%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL547+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:10:15 PM UTC 2026
% Result : Theorem 101.94s 13.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL547+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.49 % Computer : n003.cluster.edu
% 0.17/0.49 % Model : x86_64 x86_64
% 0.17/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.49 % Memory : 8046.5625MB
% 0.17/0.49 % OS : Linux 6.8.0-71-generic
% 0.17/0.49 % CPULimit : 300
% 0.17/0.49 % WCLimit : 300
% 0.17/0.49 % DateTime : Mon Sep 21 00:39:45 UTC 2026
% 0.17/0.50 % CPUTime :
% 0.17/0.54 % Drodi V4.1.1
% 101.94/13.49 % Refutation found
% 101.94/13.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 101.94/13.49 % SZS output start CNFRefutation for theBenchmark
% 101.94/13.49 fof(f1,axiom,(
% 101.94/13.49 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f2,axiom,(
% 101.94/13.49 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f3,axiom,(
% 101.94/13.49 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f4,axiom,(
% 101.94/13.49 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f5,axiom,(
% 101.94/13.49 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f6,axiom,(
% 101.94/13.49 ( implies_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f7,axiom,(
% 101.94/13.49 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f9,axiom,(
% 101.94/13.49 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f11,axiom,(
% 101.94/13.49 ( or_2<=> (! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f12,axiom,(
% 101.94/13.49 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f15,axiom,(
% 101.94/13.49 ( equivalence_3<=> (! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f21,axiom,(
% 101.94/13.49 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f27,axiom,(
% 101.94/13.49 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f29,axiom,(
% 101.94/13.49 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f32,axiom,(
% 101.94/13.49 op_or ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f33,axiom,(
% 101.94/13.49 op_implies_and ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f35,axiom,(
% 101.94/13.49 modus_ponens ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f36,axiom,(
% 101.94/13.49 modus_tollens ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f37,axiom,(
% 101.94/13.49 implies_1 ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f38,axiom,(
% 101.94/13.49 implies_2 ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f39,axiom,(
% 101.94/13.49 implies_3 ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f40,axiom,(
% 101.94/13.49 and_1 ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f42,axiom,(
% 101.94/13.49 and_3 ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f44,axiom,(
% 101.94/13.49 or_2 ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f45,axiom,(
% 101.94/13.49 or_3 ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f48,axiom,(
% 101.94/13.49 equivalence_3 ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f49,axiom,(
% 101.94/13.49 substitution_of_equivalents ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f50,axiom,(
% 101.94/13.49 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f54,axiom,(
% 101.94/13.49 ( axiom_K<=> (! [X,Y] : is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y)))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f55,axiom,(
% 101.94/13.49 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f56,axiom,(
% 101.94/13.49 ( axiom_4<=> (! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f57,axiom,(
% 101.94/13.49 ( axiom_B<=> (! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f61,axiom,(
% 101.94/13.49 ( axiom_s3<=> (! [X,Y] : is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X))))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f73,axiom,(
% 101.94/13.49 ( op_possibly=> (! [X] : possibly(X) = not(necessarily(not(X))) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f75,axiom,(
% 101.94/13.49 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f77,axiom,(
% 101.94/13.49 op_possibly ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f78,axiom,(
% 101.94/13.49 necessitation ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f79,axiom,(
% 101.94/13.49 axiom_K ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f80,axiom,(
% 101.94/13.49 axiom_M ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f81,axiom,(
% 101.94/13.49 axiom_4 ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f82,axiom,(
% 101.94/13.49 axiom_B ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f86,axiom,(
% 101.94/13.49 op_strict_implies ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f89,conjecture,(
% 101.94/13.49 axiom_s3 ),
% 101.94/13.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 101.94/13.49 fof(f90,negated_conjecture,(
% 101.94/13.49 ~(axiom_s3 )),
% 101.94/13.49 inference(negated_conjecture,[status(cth)],[f89])).
% 101.94/13.49 fof(f91,plain,(
% 101.94/13.49 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 101.94/13.49 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 101.94/13.49 fof(f92,plain,(
% 101.94/13.49 (~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))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f91])).
% 101.94/13.49 fof(f93,plain,(
% 101.94/13.49 (~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))))),
% 101.94/13.49 inference(miniscoping,[status(thm)],[f92])).
