%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL528+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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:10:13 PM UTC 2026
% Result : Theorem 188.88s 24.22s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL528+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 00:37:03 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 188.88/24.22 % Refutation found
% 188.88/24.22 % SZS status Theorem for theBenchmark: Theorem is valid
% 188.88/24.22 % SZS output start CNFRefutation for theBenchmark
% 188.88/24.22 fof(f1,axiom,(
% 188.88/24.22 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f2,axiom,(
% 188.88/24.22 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f3,axiom,(
% 188.88/24.22 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f4,axiom,(
% 188.88/24.22 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f5,axiom,(
% 188.88/24.22 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f6,axiom,(
% 188.88/24.22 ( implies_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f8,axiom,(
% 188.88/24.22 ( and_2<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f9,axiom,(
% 188.88/24.22 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f10,axiom,(
% 188.88/24.22 ( or_1<=> (! [X,Y] : is_a_theorem(implies(X,or(X,Y))) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f11,axiom,(
% 188.88/24.22 ( or_2<=> (! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f12,axiom,(
% 188.88/24.22 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.22 fof(f21,axiom,(
% 188.88/24.22 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 188.88/24.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f24,axiom,(
% 188.88/24.23 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f27,axiom,(
% 188.88/24.23 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f29,axiom,(
% 188.88/24.23 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f31,axiom,(
% 188.88/24.23 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f32,axiom,(
% 188.88/24.23 op_or ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f33,axiom,(
% 188.88/24.23 op_implies_and ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f34,axiom,(
% 188.88/24.23 op_equiv ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f35,axiom,(
% 188.88/24.23 modus_ponens ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f36,axiom,(
% 188.88/24.23 modus_tollens ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f37,axiom,(
% 188.88/24.23 implies_1 ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f38,axiom,(
% 188.88/24.23 implies_2 ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f39,axiom,(
% 188.88/24.23 implies_3 ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f41,axiom,(
% 188.88/24.23 and_2 ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f42,axiom,(
% 188.88/24.23 and_3 ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f43,axiom,(
% 188.88/24.23 or_1 ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f44,axiom,(
% 188.88/24.23 or_2 ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f45,axiom,(
% 188.88/24.23 or_3 ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f49,axiom,(
% 188.88/24.23 substitution_of_equivalents ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f50,axiom,(
% 188.88/24.23 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f54,axiom,(
% 188.88/24.23 ( axiom_K<=> (! [X,Y] : is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y)))) )) ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f55,axiom,(
% 188.88/24.23 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f63,axiom,(
% 188.88/24.23 ( axiom_m1<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) )) ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f75,axiom,(
% 188.88/24.23 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f78,axiom,(
% 188.88/24.23 necessitation ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f79,axiom,(
% 188.88/24.23 axiom_K ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f80,axiom,(
% 188.88/24.23 axiom_M ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f85,axiom,(
% 188.88/24.23 op_strict_implies ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f88,conjecture,(
% 188.88/24.23 axiom_m1 ),
% 188.88/24.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 188.88/24.23 fof(f89,negated_conjecture,(
% 188.88/24.23 ~(axiom_m1 )),
% 188.88/24.23 inference(negated_conjecture,[status(cth)],[f88])).
% 188.88/24.23 fof(f90,plain,(
% 188.88/24.23 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 188.88/24.23 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 188.88/24.23 fof(f91,plain,(
% 188.88/24.23 (~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))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f90])).
% 188.88/24.23 fof(f92,plain,(
% 188.88/24.23 (~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))))),
% 188.88/24.23 inference(miniscoping,[status(thm)],[f91])).
% 188.88/24.23 fof(f93,plain,(
% 188.88/24.23 (~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)))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f92])).
% 188.88/24.23 fof(f94,plain,(
% 188.88/24.23 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f93])).
% 188.88/24.23 fof(f98,plain,(
% 188.88/24.23 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 188.88/24.23 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 188.88/24.23 fof(f99,plain,(
% 188.88/24.23 (~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)))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f98])).
% 188.88/24.23 fof(f100,plain,(
% 188.88/24.23 (~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))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f99])).
% 188.88/24.23 fof(f101,plain,(
% 188.88/24.23 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f100])).
