])).
% 0.19/0.59 fof(f106,plain,(
% 0.19/0.59 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f105])).
% 0.19/0.59 fof(f108,plain,(
% 0.19/0.59 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f4])).
% 0.19/0.59 fof(f109,plain,(
% 0.19/0.59 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|~is_a_theorem(implies(sk0_6,implies(sk0_7,sk0_6))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f108])).
% 0.19/0.59 fof(f110,plain,(
% 0.19/0.59 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f109])).
% 0.19/0.59 fof(f112,plain,(
% 0.19/0.59 (~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)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f5])).
% 0.19/0.59 fof(f113,plain,(
% 0.19/0.59 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|~is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f112])).
% 0.19/0.59 fof(f114,plain,(
% 0.19/0.59 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f113])).
% 0.19/0.59 fof(f116,plain,(
% 0.19/0.59 (~implies_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))&(implies_3|(?[X,Y,Z]: ~is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f6])).
% 0.19/0.59 fof(f117,plain,(
% 0.19/0.59 (~implies_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))&(implies_3|~is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12)))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f116])).
% 0.19/0.59 fof(f118,plain,(
% 0.19/0.59 ![X0,X1,X2]: (~implies_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f117])).
% 0.19/0.59 fof(f120,plain,(
% 0.19/0.59 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f7])).
% 0.19/0.59 fof(f121,plain,(
% 0.19/0.59 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|~is_a_theorem(implies(and(sk0_13,sk0_14),sk0_13)))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f120])).
% 0.19/0.59 fof(f122,plain,(
% 0.19/0.59 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f121])).
% 0.19/0.59 fof(f124,plain,(
% 0.19/0.59 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),Y))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f8])).
% 0.19/0.59 fof(f125,plain,(
% 0.19/0.59 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|~is_a_theorem(implies(and(sk0_15,sk0_16),sk0_16)))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f124])).
% 0.19/0.59 fof(f126,plain,(
% 0.19/0.59 ![X0,X1]: (~and_2|is_a_theorem(implies(and(X0,X1),X1)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f125])).
% 0.19/0.59 fof(f128,plain,(
% 0.19/0.59 (~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))))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f9])).
% 0.19/0.59 fof(f129,plain,(
% 0.19/0.59 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|~is_a_theorem(implies(sk0_17,implies(sk0_18,and(sk0_17,sk0_18)))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f128])).
% 0.19/0.59 fof(f130,plain,(
% 0.19/0.59 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f129])).
% 0.19/0.59 fof(f132,plain,(
% 0.19/0.59 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|(?[X,Y]: ~is_a_theorem(implies(X,or(X,Y)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f10])).
% 0.19/0.59 fof(f133,plain,(
% 0.19/0.59 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|~is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f132])).
% 0.19/0.59 fof(f134,plain,(
% 0.19/0.59 ![X0,X1]: (~or_1|is_a_theorem(implies(X0,or(X0,X1))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f133])).
% 0.19/0.59 fof(f136,plain,(
% 0.19/0.59 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|(?[X,Y]: ~is_a_theorem(implies(Y,or(X,Y)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f11])).
% 0.19/0.59 fof(f137,plain,(
% 0.19/0.59 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|~is_a_theorem(implies(sk0_22,or(sk0_21,sk0_22))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f136])).
% 0.19/0.59 fof(f138,plain,(
% 0.19/0.59 ![X0,X1]: (~or_2|is_a_theorem(implies(X0,or(X1,X0))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f137])).
% 0.19/0.59 fof(f140,plain,(
% 0.19/0.59 (~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))))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f12])).
% 0.19/0.59 fof(f141,plain,(
% 0.19/0.59 (~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(sk0_23,sk0_25),implies(implies(sk0_24,sk0_25),implies(or(sk0_23,sk0_24),sk0_25)))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f140])).
% 0.19/0.59 fof(f142,plain,(
% 0.19/0.59 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f141])).
% 0.19/0.59 fof(f156,plain,(
% 0.19/0.59 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|(?[P]: ~is_a_theorem(implies(P,and(P,P)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f16])).
% 0.19/0.59 fof(f157,plain,(
% 0.19/0.59 (~kn1|(![P]: is_a_theorem(implies(P,and(P,P)))))&(kn1|~is_a_theorem(implies(sk0_32,and(sk0_32,sk0_32))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f156])).
% 0.19/0.59 fof(f159,plain,(
% 0.19/0.59 kn1|~is_a_theorem(implies(sk0_32,and(sk0_32,sk0_32)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f157])).
% 0.19/0.59 fof(f160,plain,(
% 0.19/0.59 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|(?[P,Q]: ~is_a_theorem(implies(and(P,Q),P))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f17])).
% 0.19/0.59 fof(f161,plain,(
% 0.19/0.59 (~kn2|(![P,Q]: is_a_theorem(implies(and(P,Q),P))))&(kn2|~is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33)))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f160])).
% 0.19/0.59 fof(f163,plain,(
% 0.19/0.59 kn2|~is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f161])).
% 0.19/0.59 fof(f168,plain,(
% 0.19/0.59 (~cn1|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))&(cn1|(?[P,Q,R]: ~is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f19])).
% 0.19/0.59 fof(f169,plain,(
% 0.19/0.59 (~cn1|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))))&(cn1|~is_a_theorem(implies(implies(sk0_38,sk0_39),implies(implies(sk0_39,sk0_40),implies(sk0_38,sk0_40)))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f168])).
% 0.19/0.59 fof(f171,plain,(
% 0.19/0.59 cn1|~is_a_theorem(implies(implies(sk0_38,sk0_39),implies(implies(sk0_39,sk0_40),implies(sk0_38,sk0_40))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f169])).
% 0.19/0.59 fof(f172,plain,(
% 0.19/0.59 (~cn2|(![P,Q]: is_a_theorem(implies(P,implies(not(P),Q)))))&(cn2|(?[P,Q]: ~is_a_theorem(implies(P,implies(not(P),Q)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f20])).
% 0.19/0.59 fof(f173,plain,(
% 0.19/0.59 (~cn2|(![P,Q]: is_a_theorem(implies(P,implies(not(P),Q)))))&(cn2|~is_a_theorem(implies(sk0_41,implies(not(sk0_41),sk0_42))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f172])).
% 0.19/0.59 fof(f174,plain,(
% 0.19/0.59 ![X0,X1]: (~cn2|is_a_theorem(implies(X0,implies(not(X0),X1))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f173])).
% 0.19/0.59 fof(f175,plain,(
% 0.19/0.59 cn2|~is_a_theorem(implies(sk0_41,implies(not(sk0_41),sk0_42)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f173])).
% 0.19/0.59 fof(f176,plain,(
% 0.19/0.59 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f21])).
% 0.19/0.59 fof(f177,plain,(
% 0.19/0.59 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43)))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f176])).
% 0.19/0.59 fof(f178,plain,(
% 0.19/0.59 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f177])).
% 0.19/0.59 fof(f179,plain,(
% 0.19/0.59 cn3|~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f177])).
% 0.19/0.59 fof(f180,plain,(
% 0.19/0.59 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|(?[P]: ~is_a_theorem(implies(or(P,P),P))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f22])).
% 0.19/0.59 fof(f181,plain,(
% 0.19/0.59 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|~is_a_theorem(implies(or(sk0_44,sk0_44),sk0_44)))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f180])).
% 0.19/0.59 fof(f182,plain,(
% 0.19/0.59 ![X0]: (~r1|is_a_theorem(implies(or(X0,X0),X0)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f181])).
% 0.19/0.59 fof(f183,plain,(
% 0.19/0.59 r1|~is_a_theorem(implies(or(sk0_44,sk0_44),sk0_44))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f181])).
% 0.19/0.59 fof(f184,plain,(
% 0.19/0.59 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f23])).
% 0.19/0.59 fof(f185,plain,(
% 0.19/0.59 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sk0_46,or(sk0_45,sk0_46))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f184])).
% 0.19/0.59 fof(f187,plain,(
% 0.19/0.59 r2|~is_a_theorem(implies(sk0_46,or(sk0_45,sk0_46)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f185])).
% 0.19/0.59 fof(f200,plain,(
% 0.19/0.59 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 0.19/0.59 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 0.19/0.59 fof(f201,plain,(
% 0.19/0.59 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f200])).
% 0.19/0.59 fof(f204,plain,(
% 0.19/0.59 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 0.19/0.59 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 0.19/0.59 fof(f205,plain,(
% 0.19/0.59 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f204])).
% 0.19/0.59 fof(f208,plain,(
% 0.19/0.59 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 0.19/0.59 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 0.19/0.59 fof(f209,plain,(
% 0.19/0.59 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f208])).
% 0.19/0.59 fof(f210,plain,(
% 0.19/0.59 op_or),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f32])).
% 0.19/0.59 fof(f211,plain,(
% 0.19/0.59 op_implies_and),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f33])).
% 0.19/0.59 fof(f212,plain,(
% 0.19/0.59 op_equiv),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f34])).
% 0.19/0.59 fof(f213,plain,(
% 0.19/0.59 modus_ponens),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f35])).
% 0.19/0.59 fof(f214,plain,(
% 0.19/0.59 modus_tollens),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f36])).
% 0.19/0.59 fof(f215,plain,(
% 0.19/0.59 implies_1),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f37])).
% 0.19/0.59 fof(f216,plain,(
% 0.19/0.59 implies_2),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f38])).
% 0.19/0.59 fof(f217,plain,(
% 0.19/0.59 implies_3),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f39])).
% 0.19/0.59 fof(f218,plain,(
% 0.19/0.59 and_1),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f40])).
% 0.19/0.59 fof(f219,plain,(
% 0.19/0.59 and_2),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f41])).
% 0.19/0.59 fof(f220,plain,(
% 0.19/0.59 and_3),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f42])).
% 0.19/0.59 fof(f221,plain,(
% 0.19/0.59 or_1),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f43])).
% 0.19/0.59 fof(f222,plain,(
% 0.19/0.59 or_2),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f44])).
% 0.19/0.59 fof(f223,plain,(
% 0.19/0.59 or_3),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f45])).
% 0.19/0.59 fof(f224,plain,(
% 0.19/0.59 equivalence_1),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f46])).
% 0.19/0.59 fof(f225,plain,(
% 0.19/0.59 equivalence_2),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f47])).
% 0.19/0.59 fof(f226,plain,(
% 0.19/0.59 equivalence_3),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f48])).
% 0.19/0.59 fof(f227,plain,(
% 0.19/0.59 substitution_of_equivalents),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f49])).
% 0.19/0.59 fof(f228,plain,(
% 0.19/0.59 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 0.19/0.59 inference(pre_NNF_transformation,[status(esa)],[f50])).
% 0.19/0.59 fof(f229,plain,(
% 0.19/0.59 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f228])).
% 0.19/0.59 fof(f230,plain,(
% 0.19/0.59 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sk0_55)&~is_a_theorem(necessarily(sk0_55))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f229])).
% 0.19/0.59 fof(f231,plain,(
% 0.19/0.59 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f230])).
% 0.19/0.59 fof(f242,plain,(
% 0.19/0.59 adjunction<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y))))),
% 0.19/0.59 inference(pre_NNF_transformation,[status(esa)],[f52])).
% 0.19/0.59 fof(f243,plain,(
% 0.19/0.59 (~adjunction|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y)))))&(adjunction|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(Y))&~is_a_theorem(and(X,Y)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f242])).
% 0.19/0.59 fof(f244,plain,(
% 0.19/0.59 (~adjunction|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y)))))&(adjunction|((is_a_theorem(sk0_58)&is_a_theorem(sk0_59))&~is_a_theorem(and(sk0_58,sk0_59))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f243])).
% 0.19/0.59 fof(f245,plain,(
% 0.19/0.59 ![X0,X1]: (~adjunction|~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f244])).
% 0.19/0.59 fof(f246,plain,(
% 0.19/0.59 adjunction|is_a_theorem(sk0_58)),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f244])).
% 0.19/0.59 fof(f247,plain,(
% 0.19/0.59 adjunction|is_a_theorem(sk0_59)),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f244])).