% 101.94/13.49 fof(f94,plain,(
% 101.94/13.49 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|((is_a_theorem(sK1_skl)&is_a_theorem(implies(sK1_skl,sK0_skl)))&~is_a_theorem(sK0_skl)))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f93])).
% 101.94/13.49 fof(f95,plain,(
% 101.94/13.49 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f94])).
% 101.94/13.49 fof(f99,plain,(
% 101.94/13.49 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 101.94/13.49 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 101.94/13.49 fof(f100,plain,(
% 101.94/13.49 (~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)))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f99])).
% 101.94/13.49 fof(f101,plain,(
% 101.94/13.49 (~substitution_of_equivalents|(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y)))&(substitution_of_equivalents|(is_a_theorem(equiv(sK2_skl,sK3_skl))&~sK2_skl=sK3_skl))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f100])).
% 101.94/13.49 fof(f102,plain,(
% 101.94/13.49 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f101])).
% 101.94/13.49 fof(f105,plain,(
% 101.94/13.49 (~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)))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f3])).
% 101.94/13.49 fof(f106,plain,(
% 101.94/13.49 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|~is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f105])).
% 101.94/13.49 fof(f107,plain,(
% 101.94/13.49 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f106])).
% 101.94/13.49 fof(f109,plain,(
% 101.94/13.49 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f4])).
% 101.94/13.49 fof(f110,plain,(
% 101.94/13.49 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|~is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f109])).
% 101.94/13.49 fof(f111,plain,(
% 101.94/13.49 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f110])).
% 101.94/13.49 fof(f113,plain,(
% 101.94/13.49 (~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)))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f5])).
% 101.94/13.49 fof(f114,plain,(
% 101.94/13.49 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f113])).
% 101.94/13.49 fof(f115,plain,(
% 101.94/13.49 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f114])).
% 101.94/13.49 fof(f117,plain,(
% 101.94/13.49 (~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))))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f6])).
% 101.94/13.49 fof(f118,plain,(
% 101.94/13.49 (~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(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl)))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(X,sK10_skl),skolemize(Y,sK11_skl),skolemize(Z,sK12_skl)],[f117])).
% 101.94/13.49 fof(f119,plain,(
% 101.94/13.49 ![X0,X1,X2]: (~implies_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f118])).
% 101.94/13.49 fof(f121,plain,(
% 101.94/13.49 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f7])).
% 101.94/13.49 fof(f122,plain,(
% 101.94/13.49 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|~is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl)))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f121])).
% 101.94/13.49 fof(f123,plain,(
% 101.94/13.49 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f122])).
% 101.94/13.49 fof(f129,plain,(
% 101.94/13.49 (~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))))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f9])).
% 101.94/13.49 fof(f130,plain,(
% 101.94/13.49 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|~is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl)))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f129])).
% 101.94/13.49 fof(f131,plain,(
% 101.94/13.49 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f130])).
% 101.94/13.49 fof(f137,plain,(
% 101.94/13.49 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|(?[X,Y]: ~is_a_theorem(implies(Y,or(X,Y)))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f11])).
% 101.94/13.49 fof(f138,plain,(
% 101.94/13.49 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|~is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f137])).
% 101.94/13.49 fof(f139,plain,(
% 101.94/13.49 ![X0,X1]: (~or_2|is_a_theorem(implies(X0,or(X1,X0))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f138])).
% 101.94/13.49 fof(f141,plain,(
% 101.94/13.49 (~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))))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f12])).
% 101.94/13.49 fof(f142,plain,(
% 101.94/13.49 (~or_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))))&(or_3|~is_a_theorem(implies(implies(sK23_skl,sK25_skl),implies(implies(sK24_skl,sK25_skl),implies(or(sK23_skl,sK24_skl),sK25_skl)))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl]),skolemize(X,sK23_skl),skolemize(Y,sK24_skl),skolemize(Z,sK25_skl)],[f141])).
% 101.94/13.49 fof(f143,plain,(
% 101.94/13.49 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f142])).
% 101.94/13.49 fof(f153,plain,(
% 101.94/13.49 (~equivalence_3|(![X,Y]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))))&(equivalence_3|(?[X,Y]: ~is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f15])).
% 101.94/13.49 fof(f154,plain,(
% 101.94/13.49 (~equivalence_3|(![X,Y]: is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))))&(equivalence_3|~is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl)))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(X,sK30_skl),skolemize(Y,sK31_skl)],[f153])).