% 188.88/24.23 fof(f104,plain,(
% 188.88/24.23 (~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)))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f3])).
% 188.88/24.23 fof(f105,plain,(
% 188.88/24.23 (~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))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f104])).
% 188.88/24.23 fof(f106,plain,(
% 188.88/24.23 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f105])).
% 188.88/24.23 fof(f108,plain,(
% 188.88/24.23 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f4])).
% 188.88/24.23 fof(f109,plain,(
% 188.88/24.23 (~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))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f108])).
% 188.88/24.23 fof(f110,plain,(
% 188.88/24.23 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f109])).
% 188.88/24.23 fof(f112,plain,(
% 188.88/24.23 (~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)))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f5])).
% 188.88/24.23 fof(f113,plain,(
% 188.88/24.23 (~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))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f112])).
% 188.88/24.23 fof(f114,plain,(
% 188.88/24.23 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f113])).
% 188.88/24.23 fof(f116,plain,(
% 188.88/24.23 (~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))))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f6])).
% 188.88/24.23 fof(f117,plain,(
% 188.88/24.23 (~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)))))),
% 188.88/24.23 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)],[f116])).
% 188.88/24.23 fof(f118,plain,(
% 188.88/24.23 ![X0,X1,X2]: (~implies_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f117])).
% 188.88/24.23 fof(f124,plain,(
% 188.88/24.23 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),Y))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f8])).
% 188.88/24.23 fof(f125,plain,(
% 188.88/24.23 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|~is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl)))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(X,sK15_skl),skolemize(Y,sK16_skl)],[f124])).
% 188.88/24.23 fof(f126,plain,(
% 188.88/24.23 ![X0,X1]: (~and_2|is_a_theorem(implies(and(X0,X1),X1)))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f125])).
% 188.88/24.23 fof(f128,plain,(
% 188.88/24.23 (~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))))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f9])).
% 188.88/24.23 fof(f129,plain,(
% 188.88/24.23 (~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)))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f128])).
% 188.88/24.23 fof(f130,plain,(
% 188.88/24.23 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f129])).
% 188.88/24.23 fof(f132,plain,(
% 188.88/24.23 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|(?[X,Y]: ~is_a_theorem(implies(X,or(X,Y)))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f10])).
% 188.88/24.23 fof(f133,plain,(
% 188.88/24.23 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|~is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(X,sK19_skl),skolemize(Y,sK20_skl)],[f132])).
% 188.88/24.23 fof(f134,plain,(
% 188.88/24.23 ![X0,X1]: (~or_1|is_a_theorem(implies(X0,or(X0,X1))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f133])).
% 188.88/24.23 fof(f136,plain,(
% 188.88/24.23 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|(?[X,Y]: ~is_a_theorem(implies(Y,or(X,Y)))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f11])).
% 188.88/24.23 fof(f137,plain,(
% 188.88/24.23 (~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))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f136])).
% 188.88/24.23 fof(f138,plain,(
% 188.88/24.23 ![X0,X1]: (~or_2|is_a_theorem(implies(X0,or(X1,X0))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f137])).
% 188.88/24.23 fof(f140,plain,(
% 188.88/24.23 (~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))))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f12])).
% 188.88/24.23 fof(f141,plain,(
% 188.88/24.23 (~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)))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl]),skolemize(X,sK23_skl),skolemize(Y,sK24_skl),skolemize(Z,sK25_skl)],[f140])).
% 188.88/24.23 fof(f142,plain,(
% 188.88/24.23 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f141])).
% 188.88/24.23 fof(f176,plain,(
% 188.88/24.23 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f21])).
% 188.88/24.23 fof(f177,plain,(
% 188.88/24.23 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f176])).
% 188.88/24.23 fof(f178,plain,(
% 188.88/24.23 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f177])).
% 188.88/24.23 fof(f179,plain,(
% 188.88/24.23 cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f177])).
% 188.88/24.23 fof(f188,plain,(
% 188.88/24.23 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|(?[P,Q]: ~is_a_theorem(implies(or(P,Q),or(Q,P)))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f24])).
% 188.88/24.23 fof(f189,plain,(
% 188.88/24.23 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f188])).
% 188.88/24.23 fof(f190,plain,(
% 188.88/24.23 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f189])).