% 0.19/0.59 fof(f248,plain,(
% 0.19/0.59 adjunction|~is_a_theorem(and(sk0_58,sk0_59))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f244])).
% 0.19/0.59 fof(f255,plain,(
% 0.19/0.59 (~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))))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f54])).
% 0.19/0.59 fof(f256,plain,(
% 0.19/0.59 (~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(sk0_62,sk0_63)),implies(necessarily(sk0_62),necessarily(sk0_63)))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f255])).
% 0.19/0.59 fof(f257,plain,(
% 0.19/0.59 ![X0,X1]: (~axiom_K|is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f256])).
% 0.19/0.59 fof(f259,plain,(
% 0.19/0.59 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f55])).
% 0.19/0.59 fof(f260,plain,(
% 0.19/0.59 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sk0_64),sk0_64)))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f259])).
% 0.19/0.59 fof(f261,plain,(
% 0.19/0.59 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f260])).
% 0.19/0.59 fof(f271,plain,(
% 0.19/0.59 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|(?[X]: ~is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f58])).
% 0.19/0.59 fof(f272,plain,(
% 0.19/0.59 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|~is_a_theorem(implies(possibly(sk0_67),necessarily(possibly(sk0_67)))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f271])).
% 0.19/0.59 fof(f273,plain,(
% 0.19/0.59 ![X0]: (~axiom_5|is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f272])).
% 0.19/0.59 fof(f295,plain,(
% 0.19/0.59 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|(?[X,Y]: ~is_a_theorem(strict_implies(and(X,Y),X))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f64])).
% 0.19/0.59 fof(f296,plain,(
% 0.19/0.59 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|~is_a_theorem(strict_implies(and(sk0_78,sk0_79),sk0_78)))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f295])).
% 0.19/0.59 fof(f297,plain,(
% 0.19/0.59 ![X0,X1]: (~axiom_m2|is_a_theorem(strict_implies(and(X0,X1),X0)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f296])).
% 0.19/0.59 fof(f298,plain,(
% 0.19/0.59 axiom_m2|~is_a_theorem(strict_implies(and(sk0_78,sk0_79),sk0_78))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f296])).
% 0.19/0.59 fof(f303,plain,(
% 0.19/0.59 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|(?[X]: ~is_a_theorem(strict_implies(X,and(X,X)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f66])).
% 0.19/0.59 fof(f304,plain,(
% 0.19/0.59 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|~is_a_theorem(strict_implies(sk0_83,and(sk0_83,sk0_83))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f303])).
% 0.19/0.59 fof(f305,plain,(
% 0.19/0.59 ![X0]: (~axiom_m4|is_a_theorem(strict_implies(X0,and(X0,X0))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f304])).
% 0.19/0.59 fof(f306,plain,(
% 0.19/0.59 axiom_m4|~is_a_theorem(strict_implies(sk0_83,and(sk0_83,sk0_83)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f304])).
% 0.19/0.59 fof(f323,plain,(
% 0.19/0.59 (~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)))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f71])).
% 0.19/0.59 fof(f324,plain,(
% 0.19/0.59 (~axiom_m9|(![X]: is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))))&(axiom_m9|~is_a_theorem(strict_implies(possibly(possibly(sk0_92)),possibly(sk0_92))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f323])).
% 0.19/0.59 fof(f326,plain,(
% 0.19/0.59 axiom_m9|~is_a_theorem(strict_implies(possibly(possibly(sk0_92)),possibly(sk0_92)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f324])).
% 0.19/0.59 fof(f327,plain,(
% 0.19/0.59 (~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))))))),
% 0.19/0.59 inference(NNF_transformation,[status(esa)],[f72])).
% 0.19/0.59 fof(f328,plain,(
% 0.19/0.59 (~axiom_m10|(![X]: is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))))&(axiom_m10|~is_a_theorem(strict_implies(possibly(sk0_93),necessarily(possibly(sk0_93)))))),
% 0.19/0.59 inference(skolemization,[status(esa)],[f327])).
% 0.19/0.59 fof(f329,plain,(
% 0.19/0.59 ![X0]: (~axiom_m10|is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f328])).
% 0.19/0.59 fof(f330,plain,(
% 0.19/0.59 axiom_m10|~is_a_theorem(strict_implies(possibly(sk0_93),necessarily(possibly(sk0_93))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f328])).
% 0.19/0.59 fof(f331,plain,(
% 0.19/0.59 ~op_possibly|(![X]: possibly(X)=not(necessarily(not(X))))),
% 0.19/0.59 inference(pre_NNF_transformation,[status(esa)],[f73])).
% 0.19/0.59 fof(f332,plain,(
% 0.19/0.59 ![X0]: (~op_possibly|possibly(X0)=not(necessarily(not(X0))))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f331])).
% 0.19/0.59 fof(f335,plain,(
% 0.19/0.59 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 0.19/0.59 inference(pre_NNF_transformation,[status(esa)],[f75])).
% 0.19/0.59 fof(f336,plain,(
% 0.19/0.59 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f335])).
% 0.19/0.59 fof(f337,plain,(
% 0.19/0.59 ~op_strict_equiv|(![X,Y]: strict_equiv(X,Y)=and(strict_implies(X,Y),strict_implies(Y,X)))),
% 0.19/0.59 inference(pre_NNF_transformation,[status(esa)],[f76])).
% 0.19/0.59 fof(f338,plain,(
% 0.19/0.59 ![X0,X1]: (~op_strict_equiv|strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0)))),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f337])).
% 0.19/0.59 fof(f339,plain,(
% 0.19/0.59 op_possibly),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f77])).
% 0.19/0.59 fof(f340,plain,(
% 0.19/0.59 necessitation),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f78])).
% 0.19/0.59 fof(f341,plain,(
% 0.19/0.59 axiom_K),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f79])).
% 0.19/0.59 fof(f342,plain,(
% 0.19/0.59 axiom_M),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f80])).
% 0.19/0.59 fof(f343,plain,(
% 0.19/0.59 axiom_5),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f81])).
% 0.19/0.59 fof(f347,plain,(
% 0.19/0.59 op_strict_implies),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f85])).
% 0.19/0.59 fof(f349,plain,(
% 0.19/0.59 op_strict_equiv),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f87])).
% 0.19/0.59 fof(f350,plain,(
% 0.19/0.59 ~axiom_m9),
% 0.19/0.59 inference(cnf_transformation,[status(esa)],[f89])).
% 0.19/0.59 fof(f351,plain,(
% 0.19/0.59 spl0_0 <=> modus_ponens),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f353,plain,(
% 0.19/0.59 ~modus_ponens|spl0_0),
% 0.19/0.59 inference(component_clause,[status(thm)],[f351])).
% 0.19/0.59 fof(f354,plain,(
% 0.19/0.59 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f355,plain,(
% 0.19/0.59 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f354])).
% 0.19/0.59 fof(f357,plain,(
% 0.19/0.59 ~spl0_0|spl0_1),
% 0.19/0.59 inference(split_clause,[status(thm)],[f94,f351,f354])).
% 0.19/0.59 fof(f370,plain,(
% 0.19/0.59 spl0_5 <=> substitution_of_equivalents),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f372,plain,(
% 0.19/0.59 ~substitution_of_equivalents|spl0_5),
% 0.19/0.59 inference(component_clause,[status(thm)],[f370])).
% 0.19/0.59 fof(f373,plain,(
% 0.19/0.59 spl0_6 <=> ~is_a_theorem(equiv(X0,X1))|X0=X1),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f374,plain,(
% 0.19/0.59 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~spl0_6)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f373])).
% 0.19/0.59 fof(f376,plain,(
% 0.19/0.59 ~spl0_5|spl0_6),
% 0.19/0.59 inference(split_clause,[status(thm)],[f101,f370,f373])).
% 0.19/0.59 fof(f385,plain,(
% 0.19/0.59 spl0_9 <=> modus_tollens),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f387,plain,(
% 0.19/0.59 ~modus_tollens|spl0_9),
% 0.19/0.59 inference(component_clause,[status(thm)],[f385])).
% 0.19/0.59 fof(f388,plain,(
% 0.19/0.59 spl0_10 <=> is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f389,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))|~spl0_10)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f388])).
% 0.19/0.59 fof(f391,plain,(
% 0.19/0.59 ~spl0_9|spl0_10),
% 0.19/0.59 inference(split_clause,[status(thm)],[f106,f385,f388])).
% 0.19/0.59 fof(f392,plain,(
% 0.19/0.59 spl0_11 <=> is_a_theorem(implies(implies(not(sk0_5),not(sk0_4)),implies(sk0_4,sk0_5)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f394,plain,(
% 0.19/0.59 ~is_a_theorem(implies(implies(not(sk0_5),not(sk0_4)),implies(sk0_4,sk0_5)))|spl0_11),
% 0.19/0.59 inference(component_clause,[status(thm)],[f392])).
% 0.19/0.59 fof(f396,plain,(
% 0.19/0.59 spl0_12 <=> implies_1),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f398,plain,(
% 0.19/0.59 ~implies_1|spl0_12),
% 0.19/0.59 inference(component_clause,[status(thm)],[f396])).
% 0.19/0.59 fof(f399,plain,(
% 0.19/0.59 spl0_13 <=> is_a_theorem(implies(X0,implies(X1,X0)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f400,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~spl0_13)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f399])).
% 0.19/0.59 fof(f402,plain,(
% 0.19/0.59 ~spl0_12|spl0_13),
% 0.19/0.59 inference(split_clause,[status(thm)],[f110,f396,f399])).
% 0.19/0.59 fof(f403,plain,(
% 0.19/0.59 spl0_14 <=> is_a_theorem(implies(sk0_6,implies(sk0_7,sk0_6)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f405,plain,(
% 0.19/0.59 ~is_a_theorem(implies(sk0_6,implies(sk0_7,sk0_6)))|spl0_14),
% 0.19/0.59 inference(component_clause,[status(thm)],[f403])).
% 0.19/0.59 fof(f407,plain,(
% 0.19/0.59 spl0_15 <=> implies_2),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f409,plain,(
% 0.19/0.59 ~implies_2|spl0_15),
% 0.19/0.59 inference(component_clause,[status(thm)],[f407])).
% 0.19/0.59 fof(f410,plain,(
% 0.19/0.59 spl0_16 <=> is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f411,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))|~spl0_16)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f410])).
% 0.19/0.59 fof(f413,plain,(
% 0.19/0.59 ~spl0_15|spl0_16),
% 0.19/0.59 inference(split_clause,[status(thm)],[f114,f407,f410])).
% 0.19/0.59 fof(f414,plain,(
% 0.19/0.59 spl0_17 <=> is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f416,plain,(
% 0.19/0.59 ~is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9)))|spl0_17),
% 0.19/0.59 inference(component_clause,[status(thm)],[f414])).
% 0.19/0.59 fof(f418,plain,(
% 0.19/0.59 spl0_18 <=> implies_3),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f420,plain,(
% 0.19/0.59 ~implies_3|spl0_18),
% 0.19/0.59 inference(component_clause,[status(thm)],[f418])).
% 0.19/0.59 fof(f421,plain,(
% 0.19/0.59 spl0_19 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f422,plain,(
% 0.19/0.59 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))|~spl0_19)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f421])).
% 0.19/0.59 fof(f424,plain,(
% 0.19/0.59 ~spl0_18|spl0_19),
% 0.19/0.59 inference(split_clause,[status(thm)],[f118,f418,f421])).
% 0.19/0.59 fof(f425,plain,(
% 0.19/0.59 spl0_20 <=> is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f427,plain,(
% 0.19/0.59 ~is_a_theorem(implies(implies(sk0_10,sk0_11),implies(implies(sk0_11,sk0_12),implies(sk0_10,sk0_12))))|spl0_20),
% 0.19/0.59 inference(component_clause,[status(thm)],[f425])).
% 0.19/0.59 fof(f429,plain,(
% 0.19/0.59 spl0_21 <=> and_1),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f431,plain,(
% 0.19/0.59 ~and_1|spl0_21),
% 0.19/0.59 inference(component_clause,[status(thm)],[f429])).