% 101.94/13.49 fof(f155,plain,(
% 101.94/13.49 ![X0,X1]: (~equivalence_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f154])).
% 101.94/13.49 fof(f177,plain,(
% 101.94/13.49 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f21])).
% 101.94/13.49 fof(f178,plain,(
% 101.94/13.49 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f177])).
% 101.94/13.49 fof(f179,plain,(
% 101.94/13.49 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f178])).
% 101.94/13.49 fof(f180,plain,(
% 101.94/13.49 cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f178])).
% 101.94/13.49 fof(f201,plain,(
% 101.94/13.49 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 101.94/13.49 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 101.94/13.49 fof(f202,plain,(
% 101.94/13.49 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f201])).
% 101.94/13.49 fof(f205,plain,(
% 101.94/13.49 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 101.94/13.49 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 101.94/13.49 fof(f206,plain,(
% 101.94/13.49 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f205])).
% 101.94/13.49 fof(f211,plain,(
% 101.94/13.49 op_or),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f32])).
% 101.94/13.49 fof(f212,plain,(
% 101.94/13.49 op_implies_and),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f33])).
% 101.94/13.49 fof(f214,plain,(
% 101.94/13.49 modus_ponens),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f35])).
% 101.94/13.49 fof(f215,plain,(
% 101.94/13.49 modus_tollens),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f36])).
% 101.94/13.49 fof(f216,plain,(
% 101.94/13.49 implies_1),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f37])).
% 101.94/13.49 fof(f217,plain,(
% 101.94/13.49 implies_2),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f38])).
% 101.94/13.49 fof(f218,plain,(
% 101.94/13.49 implies_3),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f39])).
% 101.94/13.49 fof(f219,plain,(
% 101.94/13.49 and_1),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f40])).
% 101.94/13.49 fof(f221,plain,(
% 101.94/13.49 and_3),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f42])).
% 101.94/13.49 fof(f223,plain,(
% 101.94/13.49 or_2),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f44])).
% 101.94/13.49 fof(f224,plain,(
% 101.94/13.49 or_3),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f45])).
% 101.94/13.49 fof(f227,plain,(
% 101.94/13.49 equivalence_3),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f48])).
% 101.94/13.49 fof(f228,plain,(
% 101.94/13.49 substitution_of_equivalents),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f49])).
% 101.94/13.49 fof(f229,plain,(
% 101.94/13.49 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 101.94/13.49 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 101.94/13.49 fof(f230,plain,(
% 101.94/13.49 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f229])).
% 101.94/13.49 fof(f231,plain,(
% 101.94/13.49 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f230])).
% 101.94/13.49 fof(f232,plain,(
% 101.94/13.49 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f231])).
% 101.94/13.49 fof(f256,plain,(
% 101.94/13.49 (~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))))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f54])).
% 101.94/13.49 fof(f257,plain,(
% 101.94/13.49 (~axiom_K|(![X,Y]: is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))))&(axiom_K|~is_a_theorem(implies(necessarily(implies(sK62_skl,sK63_skl)),implies(necessarily(sK62_skl),necessarily(sK63_skl)))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK62_skl,sK63_skl]),skolemize(X,sK62_skl),skolemize(Y,sK63_skl)],[f256])).
% 101.94/13.49 fof(f258,plain,(
% 101.94/13.49 ![X0,X1]: (~axiom_K|is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f257])).
% 101.94/13.49 fof(f260,plain,(
% 101.94/13.49 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f55])).
% 101.94/13.49 fof(f261,plain,(
% 101.94/13.49 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f260])).
% 101.94/13.49 fof(f262,plain,(
% 101.94/13.49 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f261])).
% 101.94/13.49 fof(f264,plain,(
% 101.94/13.49 (~axiom_4|(![X]: is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))&(axiom_4|(?[X]: ~is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f56])).
% 101.94/13.49 fof(f265,plain,(
% 101.94/13.49 (~axiom_4|(![X]: is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))&(axiom_4|~is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl)))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK65_skl]),skolemize(X,sK65_skl)],[f264])).
% 101.94/13.49 fof(f266,plain,(
% 101.94/13.49 ![X0]: (~axiom_4|is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f265])).
% 101.94/13.49 fof(f268,plain,(
% 101.94/13.49 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|(?[X]: ~is_a_theorem(implies(X,necessarily(possibly(X))))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f57])).