% 188.88/24.23 fof(f191,plain,(
% 188.88/24.23 r3|~is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f189])).
% 188.88/24.23 fof(f200,plain,(
% 188.88/24.23 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 188.88/24.23 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 188.88/24.23 fof(f201,plain,(
% 188.88/24.23 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f200])).
% 188.88/24.23 fof(f204,plain,(
% 188.88/24.23 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 188.88/24.23 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 188.88/24.23 fof(f205,plain,(
% 188.88/24.23 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f204])).
% 188.88/24.23 fof(f208,plain,(
% 188.88/24.23 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 188.88/24.23 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 188.88/24.23 fof(f209,plain,(
% 188.88/24.23 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f208])).
% 188.88/24.23 fof(f210,plain,(
% 188.88/24.23 op_or),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f32])).
% 188.88/24.23 fof(f211,plain,(
% 188.88/24.23 op_implies_and),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f33])).
% 188.88/24.23 fof(f212,plain,(
% 188.88/24.23 op_equiv),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f34])).
% 188.88/24.23 fof(f213,plain,(
% 188.88/24.23 modus_ponens),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f35])).
% 188.88/24.23 fof(f214,plain,(
% 188.88/24.23 modus_tollens),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f36])).
% 188.88/24.23 fof(f215,plain,(
% 188.88/24.23 implies_1),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f37])).
% 188.88/24.23 fof(f216,plain,(
% 188.88/24.23 implies_2),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f38])).
% 188.88/24.23 fof(f217,plain,(
% 188.88/24.23 implies_3),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f39])).
% 188.88/24.23 fof(f219,plain,(
% 188.88/24.23 and_2),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f41])).
% 188.88/24.23 fof(f220,plain,(
% 188.88/24.23 and_3),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f42])).
% 188.88/24.23 fof(f221,plain,(
% 188.88/24.23 or_1),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f43])).
% 188.88/24.23 fof(f222,plain,(
% 188.88/24.23 or_2),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f44])).
% 188.88/24.23 fof(f223,plain,(
% 188.88/24.23 or_3),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f45])).
% 188.88/24.23 fof(f227,plain,(
% 188.88/24.23 substitution_of_equivalents),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f49])).
% 188.88/24.23 fof(f228,plain,(
% 188.88/24.23 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 188.88/24.23 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 188.88/24.23 fof(f229,plain,(
% 188.88/24.23 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f228])).
% 188.88/24.23 fof(f230,plain,(
% 188.88/24.23 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f229])).
% 188.88/24.23 fof(f231,plain,(
% 188.88/24.23 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f230])).
% 188.88/24.23 fof(f255,plain,(
% 188.88/24.23 (~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))))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f54])).
% 188.88/24.23 fof(f256,plain,(
% 188.88/24.23 (~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)))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK62_skl,sK63_skl]),skolemize(X,sK62_skl),skolemize(Y,sK63_skl)],[f255])).
% 188.88/24.23 fof(f257,plain,(
% 188.88/24.23 ![X0,X1]: (~axiom_K|is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f256])).
% 188.88/24.23 fof(f259,plain,(
% 188.88/24.23 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f55])).
% 188.88/24.23 fof(f260,plain,(
% 188.88/24.23 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f259])).
% 188.88/24.23 fof(f261,plain,(
% 188.88/24.23 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f260])).
% 188.88/24.23 fof(f291,plain,(
% 188.88/24.23 (~axiom_m1|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))&(axiom_m1|(?[X,Y]: ~is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))),
% 188.88/24.23 inference(NNF_transformation,[status(thm)],[f63])).
% 188.88/24.23 fof(f292,plain,(
% 188.88/24.23 (~axiom_m1|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))&(axiom_m1|~is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl))))),
% 188.88/24.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK76_skl,sK77_skl]),skolemize(X,sK76_skl),skolemize(Y,sK77_skl)],[f291])).
% 188.88/24.23 fof(f294,plain,(
% 188.88/24.23 axiom_m1|~is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl)))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f292])).
% 188.88/24.23 fof(f335,plain,(
% 188.88/24.23 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 188.88/24.23 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 188.88/24.23 fof(f336,plain,(
% 188.88/24.23 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f335])).