% 0.19/0.59 fof(f432,plain,(
% 0.19/0.59 spl0_22 <=> is_a_theorem(implies(and(X0,X1),X0))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f433,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_22)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f432])).
% 0.19/0.59 fof(f435,plain,(
% 0.19/0.59 ~spl0_21|spl0_22),
% 0.19/0.59 inference(split_clause,[status(thm)],[f122,f429,f432])).
% 0.19/0.59 fof(f436,plain,(
% 0.19/0.59 spl0_23 <=> is_a_theorem(implies(and(sk0_13,sk0_14),sk0_13))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f438,plain,(
% 0.19/0.59 ~is_a_theorem(implies(and(sk0_13,sk0_14),sk0_13))|spl0_23),
% 0.19/0.59 inference(component_clause,[status(thm)],[f436])).
% 0.19/0.59 fof(f440,plain,(
% 0.19/0.59 spl0_24 <=> and_2),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f442,plain,(
% 0.19/0.59 ~and_2|spl0_24),
% 0.19/0.59 inference(component_clause,[status(thm)],[f440])).
% 0.19/0.59 fof(f443,plain,(
% 0.19/0.59 spl0_25 <=> is_a_theorem(implies(and(X0,X1),X1))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f444,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1))|~spl0_25)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f443])).
% 0.19/0.59 fof(f446,plain,(
% 0.19/0.59 ~spl0_24|spl0_25),
% 0.19/0.59 inference(split_clause,[status(thm)],[f126,f440,f443])).
% 0.19/0.59 fof(f447,plain,(
% 0.19/0.59 spl0_26 <=> is_a_theorem(implies(and(sk0_15,sk0_16),sk0_16))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f449,plain,(
% 0.19/0.59 ~is_a_theorem(implies(and(sk0_15,sk0_16),sk0_16))|spl0_26),
% 0.19/0.59 inference(component_clause,[status(thm)],[f447])).
% 0.19/0.59 fof(f451,plain,(
% 0.19/0.59 spl0_27 <=> and_3),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f453,plain,(
% 0.19/0.59 ~and_3|spl0_27),
% 0.19/0.59 inference(component_clause,[status(thm)],[f451])).
% 0.19/0.59 fof(f454,plain,(
% 0.19/0.59 spl0_28 <=> is_a_theorem(implies(X0,implies(X1,and(X0,X1))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f455,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1))))|~spl0_28)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f454])).
% 0.19/0.59 fof(f457,plain,(
% 0.19/0.59 ~spl0_27|spl0_28),
% 0.19/0.59 inference(split_clause,[status(thm)],[f130,f451,f454])).
% 0.19/0.59 fof(f462,plain,(
% 0.19/0.59 spl0_30 <=> or_1),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f464,plain,(
% 0.19/0.59 ~or_1|spl0_30),
% 0.19/0.59 inference(component_clause,[status(thm)],[f462])).
% 0.19/0.59 fof(f465,plain,(
% 0.19/0.59 spl0_31 <=> is_a_theorem(implies(X0,or(X0,X1)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f466,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_31)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f465])).
% 0.19/0.59 fof(f468,plain,(
% 0.19/0.59 ~spl0_30|spl0_31),
% 0.19/0.59 inference(split_clause,[status(thm)],[f134,f462,f465])).
% 0.19/0.59 fof(f469,plain,(
% 0.19/0.59 spl0_32 <=> is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f471,plain,(
% 0.19/0.59 ~is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20)))|spl0_32),
% 0.19/0.59 inference(component_clause,[status(thm)],[f469])).
% 0.19/0.59 fof(f473,plain,(
% 0.19/0.59 spl0_33 <=> or_2),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f475,plain,(
% 0.19/0.59 ~or_2|spl0_33),
% 0.19/0.59 inference(component_clause,[status(thm)],[f473])).
% 0.19/0.59 fof(f476,plain,(
% 0.19/0.59 spl0_34 <=> is_a_theorem(implies(X0,or(X1,X0)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f477,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~spl0_34)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f476])).
% 0.19/0.59 fof(f479,plain,(
% 0.19/0.59 ~spl0_33|spl0_34),
% 0.19/0.59 inference(split_clause,[status(thm)],[f138,f473,f476])).
% 0.19/0.59 fof(f480,plain,(
% 0.19/0.59 spl0_35 <=> is_a_theorem(implies(sk0_22,or(sk0_21,sk0_22)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f482,plain,(
% 0.19/0.59 ~is_a_theorem(implies(sk0_22,or(sk0_21,sk0_22)))|spl0_35),
% 0.19/0.59 inference(component_clause,[status(thm)],[f480])).
% 0.19/0.59 fof(f484,plain,(
% 0.19/0.59 spl0_36 <=> or_3),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f486,plain,(
% 0.19/0.59 ~or_3|spl0_36),
% 0.19/0.59 inference(component_clause,[status(thm)],[f484])).
% 0.19/0.59 fof(f487,plain,(
% 0.19/0.59 spl0_37 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f488,plain,(
% 0.19/0.59 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))|~spl0_37)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f487])).
% 0.19/0.59 fof(f490,plain,(
% 0.19/0.59 ~spl0_36|spl0_37),
% 0.19/0.59 inference(split_clause,[status(thm)],[f142,f484,f487])).
% 0.19/0.59 fof(f491,plain,(
% 0.19/0.59 spl0_38 <=> is_a_theorem(implies(implies(sk0_23,sk0_25),implies(implies(sk0_24,sk0_25),implies(or(sk0_23,sk0_24),sk0_25))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f493,plain,(
% 0.19/0.59 ~is_a_theorem(implies(implies(sk0_23,sk0_25),implies(implies(sk0_24,sk0_25),implies(or(sk0_23,sk0_24),sk0_25))))|spl0_38),
% 0.19/0.59 inference(component_clause,[status(thm)],[f491])).
% 0.19/0.59 fof(f495,plain,(
% 0.19/0.59 spl0_39 <=> equivalence_1),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f497,plain,(
% 0.19/0.59 ~equivalence_1|spl0_39),
% 0.19/0.59 inference(component_clause,[status(thm)],[f495])).
% 0.19/0.59 fof(f498,plain,(
% 0.19/0.59 spl0_40 <=> is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f499,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))|~spl0_40)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f498])).
% 0.19/0.59 fof(f502,plain,(
% 0.19/0.59 spl0_41 <=> is_a_theorem(implies(equiv(sk0_26,sk0_27),implies(sk0_26,sk0_27)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f504,plain,(
% 0.19/0.59 ~is_a_theorem(implies(equiv(sk0_26,sk0_27),implies(sk0_26,sk0_27)))|spl0_41),
% 0.19/0.59 inference(component_clause,[status(thm)],[f502])).
% 0.19/0.59 fof(f506,plain,(
% 0.19/0.59 spl0_42 <=> equivalence_2),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f508,plain,(
% 0.19/0.59 ~equivalence_2|spl0_42),
% 0.19/0.59 inference(component_clause,[status(thm)],[f506])).
% 0.19/0.59 fof(f509,plain,(
% 0.19/0.59 spl0_43 <=> is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f510,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))|~spl0_43)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f509])).
% 0.19/0.59 fof(f513,plain,(
% 0.19/0.59 spl0_44 <=> is_a_theorem(implies(equiv(sk0_28,sk0_29),implies(sk0_29,sk0_28)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f515,plain,(
% 0.19/0.59 ~is_a_theorem(implies(equiv(sk0_28,sk0_29),implies(sk0_29,sk0_28)))|spl0_44),
% 0.19/0.59 inference(component_clause,[status(thm)],[f513])).
% 0.19/0.59 fof(f517,plain,(
% 0.19/0.59 spl0_45 <=> equivalence_3),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f519,plain,(
% 0.19/0.59 ~equivalence_3|spl0_45),
% 0.19/0.59 inference(component_clause,[status(thm)],[f517])).
% 0.19/0.59 fof(f520,plain,(
% 0.19/0.59 spl0_46 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f521,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))|~spl0_46)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f520])).
% 0.19/0.59 fof(f524,plain,(
% 0.19/0.59 spl0_47 <=> is_a_theorem(implies(implies(sk0_30,sk0_31),implies(implies(sk0_31,sk0_30),equiv(sk0_30,sk0_31))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f526,plain,(
% 0.19/0.59 ~is_a_theorem(implies(implies(sk0_30,sk0_31),implies(implies(sk0_31,sk0_30),equiv(sk0_30,sk0_31))))|spl0_47),
% 0.19/0.59 inference(component_clause,[status(thm)],[f524])).
% 0.19/0.59 fof(f528,plain,(
% 0.19/0.59 spl0_48 <=> kn1),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f531,plain,(
% 0.19/0.59 spl0_49 <=> is_a_theorem(implies(X0,and(X0,X0)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f532,plain,(
% 0.19/0.59 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_49)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f531])).
% 0.19/0.59 fof(f535,plain,(
% 0.19/0.59 spl0_50 <=> is_a_theorem(implies(sk0_32,and(sk0_32,sk0_32)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f537,plain,(
% 0.19/0.59 ~is_a_theorem(implies(sk0_32,and(sk0_32,sk0_32)))|spl0_50),
% 0.19/0.59 inference(component_clause,[status(thm)],[f535])).
% 0.19/0.59 fof(f538,plain,(
% 0.19/0.59 spl0_48|~spl0_50),
% 0.19/0.59 inference(split_clause,[status(thm)],[f159,f528,f535])).
% 0.19/0.59 fof(f539,plain,(
% 0.19/0.59 spl0_51 <=> kn2),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f543,plain,(
% 0.19/0.59 spl0_52 <=> is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f545,plain,(
% 0.19/0.59 ~is_a_theorem(implies(and(sk0_33,sk0_34),sk0_33))|spl0_52),
% 0.19/0.59 inference(component_clause,[status(thm)],[f543])).
% 0.19/0.59 fof(f546,plain,(
% 0.19/0.59 spl0_51|~spl0_52),
% 0.19/0.59 inference(split_clause,[status(thm)],[f163,f539,f543])).
% 0.19/0.59 fof(f558,plain,(
% 0.19/0.59 spl0_56 <=> cn1),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f562,plain,(
% 0.19/0.59 spl0_57 <=> is_a_theorem(implies(implies(sk0_38,sk0_39),implies(implies(sk0_39,sk0_40),implies(sk0_38,sk0_40))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f564,plain,(
% 0.19/0.59 ~is_a_theorem(implies(implies(sk0_38,sk0_39),implies(implies(sk0_39,sk0_40),implies(sk0_38,sk0_40))))|spl0_57),
% 0.19/0.59 inference(component_clause,[status(thm)],[f562])).
% 0.19/0.59 fof(f565,plain,(
% 0.19/0.59 spl0_56|~spl0_57),
% 0.19/0.59 inference(split_clause,[status(thm)],[f171,f558,f562])).
% 0.19/0.59 fof(f566,plain,(
% 0.19/0.59 spl0_58 <=> cn2),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f569,plain,(
% 0.19/0.59 spl0_59 <=> is_a_theorem(implies(X0,implies(not(X0),X1)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f570,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(implies(X0,implies(not(X0),X1)))|~spl0_59)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f569])).
% 0.19/0.59 fof(f572,plain,(
% 0.19/0.59 ~spl0_58|spl0_59),
% 0.19/0.59 inference(split_clause,[status(thm)],[f174,f566,f569])).
% 0.19/0.59 fof(f573,plain,(
% 0.19/0.59 spl0_60 <=> is_a_theorem(implies(sk0_41,implies(not(sk0_41),sk0_42)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f575,plain,(
% 0.19/0.59 ~is_a_theorem(implies(sk0_41,implies(not(sk0_41),sk0_42)))|spl0_60),
% 0.19/0.59 inference(component_clause,[status(thm)],[f573])).
% 0.19/0.59 fof(f576,plain,(
% 0.19/0.59 spl0_58|~spl0_60),
% 0.19/0.59 inference(split_clause,[status(thm)],[f175,f566,f573])).