% 101.94/13.49 fof(f269,plain,(
% 101.94/13.49 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|~is_a_theorem(implies(sK66_skl,necessarily(possibly(sK66_skl)))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl]),skolemize(X,sK66_skl)],[f268])).
% 101.94/13.49 fof(f270,plain,(
% 101.94/13.49 ![X0]: (~axiom_B|is_a_theorem(implies(X0,necessarily(possibly(X0)))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f269])).
% 101.94/13.49 fof(f284,plain,(
% 101.94/13.49 (~axiom_s3|(![X,Y]: is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X)))))))&(axiom_s3|(?[X,Y]: ~is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X)))))))),
% 101.94/13.49 inference(NNF_transformation,[status(thm)],[f61])).
% 101.94/13.49 fof(f285,plain,(
% 101.94/13.49 (~axiom_s3|(![X,Y]: is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X)))))))&(axiom_s3|~is_a_theorem(strict_implies(strict_implies(sK73_skl,sK74_skl),strict_implies(not(possibly(sK74_skl)),not(possibly(sK73_skl))))))),
% 101.94/13.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK73_skl,sK74_skl]),skolemize(X,sK73_skl),skolemize(Y,sK74_skl)],[f284])).
% 101.94/13.49 fof(f287,plain,(
% 101.94/13.49 axiom_s3|~is_a_theorem(strict_implies(strict_implies(sK73_skl,sK74_skl),strict_implies(not(possibly(sK74_skl)),not(possibly(sK73_skl)))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f285])).
% 101.94/13.49 fof(f332,plain,(
% 101.94/13.49 ~op_possibly|(![X]: possibly(X)=not(necessarily(not(X))))),
% 101.94/13.49 inference(pre_NNF_transformation,[status(thm)],[f73])).
% 101.94/13.49 fof(f333,plain,(
% 101.94/13.49 ![X0]: (~op_possibly|possibly(X0)=not(necessarily(not(X0))))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f332])).
% 101.94/13.49 fof(f336,plain,(
% 101.94/13.49 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 101.94/13.49 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 101.94/13.49 fof(f337,plain,(
% 101.94/13.49 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f336])).
% 101.94/13.49 fof(f340,plain,(
% 101.94/13.49 op_possibly),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f77])).
% 101.94/13.49 fof(f341,plain,(
% 101.94/13.49 necessitation),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f78])).
% 101.94/13.49 fof(f342,plain,(
% 101.94/13.49 axiom_K),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f79])).
% 101.94/13.49 fof(f343,plain,(
% 101.94/13.49 axiom_M),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f80])).
% 101.94/13.49 fof(f344,plain,(
% 101.94/13.49 axiom_4),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f81])).
% 101.94/13.49 fof(f345,plain,(
% 101.94/13.49 axiom_B),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f82])).
% 101.94/13.49 fof(f349,plain,(
% 101.94/13.49 op_strict_implies),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f86])).
% 101.94/13.49 fof(f352,plain,(
% 101.94/13.49 ~axiom_s3),
% 101.94/13.49 inference(cnf_transformation,[status(thm)],[f90])).
% 101.94/13.49 fof(f353,plain,(
% 101.94/13.49 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 101.94/13.49 inference(backward_subsumption_resolution,[status(thm)],[f95,f214])).
% 101.94/13.49 fof(f355,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f107,f215])).
% 101.94/13.49 fof(f356,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 101.94/13.49 inference(backward_subsumption_resolution,[status(thm)],[f111,f216])).
% 101.94/13.49 fof(f357,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 101.94/13.49 inference(backward_subsumption_resolution,[status(thm)],[f115,f217])).
% 101.94/13.49 fof(f358,plain,(
% 101.94/13.49 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f119,f218])).
% 101.94/13.49 fof(f359,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 101.94/13.49 inference(backward_subsumption_resolution,[status(thm)],[f123,f219])).
% 101.94/13.49 fof(f361,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f131,f221])).
% 101.94/13.49 fof(f363,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 101.94/13.49 inference(backward_subsumption_resolution,[status(thm)],[f139,f223])).
% 101.94/13.49 fof(f364,plain,(
% 101.94/13.49 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f143,f224])).
% 101.94/13.49 fof(f367,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f155,f227])).
% 101.94/13.49 fof(f368,plain,(
% 101.94/13.49 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 101.94/13.49 inference(backward_subsumption_resolution,[status(thm)],[f102,f228])).