% 188.88/24.23 fof(f340,plain,(
% 188.88/24.23 necessitation),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f78])).
% 188.88/24.23 fof(f341,plain,(
% 188.88/24.23 axiom_K),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f79])).
% 188.88/24.23 fof(f342,plain,(
% 188.88/24.23 axiom_M),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f80])).
% 188.88/24.23 fof(f347,plain,(
% 188.88/24.23 op_strict_implies),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f85])).
% 188.88/24.23 fof(f350,plain,(
% 188.88/24.23 ~axiom_m1),
% 188.88/24.23 inference(cnf_transformation,[status(thm)],[f89])).
% 188.88/24.23 fof(f351,plain,(
% 188.88/24.23 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f201,f210])).
% 188.88/24.23 fof(f352,plain,(
% 188.88/24.23 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f205,f211])).
% 188.88/24.23 fof(f353,plain,(
% 188.88/24.23 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f209,f212])).
% 188.88/24.23 fof(f354,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f94,f213])).
% 188.88/24.23 fof(f355,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f106,f214])).
% 188.88/24.23 fof(f356,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f110,f215])).
% 188.88/24.23 fof(f357,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f114,f216])).
% 188.88/24.23 fof(f358,plain,(
% 188.88/24.23 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f118,f217])).
% 188.88/24.23 fof(f360,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1)))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f126,f219])).
% 188.88/24.23 fof(f361,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f130,f220])).
% 188.88/24.23 fof(f362,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f134,f221])).
% 188.88/24.23 fof(f363,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f138,f222])).
% 188.88/24.23 fof(f364,plain,(
% 188.88/24.23 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f142,f223])).
% 188.88/24.23 fof(f368,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f101,f227])).
% 188.88/24.23 fof(f370,plain,(
% 188.88/24.23 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f231,f340])).
% 188.88/24.23 fof(f371,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f257,f341])).
% 188.88/24.23 fof(f372,plain,(
% 188.88/24.23 ![X0]: (is_a_theorem(implies(necessarily(X0),X0)))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f261,f342])).
% 188.88/24.23 fof(f374,plain,(
% 188.88/24.23 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f336,f347])).
% 188.88/24.23 fof(f376,plain,(
% 188.88/24.23 ~is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl)))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f294,f350])).
% 188.88/24.23 fof(f377,plain,(
% 188.88/24.23 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 188.88/24.23 inference(backward_demodulation,[status(thm)],[f352,f351])).
% 188.88/24.23 fof(f382,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(strict_implies(X0,X1),implies(necessarily(X0),necessarily(X1)))))),
% 188.88/24.23 inference(backward_demodulation,[status(thm)],[f374,f371])).
% 188.88/24.23 fof(f384,plain,(
% 188.88/24.23 cn3|~is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl))),
% 188.88/24.23 inference(backward_demodulation,[status(thm)],[f377,f179])).
% 188.88/24.23 fof(f388,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 188.88/24.23 inference(backward_demodulation,[status(thm)],[f377,f355])).
% 188.88/24.23 fof(f389,plain,(
% 188.88/24.23 ![X0]: (~cn3|is_a_theorem(implies(or(X0,X0),X0)))),
% 188.88/24.23 inference(backward_demodulation,[status(thm)],[f377,f178])).
% 188.88/24.23 fof(f399,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1)))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f374,f370])).
% 188.88/24.23 fof(f417,plain,(
% 188.88/24.23 ![X0,X1,X2]: (implies(X0,and(X1,not(X2)))=not(and(X0,implies(X1,X2))))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f352,f352])).
% 188.88/24.23 fof(f423,plain,(
% 188.88/24.23 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f352,f377])).
% 188.88/24.23 fof(f430,plain,(
% 188.88/24.23 ![X0]: (~is_a_theorem(necessarily(X0))|is_a_theorem(X0))),
% 188.88/24.23 inference(resolution,[status(thm)],[f354,f372])).
% 188.88/24.23 fof(f438,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(X0,X1)))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f374,f430])).
% 188.88/24.23 fof(f453,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,and(X0,X1))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f361,f354])).
% 188.88/24.23 fof(f477,plain,(
% 188.88/24.23 ~is_a_theorem(implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f399,f376])).
% 188.88/24.23 fof(f507,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f357,f354])).