% 0.19/0.59 fof(f577,plain,(
% 0.19/0.59 spl0_61 <=> cn3),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f580,plain,(
% 0.19/0.59 spl0_62 <=> is_a_theorem(implies(implies(not(X0),X0),X0))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f581,plain,(
% 0.19/0.59 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0))|~spl0_62)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f580])).
% 0.19/0.59 fof(f583,plain,(
% 0.19/0.59 ~spl0_61|spl0_62),
% 0.19/0.59 inference(split_clause,[status(thm)],[f178,f577,f580])).
% 0.19/0.59 fof(f584,plain,(
% 0.19/0.59 spl0_63 <=> is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f586,plain,(
% 0.19/0.59 ~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))|spl0_63),
% 0.19/0.59 inference(component_clause,[status(thm)],[f584])).
% 0.19/0.59 fof(f587,plain,(
% 0.19/0.59 spl0_61|~spl0_63),
% 0.19/0.59 inference(split_clause,[status(thm)],[f179,f577,f584])).
% 0.19/0.59 fof(f588,plain,(
% 0.19/0.59 spl0_64 <=> r1),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f591,plain,(
% 0.19/0.59 spl0_65 <=> is_a_theorem(implies(or(X0,X0),X0))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f594,plain,(
% 0.19/0.59 ~spl0_64|spl0_65),
% 0.19/0.59 inference(split_clause,[status(thm)],[f182,f588,f591])).
% 0.19/0.59 fof(f595,plain,(
% 0.19/0.59 spl0_66 <=> is_a_theorem(implies(or(sk0_44,sk0_44),sk0_44))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f597,plain,(
% 0.19/0.59 ~is_a_theorem(implies(or(sk0_44,sk0_44),sk0_44))|spl0_66),
% 0.19/0.59 inference(component_clause,[status(thm)],[f595])).
% 0.19/0.59 fof(f598,plain,(
% 0.19/0.59 spl0_64|~spl0_66),
% 0.19/0.59 inference(split_clause,[status(thm)],[f183,f588,f595])).
% 0.19/0.59 fof(f599,plain,(
% 0.19/0.59 spl0_67 <=> r2),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f603,plain,(
% 0.19/0.59 spl0_68 <=> is_a_theorem(implies(sk0_46,or(sk0_45,sk0_46)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f605,plain,(
% 0.19/0.59 ~is_a_theorem(implies(sk0_46,or(sk0_45,sk0_46)))|spl0_68),
% 0.19/0.59 inference(component_clause,[status(thm)],[f603])).
% 0.19/0.59 fof(f606,plain,(
% 0.19/0.59 spl0_67|~spl0_68),
% 0.19/0.59 inference(split_clause,[status(thm)],[f187,f599,f603])).
% 0.19/0.59 fof(f640,plain,(
% 0.19/0.59 spl0_78 <=> op_or),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f642,plain,(
% 0.19/0.59 ~op_or|spl0_78),
% 0.19/0.59 inference(component_clause,[status(thm)],[f640])).
% 0.19/0.59 fof(f643,plain,(
% 0.19/0.59 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f644,plain,(
% 0.19/0.59 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f643])).
% 0.19/0.59 fof(f646,plain,(
% 0.19/0.59 ~spl0_78|spl0_79),
% 0.19/0.59 inference(split_clause,[status(thm)],[f201,f640,f643])).
% 0.19/0.59 fof(f654,plain,(
% 0.19/0.59 spl0_82 <=> op_implies_and),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f656,plain,(
% 0.19/0.59 ~op_implies_and|spl0_82),
% 0.19/0.59 inference(component_clause,[status(thm)],[f654])).
% 0.19/0.59 fof(f657,plain,(
% 0.19/0.59 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f658,plain,(
% 0.19/0.59 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f657])).
% 0.19/0.59 fof(f660,plain,(
% 0.19/0.59 ~spl0_82|spl0_83),
% 0.19/0.59 inference(split_clause,[status(thm)],[f205,f654,f657])).
% 0.19/0.59 fof(f664,plain,(
% 0.19/0.59 spl0_85 <=> implies(X0,X1)=or(not(X0),X1)),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f665,plain,(
% 0.19/0.59 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~spl0_85)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f664])).
% 0.19/0.59 fof(f668,plain,(
% 0.19/0.59 spl0_86 <=> op_equiv),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f670,plain,(
% 0.19/0.59 ~op_equiv|spl0_86),
% 0.19/0.59 inference(component_clause,[status(thm)],[f668])).
% 0.19/0.59 fof(f671,plain,(
% 0.19/0.59 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f672,plain,(
% 0.19/0.59 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f671])).
% 0.19/0.59 fof(f674,plain,(
% 0.19/0.59 ~spl0_86|spl0_87),
% 0.19/0.59 inference(split_clause,[status(thm)],[f209,f668,f671])).
% 0.19/0.59 fof(f675,plain,(
% 0.19/0.59 spl0_88 <=> necessitation),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f677,plain,(
% 0.19/0.59 ~necessitation|spl0_88),
% 0.19/0.59 inference(component_clause,[status(thm)],[f675])).
% 0.19/0.59 fof(f678,plain,(
% 0.19/0.59 spl0_89 <=> ~is_a_theorem(X0)|is_a_theorem(necessarily(X0))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f679,plain,(
% 0.19/0.59 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0))|~spl0_89)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f678])).
% 0.19/0.59 fof(f681,plain,(
% 0.19/0.59 ~spl0_88|spl0_89),
% 0.19/0.59 inference(split_clause,[status(thm)],[f231,f675,f678])).
% 0.19/0.59 fof(f709,plain,(
% 0.19/0.59 spl0_97 <=> adjunction),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f712,plain,(
% 0.19/0.59 spl0_98 <=> ~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f713,plain,(
% 0.19/0.59 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))|~spl0_98)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f712])).
% 0.19/0.59 fof(f715,plain,(
% 0.19/0.59 ~spl0_97|spl0_98),
% 0.19/0.59 inference(split_clause,[status(thm)],[f245,f709,f712])).
% 0.19/0.59 fof(f716,plain,(
% 0.19/0.59 spl0_99 <=> is_a_theorem(sk0_58)),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f719,plain,(
% 0.19/0.59 spl0_97|spl0_99),
% 0.19/0.59 inference(split_clause,[status(thm)],[f246,f709,f716])).
% 0.19/0.59 fof(f720,plain,(
% 0.19/0.59 spl0_100 <=> is_a_theorem(sk0_59)),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f723,plain,(
% 0.19/0.59 spl0_97|spl0_100),
% 0.19/0.59 inference(split_clause,[status(thm)],[f247,f709,f720])).
% 0.19/0.59 fof(f724,plain,(
% 0.19/0.59 spl0_101 <=> is_a_theorem(and(sk0_58,sk0_59))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f726,plain,(
% 0.19/0.59 ~is_a_theorem(and(sk0_58,sk0_59))|spl0_101),
% 0.19/0.59 inference(component_clause,[status(thm)],[f724])).
% 0.19/0.59 fof(f727,plain,(
% 0.19/0.59 spl0_97|~spl0_101),
% 0.19/0.59 inference(split_clause,[status(thm)],[f248,f709,f724])).
% 0.19/0.59 fof(f743,plain,(
% 0.19/0.59 spl0_106 <=> axiom_K),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f745,plain,(
% 0.19/0.59 ~axiom_K|spl0_106),
% 0.19/0.59 inference(component_clause,[status(thm)],[f743])).
% 0.19/0.59 fof(f746,plain,(
% 0.19/0.59 spl0_107 <=> is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f749,plain,(
% 0.19/0.59 ~spl0_106|spl0_107),
% 0.19/0.59 inference(split_clause,[status(thm)],[f257,f743,f746])).
% 0.19/0.59 fof(f754,plain,(
% 0.19/0.59 spl0_109 <=> axiom_M),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f756,plain,(
% 0.19/0.59 ~axiom_M|spl0_109),
% 0.19/0.59 inference(component_clause,[status(thm)],[f754])).
% 0.19/0.59 fof(f757,plain,(
% 0.19/0.59 spl0_110 <=> is_a_theorem(implies(necessarily(X0),X0))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f758,plain,(
% 0.19/0.59 ![X0]: (is_a_theorem(implies(necessarily(X0),X0))|~spl0_110)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f757])).
% 0.19/0.59 fof(f760,plain,(
% 0.19/0.59 ~spl0_109|spl0_110),
% 0.19/0.59 inference(split_clause,[status(thm)],[f261,f754,f757])).
% 0.19/0.59 fof(f761,plain,(
% 0.19/0.59 spl0_111 <=> is_a_theorem(implies(necessarily(sk0_64),sk0_64))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f763,plain,(
% 0.19/0.59 ~is_a_theorem(implies(necessarily(sk0_64),sk0_64))|spl0_111),
% 0.19/0.59 inference(component_clause,[status(thm)],[f761])).
% 0.19/0.59 fof(f787,plain,(
% 0.19/0.59 spl0_118 <=> axiom_5),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f789,plain,(
% 0.19/0.59 ~axiom_5|spl0_118),
% 0.19/0.59 inference(component_clause,[status(thm)],[f787])).
% 0.19/0.59 fof(f790,plain,(
% 0.19/0.59 spl0_119 <=> is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f791,plain,(
% 0.19/0.59 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))|~spl0_119)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f790])).
% 0.19/0.59 fof(f793,plain,(
% 0.19/0.59 ~spl0_118|spl0_119),
% 0.19/0.59 inference(split_clause,[status(thm)],[f273,f787,f790])).
% 0.19/0.59 fof(f794,plain,(
% 0.19/0.59 spl0_120 <=> is_a_theorem(implies(possibly(sk0_67),necessarily(possibly(sk0_67))))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f796,plain,(
% 0.19/0.59 ~is_a_theorem(implies(possibly(sk0_67),necessarily(possibly(sk0_67))))|spl0_120),
% 0.19/0.59 inference(component_clause,[status(thm)],[f794])).
% 0.19/0.59 fof(f853,plain,(
% 0.19/0.59 spl0_136 <=> axiom_m2),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f856,plain,(
% 0.19/0.59 spl0_137 <=> is_a_theorem(strict_implies(and(X0,X1),X0))),
% 0.19/0.59 introduced(split_symbol_definition)).
% 0.19/0.59 fof(f857,plain,(
% 0.19/0.59 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),X0))|~spl0_137)),
% 0.19/0.59 inference(component_clause,[status(thm)],[f856])).
% 0.19/0.59 fof(f859,plain,(
% 0.19/0.60 ~spl0_136|spl0_137),
% 0.19/0.60 inference(split_clause,[status(thm)],[f297,f853,f856])).
% 0.19/0.60 fof(f860,plain,(
% 0.19/0.60 spl0_138 <=> is_a_theorem(strict_implies(and(sk0_78,sk0_79),sk0_78))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f862,plain,(
% 0.19/0.60 ~is_a_theorem(strict_implies(and(sk0_78,sk0_79),sk0_78))|spl0_138),
% 0.19/0.60 inference(component_clause,[status(thm)],[f860])).
% 0.19/0.60 fof(f863,plain,(
% 0.19/0.60 spl0_136|~spl0_138),
% 0.19/0.60 inference(split_clause,[status(thm)],[f298,f853,f860])).
% 0.19/0.60 fof(f875,plain,(
% 0.19/0.60 spl0_142 <=> axiom_m4),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f878,plain,(
% 0.19/0.60 spl0_143 <=> is_a_theorem(strict_implies(X0,and(X0,X0)))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f881,plain,(
% 0.19/0.60 ~spl0_142|spl0_143),
% 0.19/0.60 inference(split_clause,[status(thm)],[f305,f875,f878])).
% 0.19/0.60 fof(f882,plain,(
% 0.19/0.60 spl0_144 <=> is_a_theorem(strict_implies(sk0_83,and(sk0_83,sk0_83)))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f884,plain,(
% 0.19/0.60 ~is_a_theorem(strict_implies(sk0_83,and(sk0_83,sk0_83)))|spl0_144),
% 0.19/0.60 inference(component_clause,[status(thm)],[f882])).