% 101.94/13.49 fof(f370,plain,(
% 101.94/13.49 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f202,f211])).
% 101.94/13.49 fof(f375,plain,(
% 101.94/13.49 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f376,f370])).
% 101.94/13.49 fof(f376,plain,(
% 101.94/13.49 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f206,f212])).
% 101.94/13.49 fof(f383,plain,(
% 101.94/13.49 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f232,f341])).
% 101.94/13.49 fof(f385,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f258,f342])).
% 101.94/13.49 fof(f386,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(implies(necessarily(X0),X0)))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f262,f343])).
% 101.94/13.49 fof(f389,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f266,f344])).
% 101.94/13.49 fof(f390,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(implies(X0,necessarily(possibly(X0)))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f270,f345])).
% 101.94/13.49 fof(f392,plain,(
% 101.94/13.49 ~is_a_theorem(strict_implies(strict_implies(sK73_skl,sK74_skl),strict_implies(not(possibly(sK74_skl)),not(possibly(sK73_skl)))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f287,f352])).
% 101.94/13.49 fof(f393,plain,(
% 101.94/13.49 cn3|~is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f375,f180])).
% 101.94/13.49 fof(f397,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f375,f355])).
% 101.94/13.49 fof(f398,plain,(
% 101.94/13.49 ![X0]: (~cn3|is_a_theorem(implies(or(X0,X0),X0)))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f375,f179])).
% 101.94/13.49 fof(f400,plain,(
% 101.94/13.49 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f376,f375])).
% 101.94/13.49 fof(f403,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(or(X0,necessarily(possibly(not(X0))))))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f375,f390])).
% 101.94/13.49 fof(f408,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(necessarily(or(X0,X1)),implies(necessarily(not(X0)),necessarily(X1)))))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f375,f385])).
% 101.94/13.49 fof(f426,plain,(
% 101.94/13.49 ![X0]: (possibly(X0)=not(necessarily(not(X0))))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f333,f340])).
% 101.94/13.49 fof(f427,plain,(
% 101.94/13.49 ![X0]: (possibly(necessarily(not(X0)))=not(necessarily(possibly(X0))))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f426,f426])).
% 101.94/13.49 fof(f428,plain,(
% 101.94/13.49 ![X0,X1]: (possibly(and(X0,not(X1)))=not(necessarily(implies(X0,X1))))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f376,f426])).
% 101.94/13.49 fof(f432,plain,(
% 101.94/13.49 ![X0,X1]: (or(necessarily(not(X0)),X1)=implies(possibly(X0),X1))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f426,f375])).
% 101.94/13.49 fof(f433,plain,(
% 101.94/13.49 ![X0,X1]: (implies(X0,necessarily(not(X1)))=not(and(X0,possibly(X1))))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f426,f376])).
% 101.94/13.49 fof(f436,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(strict_implies(X0,X1),implies(necessarily(X0),necessarily(X1)))))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f437,f385])).
% 101.94/13.49 fof(f437,plain,(
% 101.94/13.49 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f337,f349])).
% 101.94/13.49 fof(f438,plain,(
% 101.94/13.49 ![X0,X1]: (strict_implies(not(X0),X1)=necessarily(or(X0,X1)))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f375,f437])).
% 101.94/13.49 fof(f439,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(necessarily(implies(X0,X1)),necessarily(strict_implies(X0,X1)))))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f437,f389])).
% 101.94/13.49 fof(f442,plain,(
% 101.94/13.49 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1)))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f437,f383])).
% 101.94/13.49 fof(f447,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(strict_implies(X0,X1),necessarily(strict_implies(X0,X1)))))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f437,f439])).
% 101.94/13.49 fof(f458,plain,(
% 101.94/13.49 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))))),
% 101.94/13.49 inference(resolution,[status(thm)],[f353,f367])).
% 101.94/13.49 fof(f459,plain,(
% 101.94/13.49 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X2,X1),implies(or(X0,X2),X1))))),
% 101.94/13.49 inference(resolution,[status(thm)],[f353,f364])).
% 101.94/13.49 fof(f460,plain,(
% 101.94/13.49 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X2),implies(X0,X2))))),
% 101.94/13.49 inference(resolution,[status(thm)],[f353,f358])).
% 101.94/13.49 fof(f467,plain,(
% 101.94/13.49 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 101.94/13.49 inference(resolution,[status(thm)],[f357,f353])).
% 101.94/13.49 fof(f488,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f375,f397])).
% 101.94/13.49 fof(f500,plain,(
% 101.94/13.49 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(necessarily(X0),necessarily(X1))))),
% 101.94/13.49 inference(resolution,[status(thm)],[f436,f353])).
% 101.94/13.49 fof(f876,plain,(
% 101.94/13.49 ![X0,X1]: (possibly(and(X0,not(X1)))=not(strict_implies(X0,X1)))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f437,f428])).
% 101.94/13.49 fof(f1026,plain,(
% 101.94/13.49 ~is_a_theorem(strict_implies(strict_implies(sK73_skl,sK74_skl),necessarily(or(possibly(sK74_skl),not(possibly(sK73_skl))))))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f438,f392])).
% 101.94/13.49 fof(f1054,plain,(
% 101.94/13.49 ~is_a_theorem(implies(strict_implies(sK73_skl,sK74_skl),necessarily(or(possibly(sK74_skl),not(possibly(sK73_skl))))))),
% 101.94/13.49 inference(resolution,[status(thm)],[f442,f1026])).
% 101.94/13.49 fof(f1086,plain,(
% 101.94/13.49 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1)))),
% 101.94/13.49 inference(resolution,[status(thm)],[f458,f353])).
% 101.94/13.49 fof(f1093,plain,(
% 101.94/13.49 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X2,X1))|is_a_theorem(implies(or(X0,X2),X1)))),
% 101.94/13.49 inference(resolution,[status(thm)],[f459,f353])).
% 101.94/13.49 fof(f1115,plain,(
% 101.94/13.49 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(X0,X2)))),
% 101.94/13.49 inference(resolution,[status(thm)],[f460,f353])).
% 101.94/13.49 fof(f1156,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 101.94/13.49 inference(resolution,[status(thm)],[f467,f361])).
% 101.94/13.49 fof(f1157,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 101.94/13.49 inference(resolution,[status(thm)],[f467,f356])).
% 101.94/13.49 fof(f1264,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(necessarily(X0),necessarily(X1)))|~is_a_theorem(implies(X0,X1)))),
% 101.94/13.49 inference(resolution,[status(thm)],[f500,f442])).
% 101.94/13.49 fof(f8864,plain,(
% 101.94/13.49 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|X0=X1)),
% 101.94/13.49 inference(resolution,[status(thm)],[f1086,f368])).
% 101.94/13.49 fof(f8947,plain,(
% 101.94/13.49 ~is_a_theorem(implies(sK43_skl,sK43_skl))|~is_a_theorem(implies(sK43_skl,sK43_skl))|cn3),
% 101.94/13.49 inference(resolution,[status(thm)],[f1093,f393])).
% 101.94/13.49 fof(f8962,plain,(
% 101.94/13.49 ~is_a_theorem(implies(sK43_skl,sK43_skl))|cn3),
% 101.94/13.49 inference(duplicate_literals_removal,[status(thm)],[f8947])).
% 101.94/13.49 fof(f8963,plain,(
% 101.94/13.49 cn3),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f8962,f1157])).
% 101.94/13.49 fof(f8995,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 101.94/13.49 inference(backward_subsumption_resolution,[status(thm)],[f398,f8963])).
% 101.94/13.49 fof(f9186,plain,(
% 101.94/13.49 ![X0]: (~is_a_theorem(implies(strict_implies(sK73_skl,sK74_skl),X0))|~is_a_theorem(implies(X0,necessarily(or(possibly(sK74_skl),not(possibly(sK73_skl)))))))),
% 101.94/13.49 inference(resolution,[status(thm)],[f1115,f1054])).
% 101.94/13.49 fof(f9232,plain,(
% 101.94/13.49 ~is_a_theorem(implies(necessarily(strict_implies(sK73_skl,sK74_skl)),necessarily(or(possibly(sK74_skl),not(possibly(sK73_skl))))))),
% 101.94/13.49 inference(resolution,[status(thm)],[f9186,f447])).
% 101.94/13.49 fof(f10114,plain,(
% 101.94/13.49 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|X0=or(X0,X0))),
% 101.94/13.49 inference(resolution,[status(thm)],[f8864,f8995])).
% 101.94/13.49 fof(f10129,plain,(
% 101.94/13.49 ![X0]: (~is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0)))|necessarily(necessarily(X0))=necessarily(X0))),
% 101.94/13.49 inference(resolution,[status(thm)],[f8864,f389])).