% 0.19/0.60 fof(f885,plain,(
% 0.19/0.60 spl0_142|~spl0_144),
% 0.19/0.60 inference(split_clause,[status(thm)],[f306,f875,f882])).
% 0.19/0.60 fof(f930,plain,(
% 0.19/0.60 spl0_157 <=> axiom_m9),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f931,plain,(
% 0.19/0.60 axiom_m9|~spl0_157),
% 0.19/0.60 inference(component_clause,[status(thm)],[f930])).
% 0.19/0.60 fof(f933,plain,(
% 0.19/0.60 spl0_158 <=> is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f934,plain,(
% 0.19/0.60 ![X0]: (is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))|~spl0_158)),
% 0.19/0.60 inference(component_clause,[status(thm)],[f933])).
% 0.19/0.60 fof(f937,plain,(
% 0.19/0.60 spl0_159 <=> is_a_theorem(strict_implies(possibly(possibly(sk0_92)),possibly(sk0_92)))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f939,plain,(
% 0.19/0.60 ~is_a_theorem(strict_implies(possibly(possibly(sk0_92)),possibly(sk0_92)))|spl0_159),
% 0.19/0.60 inference(component_clause,[status(thm)],[f937])).
% 0.19/0.60 fof(f940,plain,(
% 0.19/0.60 spl0_157|~spl0_159),
% 0.19/0.60 inference(split_clause,[status(thm)],[f326,f930,f937])).
% 0.19/0.60 fof(f941,plain,(
% 0.19/0.60 spl0_160 <=> axiom_m10),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f944,plain,(
% 0.19/0.60 spl0_161 <=> is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f947,plain,(
% 0.19/0.60 ~spl0_160|spl0_161),
% 0.19/0.60 inference(split_clause,[status(thm)],[f329,f941,f944])).
% 0.19/0.60 fof(f948,plain,(
% 0.19/0.60 spl0_162 <=> is_a_theorem(strict_implies(possibly(sk0_93),necessarily(possibly(sk0_93))))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f950,plain,(
% 0.19/0.60 ~is_a_theorem(strict_implies(possibly(sk0_93),necessarily(possibly(sk0_93))))|spl0_162),
% 0.19/0.60 inference(component_clause,[status(thm)],[f948])).
% 0.19/0.60 fof(f951,plain,(
% 0.19/0.60 spl0_160|~spl0_162),
% 0.19/0.60 inference(split_clause,[status(thm)],[f330,f941,f948])).
% 0.19/0.60 fof(f952,plain,(
% 0.19/0.60 spl0_163 <=> op_possibly),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f954,plain,(
% 0.19/0.60 ~op_possibly|spl0_163),
% 0.19/0.60 inference(component_clause,[status(thm)],[f952])).
% 0.19/0.60 fof(f955,plain,(
% 0.19/0.60 spl0_164 <=> possibly(X0)=not(necessarily(not(X0)))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f956,plain,(
% 0.19/0.60 ![X0]: (possibly(X0)=not(necessarily(not(X0)))|~spl0_164)),
% 0.19/0.60 inference(component_clause,[status(thm)],[f955])).
% 0.19/0.60 fof(f958,plain,(
% 0.19/0.60 ~spl0_163|spl0_164),
% 0.19/0.60 inference(split_clause,[status(thm)],[f332,f952,f955])).
% 0.19/0.60 fof(f962,plain,(
% 0.19/0.60 spl0_166 <=> necessarily(X0)=not(possibly(not(X0)))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f963,plain,(
% 0.19/0.60 ![X0]: (necessarily(X0)=not(possibly(not(X0)))|~spl0_166)),
% 0.19/0.60 inference(component_clause,[status(thm)],[f962])).
% 0.19/0.60 fof(f966,plain,(
% 0.19/0.60 spl0_167 <=> op_strict_implies),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f968,plain,(
% 0.19/0.60 ~op_strict_implies|spl0_167),
% 0.19/0.60 inference(component_clause,[status(thm)],[f966])).
% 0.19/0.60 fof(f969,plain,(
% 0.19/0.60 spl0_168 <=> strict_implies(X0,X1)=necessarily(implies(X0,X1))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f970,plain,(
% 0.19/0.60 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1))|~spl0_168)),
% 0.19/0.60 inference(component_clause,[status(thm)],[f969])).
% 0.19/0.60 fof(f972,plain,(
% 0.19/0.60 ~spl0_167|spl0_168),
% 0.19/0.60 inference(split_clause,[status(thm)],[f336,f966,f969])).
% 0.19/0.60 fof(f973,plain,(
% 0.19/0.60 spl0_169 <=> op_strict_equiv),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f975,plain,(
% 0.19/0.60 ~op_strict_equiv|spl0_169),
% 0.19/0.60 inference(component_clause,[status(thm)],[f973])).
% 0.19/0.60 fof(f976,plain,(
% 0.19/0.60 spl0_170 <=> strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f979,plain,(
% 0.19/0.60 ~spl0_169|spl0_170),
% 0.19/0.60 inference(split_clause,[status(thm)],[f338,f973,f976])).
% 0.19/0.60 fof(f980,plain,(
% 0.19/0.60 $false|spl0_169),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f975,f349])).
% 0.19/0.60 fof(f981,plain,(
% 0.19/0.60 spl0_169),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f980])).
% 0.19/0.60 fof(f982,plain,(
% 0.19/0.60 $false|spl0_0),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f353,f213])).
% 0.19/0.60 fof(f983,plain,(
% 0.19/0.60 spl0_0),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f982])).
% 0.19/0.60 fof(f984,plain,(
% 0.19/0.60 $false|spl0_88),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f677,f340])).
% 0.19/0.60 fof(f985,plain,(
% 0.19/0.60 spl0_88),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f984])).
% 0.19/0.60 fof(f986,plain,(
% 0.19/0.60 $false|spl0_5),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f372,f227])).
% 0.19/0.60 fof(f987,plain,(
% 0.19/0.60 spl0_5),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f986])).
% 0.19/0.60 fof(f988,plain,(
% 0.19/0.60 $false|spl0_167),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f968,f347])).
% 0.19/0.60 fof(f989,plain,(
% 0.19/0.60 spl0_167),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f988])).
% 0.19/0.60 fof(f990,plain,(
% 0.19/0.60 $false|spl0_163),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f954,f339])).
% 0.19/0.60 fof(f991,plain,(
% 0.19/0.60 spl0_163),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f990])).
% 0.19/0.60 fof(f992,plain,(
% 0.19/0.60 $false|spl0_86),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f670,f212])).
% 0.19/0.60 fof(f993,plain,(
% 0.19/0.60 spl0_86),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f992])).
% 0.19/0.60 fof(f994,plain,(
% 0.19/0.60 $false|spl0_82),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f656,f211])).
% 0.19/0.60 fof(f995,plain,(
% 0.19/0.60 spl0_82),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f994])).
% 0.19/0.60 fof(f996,plain,(
% 0.19/0.60 $false|spl0_78),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f642,f210])).
% 0.19/0.60 fof(f997,plain,(
% 0.19/0.60 spl0_78),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f996])).
% 0.19/0.60 fof(f998,plain,(
% 0.19/0.60 $false|~spl0_158|spl0_159),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f939,f934])).
% 0.19/0.60 fof(f999,plain,(
% 0.19/0.60 ~spl0_158|spl0_159),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f998])).
% 0.19/0.60 fof(f1004,plain,(
% 0.19/0.60 $false|~spl0_110|spl0_111),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f763,f758])).
% 0.19/0.60 fof(f1005,plain,(
% 0.19/0.60 ~spl0_110|spl0_111),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1004])).
% 0.19/0.60 fof(f1006,plain,(
% 0.19/0.60 $false|spl0_109),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f756,f342])).
% 0.19/0.60 fof(f1007,plain,(
% 0.19/0.60 spl0_109),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1006])).
% 0.19/0.60 fof(f1011,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1))|~spl0_89|~spl0_168)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f970,f679])).
% 0.19/0.60 fof(f1019,plain,(
% 0.19/0.60 $false|~spl0_34|spl0_68),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f605,f477])).
% 0.19/0.60 fof(f1020,plain,(
% 0.19/0.60 ~spl0_34|spl0_68),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1019])).
% 0.19/0.60 fof(f1021,plain,(
% 0.19/0.60 $false|spl0_33),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f475,f222])).
% 0.19/0.60 fof(f1022,plain,(
% 0.19/0.60 spl0_33),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1021])).
% 0.19/0.60 fof(f1025,plain,(
% 0.19/0.60 $false|~spl0_22|spl0_52),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f545,f433])).
% 0.19/0.60 fof(f1026,plain,(
% 0.19/0.60 ~spl0_22|spl0_52),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1025])).
% 0.19/0.60 fof(f1027,plain,(
% 0.19/0.60 $false|spl0_21),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f431,f218])).
% 0.19/0.60 fof(f1028,plain,(
% 0.19/0.60 spl0_21),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1027])).
% 0.19/0.60 fof(f1029,plain,(
% 0.19/0.60 $false|~spl0_49|spl0_50),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f537,f532])).
% 0.19/0.60 fof(f1030,plain,(
% 0.19/0.60 ~spl0_49|spl0_50),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1029])).
% 0.19/0.60 fof(f1031,plain,(
% 0.19/0.60 $false|~spl0_31|spl0_32),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f471,f466])).
% 0.19/0.60 fof(f1032,plain,(
% 0.19/0.60 ~spl0_31|spl0_32),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1031])).
% 0.19/0.60 fof(f1033,plain,(
% 0.19/0.60 $false|spl0_30),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f464,f221])).
% 0.19/0.60 fof(f1034,plain,(
% 0.19/0.60 spl0_30),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1033])).
% 0.19/0.60 fof(f1035,plain,(
% 0.19/0.60 $false|~spl0_25|spl0_26),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f449,f444])).
% 0.19/0.60 fof(f1036,plain,(
% 0.19/0.60 ~spl0_25|spl0_26),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1035])).
% 0.19/0.60 fof(f1037,plain,(
% 0.19/0.60 $false|spl0_24),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f442,f219])).
% 0.19/0.60 fof(f1038,plain,(
% 0.19/0.60 spl0_24),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1037])).
% 0.19/0.60 fof(f1042,plain,(
% 0.19/0.60 $false|~spl0_13|spl0_14),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f405,f400])).
% 0.19/0.60 fof(f1043,plain,(
% 0.19/0.60 ~spl0_13|spl0_14),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1042])).
% 0.19/0.60 fof(f1044,plain,(
% 0.19/0.60 $false|spl0_12),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f398,f215])).
% 0.19/0.60 fof(f1045,plain,(
% 0.19/0.60 spl0_12),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1044])).
% 0.19/0.60 fof(f1052,plain,(
% 0.19/0.60 $false|~spl0_119|spl0_120),
% 0.19/0.60 inference(backward_subsumption_resolution,[status(thm)],[f796,f791])).
% 0.19/0.60 fof(f1053,plain,(
% 0.19/0.60 ~spl0_119|spl0_120),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1052])).
% 0.19/0.60 fof(f1054,plain,(
% 0.19/0.60 $false|spl0_118),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f789,f343])).
% 0.19/0.60 fof(f1055,plain,(
% 0.19/0.60 spl0_118),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1054])).
% 0.19/0.60 fof(f1064,plain,(
% 0.19/0.60 ![X0]: (~is_a_theorem(necessarily(X0))|is_a_theorem(X0)|~spl0_1|~spl0_110)),
% 0.19/0.60 inference(resolution,[status(thm)],[f355,f758])).
% 0.19/0.60 fof(f1067,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(not(X0),X1))|~spl0_1|~spl0_59)),
% 0.19/0.60 inference(resolution,[status(thm)],[f355,f570])).
% 0.19/0.60 fof(f1068,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,and(X0,X1)))|~spl0_1|~spl0_28)),
% 0.19/0.60 inference(resolution,[status(thm)],[f355,f455])).
% 0.19/0.60 fof(f1069,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,X0))|~spl0_1|~spl0_13)),
% 0.19/0.60 inference(resolution,[status(thm)],[f355,f400])).
% 0.19/0.60 fof(f1078,plain,(
% 0.19/0.60 spl0_171 <=> ~is_a_theorem(X0)|is_a_theorem(X0)),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f1081,plain,(
% 0.19/0.60 spl0_172 <=> ~is_a_theorem(X1)),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f1082,plain,(
% 0.19/0.60 ![X0]: (~is_a_theorem(X0)|~spl0_172)),
% 0.19/0.60 inference(component_clause,[status(thm)],[f1081])).
% 0.19/0.60 fof(f1084,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(X0)|~spl0_13|~spl0_1)),
% 0.19/0.60 inference(resolution,[status(thm)],[f1069,f355])).
% 0.19/0.60 fof(f1085,plain,(
% 0.19/0.60 spl0_171|spl0_172|~spl0_13|~spl0_1),
% 0.19/0.60 inference(split_clause,[status(thm)],[f1084,f1078,f1081,f399,f354])).
% 0.19/0.60 fof(f1087,plain,(
% 0.19/0.60 spl0_173 <=> ~is_a_theorem(X0)|~is_a_theorem(not(X0))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f1090,plain,(
% 0.19/0.60 spl0_174 <=> is_a_theorem(X1)),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f1091,plain,(
% 0.19/0.60 ![X0]: (is_a_theorem(X0)|~spl0_174)),
% 0.19/0.60 inference(component_clause,[status(thm)],[f1090])).
% 0.19/0.60 fof(f1093,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(not(X0))|is_a_theorem(X1)|~spl0_59|~spl0_1)),
% 0.19/0.60 inference(resolution,[status(thm)],[f1067,f355])).
% 0.19/0.60 fof(f1094,plain,(
% 0.19/0.60 spl0_173|spl0_174|~spl0_59|~spl0_1),
% 0.19/0.60 inference(split_clause,[status(thm)],[f1093,f1087,f1090,f569,f354])).
% 0.19/0.60 fof(f1095,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(necessarily(not(X0)))|is_a_theorem(implies(possibly(X0),X1))|~spl0_1|~spl0_59|~spl0_164)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f956,f1067])).
% 0.19/0.60 fof(f1096,plain,(
% 0.19/0.60 $false|~spl0_22|spl0_23),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f438,f433])).
% 0.19/0.60 fof(f1097,plain,(
% 0.19/0.60 ~spl0_22|spl0_23),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1096])).
% 0.19/0.60 fof(f1098,plain,(
% 0.19/0.60 $false|~spl0_34|spl0_35),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f482,f477])).
% 0.19/0.60 fof(f1099,plain,(
% 0.19/0.60 ~spl0_34|spl0_35),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1098])).
% 0.19/0.60 fof(f1103,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(X0,X1))|~spl0_1|~spl0_110|~spl0_168)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f970,f1064])).
% 0.19/0.60 fof(f1104,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1))|~spl0_89|~spl0_168)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f970,f679])).
% 0.19/0.60 fof(f1125,plain,(
% 0.19/0.60 ![X0,X1]: (possibly(and(X0,not(X1)))=not(necessarily(implies(X0,X1)))|~spl0_164|~spl0_83)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f658,f956])).
% 0.19/0.60 fof(f1126,plain,(
% 0.19/0.60 ![X0,X1]: (possibly(and(X0,not(X1)))=not(strict_implies(X0,X1))|~spl0_168|~spl0_164|~spl0_83)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f970,f1125])).
% 0.19/0.60 fof(f1129,plain,(
% 0.19/0.60 ~is_a_theorem(implies(and(sk0_78,sk0_79),sk0_78))|~spl0_89|~spl0_168|spl0_138),
% 0.19/0.60 inference(resolution,[status(thm)],[f1011,f862])).
% 0.19/0.60 fof(f1130,plain,(
% 0.19/0.60 $false|~spl0_22|~spl0_89|~spl0_168|spl0_138),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f1129,f433])).
% 0.19/0.60 fof(f1131,plain,(
% 0.19/0.60 ~spl0_22|~spl0_89|~spl0_168|spl0_138),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1130])).
% 0.19/0.60 fof(f1132,plain,(
% 0.19/0.60 ~is_a_theorem(implies(sk0_83,and(sk0_83,sk0_83)))|~spl0_89|~spl0_168|spl0_144),
% 0.19/0.60 inference(resolution,[status(thm)],[f1011,f884])).
% 0.19/0.60 fof(f1149,plain,(
% 0.19/0.60 $false|~spl0_19|spl0_20),
% 0.19/0.60 inference(backward_subsumption_resolution,[status(thm)],[f427,f422])).
% 0.19/0.60 fof(f1150,plain,(
% 0.19/0.60 ~spl0_19|spl0_20),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1149])).
% 0.19/0.60 fof(f1151,plain,(
% 0.19/0.60 $false|spl0_18),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f420,f217])).
% 0.19/0.60 fof(f1152,plain,(
% 0.19/0.60 spl0_18),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1151])).
% 0.19/0.60 fof(f1153,plain,(
% 0.19/0.60 $false|~spl0_19|spl0_57),
% 0.19/0.60 inference(backward_subsumption_resolution,[status(thm)],[f564,f422])).
% 0.19/0.60 fof(f1154,plain,(
% 0.19/0.60 ~spl0_19|spl0_57),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1153])).
% 0.19/0.60 fof(f1164,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(and(X1,X0))|~is_a_theorem(X1)|~spl0_1|~spl0_28)),
% 0.19/0.60 inference(resolution,[status(thm)],[f355,f1068])).
% 0.19/0.60 fof(f1170,plain,(
% 0.19/0.60 $false|~spl0_172|~spl0_137),
% 0.19/0.60 inference(backward_subsumption_resolution,[status(thm)],[f857,f1082])).
% 0.19/0.60 fof(f1171,plain,(
% 0.19/0.60 ~spl0_172|~spl0_137),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1170])).
% 0.19/0.60 fof(f1202,plain,(
% 0.19/0.60 ![X0]: (necessarily(possibly(not(X0)))=not(possibly(necessarily(X0)))|~spl0_166)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f963,f963])).
% 0.19/0.60 fof(f1267,plain,(
% 0.19/0.60 ![X0,X1]: (is_a_theorem(strict_implies(equiv(X0,X1),implies(X0,X1)))|~spl0_137|~spl0_87)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f672,f857])).
% 0.19/0.60 fof(f1275,plain,(
% 0.19/0.60 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f658,f644])).
% 0.19/0.60 fof(f1279,plain,(
% 0.19/0.60 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0)))|~spl0_83|~spl0_79|~spl0_10)),
% 0.19/0.60 inference(backward_demodulation,[status(thm)],[f1275,f389])).
% 0.19/0.60 fof(f1288,plain,(
% 0.19/0.60 ![X0,X1]: (is_a_theorem(or(X0,implies(X1,not(X0))))|~spl0_13|~spl0_83|~spl0_79)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f1275,f400])).
% 0.19/0.60 fof(f1309,plain,(
% 0.19/0.60 ![X0,X1]: (strict_implies(not(X0),X1)=necessarily(or(X0,X1))|~spl0_168|~spl0_83|~spl0_79)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f1275,f970])).
% 0.19/0.60 fof(f1317,plain,(
% 0.19/0.60 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,not(not(X0)))))|~spl0_13|~spl0_83|~spl0_79|~spl0_85)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f665,f1288])).
% 0.19/0.60 fof(f1341,plain,(
% 0.19/0.60 ~is_a_theorem(sk0_59)|~is_a_theorem(sk0_58)|~spl0_1|~spl0_28|spl0_101),
% 0.19/0.60 inference(resolution,[status(thm)],[f1164,f726])).
% 0.19/0.60 fof(f1342,plain,(
% 0.19/0.60 ~spl0_100|~spl0_99|~spl0_1|~spl0_28|spl0_101),
% 0.19/0.60 inference(split_clause,[status(thm)],[f1341,f720,f716,f354,f454,f724])).
% 0.19/0.60 fof(f1355,plain,(
% 0.19/0.60 ~is_a_theorem(implies(possibly(sk0_93),necessarily(possibly(sk0_93))))|spl0_162|~spl0_89|~spl0_168),
% 0.19/0.60 inference(resolution,[status(thm)],[f950,f1104])).
% 0.19/0.60 fof(f1367,plain,(
% 0.19/0.60 $false|spl0_27),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f453,f220])).
% 0.19/0.60 fof(f1368,plain,(
% 0.19/0.60 spl0_27),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1367])).
% 0.19/0.60 fof(f1385,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1))|~spl0_98|~spl0_87)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f672,f713])).
% 0.19/0.60 fof(f1415,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1))|~spl0_1|~spl0_16)),
% 0.19/0.60 inference(resolution,[status(thm)],[f355,f411])).
% 0.19/0.60 fof(f1453,plain,(
% 0.19/0.60 ~is_a_theorem(implies(or(sk0_43,sk0_43),sk0_43))|~spl0_83|~spl0_79|spl0_63),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f1275,f586])).
% 0.19/0.60 fof(f1523,plain,(
% 0.19/0.60 $false|~spl0_40|spl0_41),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f504,f499])).
% 0.19/0.60 fof(f1524,plain,(
% 0.19/0.60 ~spl0_40|spl0_41),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1523])).
% 0.19/0.60 fof(f1525,plain,(
% 0.19/0.60 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))|~spl0_137|~spl0_87|~spl0_1|~spl0_110|~spl0_168)),
% 0.19/0.60 inference(resolution,[status(thm)],[f1267,f1103])).
% 0.19/0.60 fof(f1526,plain,(
% 0.19/0.60 spl0_40|~spl0_137|~spl0_87|~spl0_1|~spl0_110|~spl0_168),
% 0.19/0.60 inference(split_clause,[status(thm)],[f1525,f498,f856,f671,f354,f757,f969])).
% 0.19/0.60 fof(f1530,plain,(
% 0.19/0.60 $false|spl0_39),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f497,f224])).
% 0.19/0.60 fof(f1531,plain,(
% 0.19/0.60 spl0_39),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1530])).
% 0.19/0.60 fof(f1533,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,not(not(X0))))|~spl0_13|~spl0_83|~spl0_79|~spl0_85|~spl0_1)),
% 0.19/0.60 inference(resolution,[status(thm)],[f1317,f355])).
% 0.19/0.60 fof(f1546,plain,(
% 0.19/0.60 $false|~spl0_43|spl0_44),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f515,f510])).
% 0.19/0.60 fof(f1547,plain,(
% 0.19/0.60 ~spl0_43|spl0_44),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1546])).
% 0.19/0.60 fof(f1548,plain,(
% 0.19/0.60 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))|~spl0_25|~spl0_87)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f672,f444])).
% 0.19/0.60 fof(f1549,plain,(
% 0.19/0.60 spl0_43|~spl0_25|~spl0_87),
% 0.19/0.60 inference(split_clause,[status(thm)],[f1548,f509,f443,f671])).
% 0.19/0.60 fof(f1550,plain,(
% 0.19/0.60 $false|spl0_42),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f508,f225])).
% 0.19/0.60 fof(f1551,plain,(
% 0.19/0.60 spl0_42),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1550])).
% 0.19/0.60 fof(f1552,plain,(
% 0.19/0.60 ~is_a_theorem(implies(sk0_41,or(sk0_41,sk0_42)))|~spl0_83|~spl0_79|spl0_60),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f1275,f575])).
% 0.19/0.60 fof(f1553,plain,(
% 0.19/0.60 $false|~spl0_31|~spl0_83|~spl0_79|spl0_60),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f1552,f466])).
% 0.19/0.60 fof(f1554,plain,(
% 0.19/0.60 ~spl0_31|~spl0_83|~spl0_79|spl0_60),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1553])).