% 101.94/13.49 fof(f10204,plain,(
% 101.94/13.49 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|and(X0,X0)=X0)),
% 101.94/13.49 inference(resolution,[status(thm)],[f8864,f1156])).
% 101.94/13.49 fof(f10231,plain,(
% 101.94/13.49 ![X0]: (X0=or(X0,X0))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f10114,f363])).
% 101.94/13.49 fof(f10240,plain,(
% 101.94/13.49 ![X0]: (necessarily(necessarily(X0))=necessarily(X0))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f10129,f386])).
% 101.94/13.49 fof(f10282,plain,(
% 101.94/13.49 ![X0]: (and(X0,X0)=X0)),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f10204,f359])).
% 101.94/13.49 fof(f10663,plain,(
% 101.94/13.49 ~is_a_theorem(implies(strict_implies(sK73_skl,sK74_skl),or(possibly(sK74_skl),not(possibly(sK73_skl)))))),
% 101.94/13.49 inference(resolution,[status(thm)],[f1264,f9232])).
% 101.94/13.49 fof(f10968,plain,(
% 101.94/13.49 ![X0]: (possibly(not(X0))=not(strict_implies(not(X0),X0)))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f10282,f876])).
% 101.94/13.49 fof(f10970,plain,(
% 101.94/13.49 ![X0,X1]: (or(not(X0),X1)=implies(implies(not(X0),X0),X1))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f10282,f400])).
% 101.94/13.49 fof(f10973,plain,(
% 101.94/13.49 ![X0]: (implies(not(X0),X0)=not(not(X0)))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f10282,f376])).
% 101.94/13.49 fof(f11139,plain,(
% 101.94/13.49 ![X0]: (possibly(not(X0))=not(necessarily(or(X0,X0))))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f438,f10968])).
% 101.94/13.49 fof(f11140,plain,(
% 101.94/13.49 ![X0]: (possibly(not(X0))=not(necessarily(X0)))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f10231,f11139])).
% 101.94/13.49 fof(f11142,plain,(
% 101.94/13.49 ![X0,X1]: (or(not(X0),X1)=implies(or(X0,X0),X1))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f375,f10970])).
% 101.94/13.49 fof(f11143,plain,(
% 101.94/13.49 ![X0,X1]: (or(not(X0),X1)=implies(X0,X1))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f10231,f11142])).
% 101.94/13.49 fof(f11149,plain,(
% 101.94/13.49 ![X0]: (or(X0,X0)=not(not(X0)))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f375,f10973])).
% 101.94/13.49 fof(f11150,plain,(
% 101.94/13.49 ![X0]: (X0=not(not(X0)))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f10231,f11149])).
% 101.94/13.49 fof(f11340,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f11150,f488])).
% 101.94/13.49 fof(f11749,plain,(
% 101.94/13.49 ![X0,X1]: (~is_a_theorem(implies(or(X0,X1),or(X1,X0)))|or(X0,X1)=or(X1,X0))),
% 101.94/13.49 inference(resolution,[status(thm)],[f11340,f8864])).
% 101.94/13.49 fof(f11763,plain,(
% 101.94/13.49 ![X0,X1]: (or(X0,X1)=or(X1,X0))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f11749,f11340])).
% 101.94/13.49 fof(f24879,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(or(X0,necessarily(not(necessarily(X0))))))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f11140,f403])).
% 101.94/13.49 fof(f25576,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(not(necessarily(necessarily(not(X0))))))))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f432,f24879])).
% 101.94/13.49 fof(f25586,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(not(and(possibly(X0),possibly(necessarily(necessarily(not(X0))))))))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f433,f25576])).
% 101.94/13.49 fof(f25587,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(not(and(possibly(X0),possibly(necessarily(not(X0)))))))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f10240,f25586])).
% 101.94/13.49 fof(f25588,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(not(and(possibly(X0),not(necessarily(possibly(X0)))))))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f427,f25587])).
% 101.94/13.49 fof(f25589,plain,(
% 101.94/13.49 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f376,f25588])).
% 101.94/13.49 fof(f25597,plain,(
% 101.94/13.49 ![X0]: (~is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0)))|necessarily(possibly(X0))=possibly(X0))),
% 101.94/13.49 inference(resolution,[status(thm)],[f25589,f8864])).
% 101.94/13.49 fof(f25610,plain,(
% 101.94/13.49 ![X0]: (necessarily(possibly(X0))=possibly(X0))),
% 101.94/13.49 inference(forward_subsumption_resolution,[status(thm)],[f25597,f386])).
% 101.94/13.49 fof(f25916,plain,(
% 101.94/13.49 ![X0]: (possibly(necessarily(not(X0)))=not(possibly(X0)))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f25610,f427])).
% 101.94/13.49 fof(f25969,plain,(
% 101.94/13.49 ![X0]: (possibly(necessarily(X0))=not(possibly(not(X0))))),
% 101.94/13.49 inference(paramodulation,[status(thm)],[f11150,f25916])).
% 101.94/13.49 fof(f26107,plain,(
% 101.94/13.49 ![X0]: (possibly(necessarily(X0))=not(not(necessarily(X0))))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f11140,f25969])).
% 101.94/13.49 fof(f26108,plain,(
% 101.94/13.49 ![X0]: (possibly(necessarily(X0))=necessarily(X0))),
% 101.94/13.49 inference(forward_demodulation,[status(thm)],[f11150,f26107])).
% 101.94/13.49 fof(f27509,plain,(
% 101.94/13.49 ![X0]: (necessarily(not(X0))=not(possibly(X0)))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f26108,f25916])).
% 101.94/13.49 fof(f27819,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(necessarily(or(X0,X1)),implies(not(possibly(X0)),necessarily(X1)))))),
% 101.94/13.49 inference(backward_demodulation,[status(thm)],[f27509,f408])).
% 101.94/13.49 fof(f27888,plain,(
% 101.94/13.49 ![X0,X1]: (is_a_theorem(implies(necessarily(or(X0,X1)),or(possibly(X0),necessarily(X1)))))),
% 95.47/13.59 inference(forward_demodulation,[status(thm)],[f375,f27819])).
% 95.47/13.59 fof(f29197,plain,(
% 95.47/13.59 ![X0,X1]: (is_a_theorem(implies(necessarily(or(X0,not(X1))),or(possibly(X0),not(possibly(X1))))))),
% 95.47/13.59 inference(paramodulation,[status(thm)],[f27509,f27888])).
% 95.47/13.59 fof(f29479,plain,(
% 95.47/13.59 ![X0,X1]: (or(X0,not(X1))=implies(X1,X0))),
% 95.47/13.59 inference(paramodulation,[status(thm)],[f11763,f11143])).
% 95.47/13.59 fof(f53759,plain,(
% 95.47/13.59 ~is_a_theorem(implies(strict_implies(sK73_skl,sK74_skl),implies(possibly(sK73_skl),possibly(sK74_skl))))),
% 95.47/13.59 inference(backward_demodulation,[status(thm)],[f29479,f10663])).
% 95.47/13.59 fof(f53806,plain,(
% 95.47/13.59 ![X0,X1]: (is_a_theorem(implies(necessarily(or(X0,not(X1))),implies(possibly(X1),possibly(X0)))))),
% 95.47/13.59 inference(backward_demodulation,[status(thm)],[f29479,f29197])).
% 95.47/13.59 fof(f54195,plain,(
% 95.47/13.59 ![X0,X1]: (is_a_theorem(implies(necessarily(implies(X0,X1)),implies(possibly(X0),possibly(X1)))))),
% 95.47/13.59 inference(forward_demodulation,[status(thm)],[f29479,f53806])).
% 95.47/13.59 fof(f54196,plain,(
% 95.47/13.59 ![X0,X1]: (is_a_theorem(implies(strict_implies(X0,X1),implies(possibly(X0),possibly(X1)))))),
% 95.47/13.59 inference(forward_demodulation,[status(thm)],[f437,f54195])).
% 95.47/13.59 fof(f69348,plain,(
% 95.47/13.59 $false),
% 95.47/13.59 inference(forward_subsumption_resolution,[status(thm)],[f53759,f54196])).
% 95.47/13.59 % SZS output end CNFRefutation for theBenchmark.p
% 29.68/13.68 % Elapsed time: 13.145251 seconds
% 29.68/13.68 % CPU time: 103.493092 seconds
% 29.68/13.68 % Total memory used: 1.083 GB
% 29.68/13.68 % Net memory used: 1.014 GB
%------------------------------------------------------------------------------