% 0.19/0.60 fof(f1556,plain,(
% 0.19/0.60 spl0_183 <=> ~is_a_theorem(X0)|is_a_theorem(not(not(X0)))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f1557,plain,(
% 0.19/0.60 ![X0]: (~is_a_theorem(X0)|is_a_theorem(not(not(X0)))|~spl0_183)),
% 0.19/0.60 inference(component_clause,[status(thm)],[f1556])).
% 0.19/0.60 fof(f1559,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(not(not(X0)))|~spl0_13|~spl0_83|~spl0_79|~spl0_85|~spl0_1)),
% 0.19/0.60 inference(resolution,[status(thm)],[f1533,f355])).
% 0.19/0.60 fof(f1560,plain,(
% 0.19/0.60 spl0_183|spl0_172|~spl0_13|~spl0_83|~spl0_79|~spl0_85|~spl0_1),
% 0.19/0.60 inference(split_clause,[status(thm)],[f1559,f1556,f1081,f399,f657,f643,f664,f354])).
% 0.19/0.60 fof(f1645,plain,(
% 0.19/0.60 ~is_a_theorem(implies(or(sk0_5,not(sk0_4)),implies(sk0_4,sk0_5)))|~spl0_83|~spl0_79|spl0_11),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f1275,f394])).
% 0.19/0.60 fof(f1760,plain,(
% 0.19/0.60 $false|~spl0_16|spl0_17),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f416,f411])).
% 0.19/0.60 fof(f1761,plain,(
% 0.19/0.60 ~spl0_16|spl0_17),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1760])).
% 0.19/0.60 fof(f1762,plain,(
% 0.19/0.60 $false|spl0_15),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f409,f216])).
% 0.19/0.60 fof(f1763,plain,(
% 0.19/0.60 spl0_15),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1762])).
% 0.19/0.60 fof(f1783,plain,(
% 0.19/0.60 $false|~spl0_10|~spl0_83|~spl0_79|spl0_11),
% 0.19/0.60 inference(backward_subsumption_resolution,[status(thm)],[f1645,f1279])).
% 0.19/0.60 fof(f1784,plain,(
% 0.19/0.60 ~spl0_10|~spl0_83|~spl0_79|spl0_11),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1783])).
% 0.19/0.60 fof(f1785,plain,(
% 0.19/0.60 $false|spl0_9),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f387,f214])).
% 0.19/0.60 fof(f1786,plain,(
% 0.19/0.60 spl0_9),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1785])).
% 0.19/0.60 fof(f1792,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(or(X0,not(X1)))|is_a_theorem(implies(X1,X0))|~spl0_83|~spl0_79|~spl0_10|~spl0_1)),
% 0.19/0.60 inference(resolution,[status(thm)],[f1279,f355])).
% 0.19/0.60 fof(f1878,plain,(
% 0.19/0.60 $false|~spl0_37|spl0_38),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f493,f488])).
% 0.19/0.60 fof(f1879,plain,(
% 0.19/0.60 ~spl0_37|spl0_38),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1878])).
% 0.19/0.60 fof(f1880,plain,(
% 0.19/0.60 $false|spl0_36),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f486,f223])).
% 0.19/0.60 fof(f1881,plain,(
% 0.19/0.60 spl0_36),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1880])).
% 0.19/0.60 fof(f1885,plain,(
% 0.19/0.60 $false|~spl0_46|spl0_47),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f526,f521])).
% 0.19/0.60 fof(f1886,plain,(
% 0.19/0.60 ~spl0_46|spl0_47),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1885])).
% 0.19/0.60 fof(f1887,plain,(
% 0.19/0.60 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))|~spl0_28|~spl0_87)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f672,f455])).
% 0.19/0.60 fof(f1888,plain,(
% 0.19/0.60 spl0_46|~spl0_28|~spl0_87),
% 0.19/0.60 inference(split_clause,[status(thm)],[f1887,f520,f454,f671])).
% 0.19/0.60 fof(f1891,plain,(
% 0.19/0.60 $false|spl0_45),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f519,f226])).
% 0.19/0.60 fof(f1892,plain,(
% 0.19/0.60 spl0_45),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1891])).
% 0.19/0.60 fof(f1893,plain,(
% 0.19/0.60 $false|~spl0_119|spl0_162|~spl0_89|~spl0_168),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f1355,f791])).
% 0.19/0.60 fof(f1894,plain,(
% 0.19/0.60 ~spl0_119|spl0_162|~spl0_89|~spl0_168),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f1893])).
% 0.19/0.60 fof(f2375,plain,(
% 0.19/0.60 ![X0,X1]: (is_a_theorem(implies(possibly(X0),X1))|~is_a_theorem(not(X0))|~spl0_1|~spl0_59|~spl0_164|~spl0_89)),
% 0.19/0.60 inference(resolution,[status(thm)],[f1095,f679])).
% 0.19/0.60 fof(f2384,plain,(
% 0.19/0.60 ![X0,X1]: (is_a_theorem(implies(possibly(not(X0)),X1))|~is_a_theorem(X0)|~spl0_1|~spl0_59|~spl0_164|~spl0_89|~spl0_183)),
% 0.19/0.60 inference(resolution,[status(thm)],[f2375,f1557])).
% 0.19/0.60 fof(f2389,plain,(
% 0.19/0.60 ![X0,X1,X2]: (is_a_theorem(implies(possibly(and(X0,not(X1))),X2))|~is_a_theorem(implies(X0,X1))|~spl0_1|~spl0_59|~spl0_164|~spl0_89|~spl0_83)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f658,f2375])).
% 0.19/0.60 fof(f2390,plain,(
% 0.19/0.60 ![X0,X1,X2]: (is_a_theorem(implies(not(strict_implies(X0,X1)),X2))|~is_a_theorem(implies(X0,X1))|~spl0_168|~spl0_1|~spl0_59|~spl0_164|~spl0_89|~spl0_83)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f1126,f2389])).
% 0.19/0.60 fof(f2391,plain,(
% 0.19/0.60 ![X0,X1,X2]: (is_a_theorem(or(strict_implies(X0,X1),X2))|~is_a_theorem(implies(X0,X1))|~spl0_79|~spl0_168|~spl0_1|~spl0_59|~spl0_164|~spl0_89|~spl0_83)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f1275,f2390])).
% 0.19/0.60 fof(f2395,plain,(
% 0.19/0.60 spl0_184 <=> ~is_a_theorem(X0)|~is_a_theorem(possibly(not(X0)))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f2400,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(possibly(not(X0)))|is_a_theorem(X1)|~spl0_59|~spl0_164|~spl0_89|~spl0_183|~spl0_1)),
% 0.19/0.60 inference(resolution,[status(thm)],[f2384,f355])).
% 0.19/0.60 fof(f2401,plain,(
% 0.19/0.60 spl0_184|spl0_174|~spl0_59|~spl0_164|~spl0_89|~spl0_183|~spl0_1),
% 0.19/0.60 inference(split_clause,[status(thm)],[f2400,f2395,f1090,f569,f955,f678,f1556,f354])).
% 0.19/0.60 fof(f2450,plain,(
% 0.19/0.60 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_1|~spl0_16|~spl0_28)),
% 0.19/0.60 inference(resolution,[status(thm)],[f1415,f455])).
% 0.19/0.60 fof(f2451,plain,(
% 0.19/0.60 spl0_49|~spl0_1|~spl0_16|~spl0_28),
% 0.19/0.60 inference(split_clause,[status(thm)],[f2450,f531,f354,f410,f454])).
% 0.19/0.60 fof(f2452,plain,(
% 0.19/0.60 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_1|~spl0_16|~spl0_13)),
% 0.19/0.60 inference(resolution,[status(thm)],[f1415,f400])).
% 0.19/0.60 fof(f2459,plain,(
% 0.19/0.60 ![X0]: (is_a_theorem(or(X0,not(X0)))|~spl0_1|~spl0_16|~spl0_13|~spl0_83|~spl0_79)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f1275,f2452])).
% 0.19/0.60 fof(f2460,plain,(
% 0.19/0.60 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1)))|~spl0_37|~spl0_1|~spl0_16)),
% 0.19/0.60 inference(resolution,[status(thm)],[f488,f1415])).
% 0.19/0.60 fof(f2477,plain,(
% 0.19/0.60 $false|~spl0_49|~spl0_89|~spl0_168|spl0_144),
% 0.19/0.60 inference(backward_subsumption_resolution,[status(thm)],[f1132,f532])).
% 0.19/0.60 fof(f2478,plain,(
% 0.19/0.60 ~spl0_49|~spl0_89|~spl0_168|spl0_144),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f2477])).
% 0.19/0.60 fof(f2678,plain,(
% 0.19/0.60 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(X2,strict_implies(X0,X1)))|~spl0_168|~spl0_59|~spl0_164|~spl0_89|~spl0_83|~spl0_79|~spl0_10|~spl0_1)),
% 0.19/0.60 inference(resolution,[status(thm)],[f2391,f1792])).
% 0.19/0.60 fof(f2804,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1))|~spl0_37|~spl0_16|~spl0_1)),
% 0.19/0.60 inference(resolution,[status(thm)],[f2460,f355])).
% 0.19/0.60 fof(f2835,plain,(
% 0.19/0.60 spl0_190 <=> ~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f2838,plain,(
% 0.19/0.60 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(X2)|is_a_theorem(strict_implies(X0,X1))|~spl0_168|~spl0_59|~spl0_164|~spl0_89|~spl0_83|~spl0_79|~spl0_10|~spl0_1)),
% 0.19/0.60 inference(resolution,[status(thm)],[f2678,f355])).
% 0.19/0.60 fof(f2839,plain,(
% 0.19/0.60 spl0_190|spl0_172|~spl0_168|~spl0_59|~spl0_164|~spl0_89|~spl0_83|~spl0_79|~spl0_10|~spl0_1),
% 0.19/0.60 inference(split_clause,[status(thm)],[f2838,f2835,f1081,f969,f569,f955,f678,f657,f643,f388,f354])).
% 0.19/0.60 fof(f2843,plain,(
% 0.19/0.60 ~is_a_theorem(implies(sk0_43,sk0_43))|~spl0_37|~spl0_16|~spl0_1|~spl0_83|~spl0_79|spl0_63),
% 0.19/0.60 inference(resolution,[status(thm)],[f2804,f1453])).
% 0.19/0.60 fof(f2844,plain,(
% 0.19/0.60 $false|~spl0_13|~spl0_37|~spl0_16|~spl0_1|~spl0_83|~spl0_79|spl0_63),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f2843,f2452])).
% 0.19/0.60 fof(f2845,plain,(
% 0.19/0.60 ~spl0_13|~spl0_37|~spl0_16|~spl0_1|~spl0_83|~spl0_79|spl0_63),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f2844])).
% 0.19/0.60 fof(f2846,plain,(
% 0.19/0.60 ~is_a_theorem(implies(sk0_44,sk0_44))|~spl0_37|~spl0_16|~spl0_1|spl0_66),
% 0.19/0.60 inference(resolution,[status(thm)],[f2804,f597])).
% 0.19/0.60 fof(f2847,plain,(
% 0.19/0.60 $false|~spl0_13|~spl0_37|~spl0_16|~spl0_1|spl0_66),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f2846,f2452])).
% 0.19/0.60 fof(f2848,plain,(
% 0.19/0.60 ~spl0_13|~spl0_37|~spl0_16|~spl0_1|spl0_66),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f2847])).
% 0.19/0.60 fof(f2854,plain,(
% 0.19/0.60 ![X0]: (is_a_theorem(implies(or(X0,X0),X0))|~spl0_83|~spl0_79|~spl0_62)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f1275,f581])).
% 0.19/0.60 fof(f3040,plain,(
% 0.19/0.60 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|X0=X1|~spl0_98|~spl0_87|~spl0_6)),
% 0.19/0.60 inference(resolution,[status(thm)],[f1385,f374])).
% 0.19/0.60 fof(f3052,plain,(
% 0.19/0.60 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|X0=or(X0,X0)|~spl0_98|~spl0_87|~spl0_6|~spl0_83|~spl0_79|~spl0_62)),
% 0.19/0.60 inference(resolution,[status(thm)],[f3040,f2854])).
% 0.19/0.60 fof(f3053,plain,(
% 0.19/0.60 ![X0]: (X0=or(X0,X0)|~spl0_31|~spl0_98|~spl0_87|~spl0_6|~spl0_83|~spl0_79|~spl0_62)),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f3052,f466])).
% 0.19/0.60 fof(f3069,plain,(
% 0.19/0.60 ![X0]: (~is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0)))|necessarily(possibly(X0))=possibly(X0)|~spl0_98|~spl0_87|~spl0_6|~spl0_119)),
% 0.19/0.60 inference(resolution,[status(thm)],[f3040,f791])).
% 0.19/0.60 fof(f3070,plain,(
% 0.19/0.60 ![X0]: (necessarily(possibly(X0))=possibly(X0)|~spl0_110|~spl0_98|~spl0_87|~spl0_6|~spl0_119)),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f3069,f758])).
% 0.19/0.60 fof(f3105,plain,(
% 0.19/0.60 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|and(X0,X0)=X0|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(resolution,[status(thm)],[f3040,f532])).
% 0.19/0.60 fof(f3106,plain,(
% 0.19/0.60 ![X0]: (and(X0,X0)=X0|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f3105,f444])).
% 0.19/0.60 fof(f3165,plain,(
% 0.19/0.60 ![X0]: (possibly(not(X0))=not(strict_implies(not(X0),X0))|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f3106,f1126])).
% 0.19/0.60 fof(f3166,plain,(
% 0.19/0.60 ![X0]: (possibly(not(X0))=not(necessarily(or(X0,X0)))|~spl0_79|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f1309,f3165])).
% 0.19/0.60 fof(f3167,plain,(
% 0.19/0.60 ![X0]: (possibly(not(X0))=not(necessarily(X0))|~spl0_31|~spl0_62|~spl0_79|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f3053,f3166])).
% 0.19/0.60 fof(f3171,plain,(
% 0.19/0.60 ![X0]: (implies(not(X0),X0)=not(not(X0))|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f3106,f658])).
% 0.19/0.60 fof(f3172,plain,(
% 0.19/0.60 ![X0]: (or(X0,X0)=not(not(X0))|~spl0_79|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f1275,f3171])).
% 0.19/0.60 fof(f3173,plain,(
% 0.19/0.60 ![X0]: (X0=not(not(X0))|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f3053,f3172])).
% 0.19/0.60 fof(f3181,plain,(
% 0.19/0.60 ![X0]: (necessarily(not(X0))=not(possibly(X0))|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49|~spl0_164)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f956,f3173])).
% 0.19/0.60 fof(f3220,plain,(
% 0.19/0.60 ![X0,X1]: (or(not(X0),X1)=implies(X0,X1)|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f3173,f1275])).
% 0.19/0.60 fof(f3221,plain,(
% 0.19/0.60 spl0_85|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49),
% 0.19/0.60 inference(split_clause,[status(thm)],[f3220,f664,f465,f580,f643,f657,f443,f712,f671,f373,f531])).
% 0.19/0.60 fof(f3473,plain,(
% 0.19/0.60 spl0_203 <=> ~is_a_theorem(implies(X0,X0))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f3474,plain,(
% 0.19/0.60 ![X0]: (~is_a_theorem(implies(X0,X0))|~spl0_203)),
% 0.19/0.60 inference(component_clause,[status(thm)],[f3473])).
% 0.19/0.60 fof(f3493,plain,(
% 0.19/0.60 $false|~spl0_1|~spl0_16|~spl0_13|~spl0_203),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f3474,f2452])).
% 0.19/0.60 fof(f3494,plain,(
% 0.19/0.60 ~spl0_1|~spl0_16|~spl0_13|~spl0_203),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f3493])).
% 0.19/0.60 fof(f4453,plain,(
% 0.19/0.60 $false|spl0_106),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f745,f341])).
% 0.19/0.60 fof(f4454,plain,(
% 0.19/0.60 spl0_106),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f4453])).
% 0.19/0.60 fof(f5373,plain,(
% 0.19/0.60 ![X0]: (necessarily(X0)=not(possibly(not(X0)))|~spl0_164|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f3173,f3181])).
% 0.19/0.60 fof(f5374,plain,(
% 0.19/0.60 spl0_166|~spl0_164|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49),
% 0.19/0.60 inference(split_clause,[status(thm)],[f5373,f962,f955,f465,f580,f643,f657,f443,f712,f671,f373,f531])).
% 0.19/0.60 fof(f5404,plain,(
% 0.19/0.60 ![X0]: (possibly(not(X0))=not(possibly(necessarily(X0)))|~spl0_110|~spl0_98|~spl0_87|~spl0_6|~spl0_119|~spl0_166)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f3070,f1202])).
% 0.19/0.60 fof(f5405,plain,(
% 0.19/0.60 ![X0]: (not(necessarily(X0))=not(possibly(necessarily(X0)))|~spl0_31|~spl0_62|~spl0_79|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_49|~spl0_110|~spl0_98|~spl0_87|~spl0_6|~spl0_119|~spl0_166)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f3167,f5404])).
% 0.19/0.60 fof(f5658,plain,(
% 0.19/0.60 spl0_211 <=> ~is_a_theorem(or(X0,not(X0)))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f5659,plain,(
% 0.19/0.60 ![X0]: (~is_a_theorem(or(X0,not(X0)))|~spl0_211)),
% 0.19/0.60 inference(component_clause,[status(thm)],[f5658])).
% 0.19/0.60 fof(f5674,plain,(
% 0.19/0.60 $false|~spl0_1|~spl0_16|~spl0_13|~spl0_83|~spl0_79|~spl0_211),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f5659,f2459])).
% 0.19/0.60 fof(f5675,plain,(
% 0.19/0.60 ~spl0_1|~spl0_16|~spl0_13|~spl0_83|~spl0_79|~spl0_211),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f5674])).
% 0.19/0.60 fof(f5789,plain,(
% 0.19/0.60 spl0_212 <=> ~is_a_theorem(implies(necessarily(X0),X0))),
% 0.19/0.60 introduced(split_symbol_definition)).
% 0.19/0.60 fof(f5790,plain,(
% 0.19/0.60 ![X0]: (~is_a_theorem(implies(necessarily(X0),X0))|~spl0_212)),
% 0.19/0.60 inference(component_clause,[status(thm)],[f5789])).
% 0.19/0.60 fof(f7829,plain,(
% 0.19/0.60 $false|~spl0_174|spl0_159),
% 0.19/0.60 inference(backward_subsumption_resolution,[status(thm)],[f939,f1091])).
% 0.19/0.60 fof(f7830,plain,(
% 0.19/0.60 ~spl0_174|spl0_159),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f7829])).
% 0.19/0.60 fof(f7839,plain,(
% 0.19/0.60 $false|~spl0_157),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f931,f350])).
% 0.19/0.60 fof(f7840,plain,(
% 0.19/0.60 ~spl0_157),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f7839])).
% 0.19/0.60 fof(f8134,plain,(
% 0.19/0.60 $false|~spl0_110|~spl0_212),
% 0.19/0.60 inference(forward_subsumption_resolution,[status(thm)],[f5790,f758])).
% 0.19/0.60 fof(f8135,plain,(
% 0.19/0.60 ~spl0_110|~spl0_212),
% 0.19/0.60 inference(contradiction_clause,[status(thm)],[f8134])).
% 0.19/0.60 fof(f8186,plain,(
% 0.19/0.60 ![X0]: (is_a_theorem(strict_implies(X0,X0))|~spl0_137|~spl0_25|~spl0_98|~spl0_87|~spl0_6|~spl0_49)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f3106,f857])).
% 0.19/0.60 fof(f13925,plain,(
% 0.19/0.60 ![X0]: (possibly(necessarily(X0))=not(not(necessarily(X0)))|~spl0_31|~spl0_62|~spl0_79|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_49|~spl0_110|~spl0_98|~spl0_87|~spl0_6|~spl0_119|~spl0_166)),
% 0.19/0.60 inference(paramodulation,[status(thm)],[f5405,f3173])).
% 0.19/0.60 fof(f13926,plain,(
% 0.19/0.60 ![X0]: (possibly(necessarily(X0))=necessarily(X0)|~spl0_31|~spl0_62|~spl0_79|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_49|~spl0_110|~spl0_98|~spl0_87|~spl0_6|~spl0_119|~spl0_166)),
% 0.19/0.60 inference(forward_demodulation,[status(thm)],[f3173,f13925])).
% 0.19/0.60 fof(f13936,plain,(
% 0.19/0.60 ![X0]: (possibly(possibly(X0))=necessarily(possibly(X0))|~spl0_31|~spl0_62|~spl0_79|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_49|~spl0_166|~spl0_110|~spl0_98|~spl0_87|~spl0_6|~spl0_119)),
% 1.94/0.62 inference(paramodulation,[status(thm)],[f3070,f13926])).
% 1.94/0.62 fof(f13937,plain,(
% 1.94/0.62 ![X0]: (possibly(possibly(X0))=possibly(X0)|~spl0_31|~spl0_62|~spl0_79|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_49|~spl0_166|~spl0_110|~spl0_98|~spl0_87|~spl0_6|~spl0_119)),
% 1.94/0.62 inference(forward_demodulation,[status(thm)],[f3070,f13936])).
% 1.94/0.62 fof(f13950,plain,(
% 1.94/0.62 ~is_a_theorem(strict_implies(possibly(sk0_92),possibly(sk0_92)))|~spl0_31|~spl0_62|~spl0_79|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_49|~spl0_166|~spl0_110|~spl0_98|~spl0_87|~spl0_6|~spl0_119|spl0_159),
% 1.94/0.62 inference(backward_demodulation,[status(thm)],[f13937,f939])).
% 1.94/0.62 fof(f14125,plain,(
% 1.94/0.62 $false|~spl0_137|~spl0_31|~spl0_62|~spl0_79|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_49|~spl0_166|~spl0_110|~spl0_98|~spl0_87|~spl0_6|~spl0_119|spl0_159),
% 1.94/0.62 inference(backward_subsumption_resolution,[status(thm)],[f13950,f8186])).
% 1.94/0.62 fof(f14126,plain,(
% 1.94/0.62 ~spl0_137|~spl0_31|~spl0_62|~spl0_79|~spl0_168|~spl0_164|~spl0_83|~spl0_25|~spl0_49|~spl0_166|~spl0_110|~spl0_98|~spl0_87|~spl0_6|~spl0_119|spl0_159),
% 1.94/0.62 inference(contradiction_clause,[status(thm)],[f14125])).
% 1.94/0.62 fof(f14127,plain,(
% 1.94/0.62 $false),
% 1.94/0.62 inference(sat_refutation,[status(thm)],[f357,f376,f391,f402,f413,f424,f435,f446,f457,f468,f479,f490,f538,f546,f565,f572,f576,f583,f587,f594,f598,f606,f646,f660,f674,f681,f715,f719,f723,f727,f749,f760,f793,f859,f863,f881,f885,f940,f947,f951,f958,f972,f979,f981,f983,f985,f987,f989,f991,f993,f995,f997,f999,f1005,f1007,f1020,f1022,f1026,f1028,f1030,f1032,f1034,f1036,f1038,f1043,f1045,f1053,f1055,f1085,f1094,f1097,f1099,f1131,f1150,f1152,f1154,f1171,f1342,f1368,f1524,f1526,f1531,f1547,f1549,f1551,f1554,f1560,f1761,f1763,f1784,f1786,f1879,f1881,f1886,f1888,f1892,f1894,f2401,f2451,f2478,f2839,f2845,f2848,f3221,f3494,f4454,f5374,f5675,f7830,f7840,f8135,f14126])).
% 1.94/0.62 % SZS output end CNFRefutation for theBenchmark.p
% 1.94/0.62 % Elapsed time: 0.274397 seconds
% 1.94/0.62 % CPU time: 2.004575 seconds
% 1.94/0.62 % Memory used: 98.239 MB
%------------------------------------------------------------------------------