% 188.88/24.23 fof(f530,plain,(
% 188.88/24.23 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X2),implies(X0,X2))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f358,f354])).
% 188.88/24.23 fof(f536,plain,(
% 188.88/24.23 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X2,X1),implies(or(X0,X2),X1))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f364,f354])).
% 188.88/24.23 fof(f551,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(necessarily(X0),necessarily(X1))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f382,f354])).
% 188.88/24.23 fof(f556,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f453,f354])).
% 188.88/24.23 fof(f565,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1)))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f353,f556])).
% 188.88/24.23 fof(f572,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(or(X0,not(X1)))|is_a_theorem(implies(X1,X0)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f388,f354])).
% 188.88/24.23 fof(f642,plain,(
% 188.88/24.23 ![X0,X1,X2]: (implies(X0,and(not(X1),not(X2)))=not(and(X0,or(X1,X2))))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f377,f417])).
% 188.88/24.23 fof(f654,plain,(
% 188.88/24.23 ![X0,X1,X2,X3]: (or(and(X0,implies(X1,X2)),X3)=implies(implies(X0,and(X1,not(X2))),X3))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f417,f377])).
% 188.88/24.23 fof(f684,plain,(
% 188.88/24.23 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(X0,X1),not(X2)),implies(X2,and(X0,not(X1))))))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f423,f388])).
% 188.88/24.23 fof(f825,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f507,f364])).
% 188.88/24.23 fof(f828,plain,(
% 188.88/24.23 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f507,f361])).
% 188.88/24.23 fof(f829,plain,(
% 188.88/24.23 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f507,f356])).
% 188.88/24.23 fof(f851,plain,(
% 188.88/24.23 ![X0]: (is_a_theorem(or(X0,not(X0))))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f377,f829])).
% 188.88/24.23 fof(f886,plain,(
% 188.88/24.23 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(X0,X2)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f530,f354])).
% 188.88/24.23 fof(f932,plain,(
% 188.88/24.23 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X2,X1))|is_a_theorem(implies(or(X0,X2),X1)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f536,f354])).
% 188.88/24.23 fof(f1074,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f825,f354])).
% 188.88/24.23 fof(f1152,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(necessarily(X0))|is_a_theorem(necessarily(X1)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f551,f354])).
% 188.88/24.23 fof(f1201,plain,(
% 188.88/24.23 ~is_a_theorem(implies(sK43_skl,sK43_skl))|cn3),
% 188.88/24.23 inference(resolution,[status(thm)],[f1074,f384])).
% 188.88/24.23 fof(f1207,plain,(
% 188.88/24.23 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f389,f1208])).
% 188.88/24.23 fof(f1208,plain,(
% 188.88/24.23 cn3),
% 188.88/24.23 inference(forward_subsumption_resolution,[status(thm)],[f1201,f829])).
% 188.88/24.23 fof(f1487,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(necessarily(X1))|~is_a_theorem(X0))),
% 188.88/24.23 inference(resolution,[status(thm)],[f1152,f370])).
% 188.88/24.23 fof(f1501,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(necessarily(X0))|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X0)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f1487,f399])).
% 188.88/24.23 fof(f2204,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(necessarily(implies(X0,X1)))|~is_a_theorem(or(X1,not(X0))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f1501,f388])).
% 188.88/24.23 fof(f2263,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(or(X1,not(X0))))),
% 188.88/24.23 inference(forward_demodulation,[status(thm)],[f374,f2204])).
% 188.88/24.23 fof(f7236,plain,(
% 188.88/24.23 ![X0]: (~is_a_theorem(implies(and(sK76_skl,sK77_skl),X0))|~is_a_theorem(implies(X0,and(sK77_skl,sK76_skl))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f886,f477])).
% 188.88/24.23 fof(f7571,plain,(
% 188.88/24.23 ![X0]: (~is_a_theorem(implies(and(sK76_skl,sK77_skl),not(X0)))|~is_a_theorem(or(X0,and(sK77_skl,sK76_skl))))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f377,f7236])).
% 188.88/24.23 fof(f7929,plain,(
% 188.88/24.23 ~is_a_theorem(implies(sK47_skl,or(sK48_skl,sK47_skl)))|~is_a_theorem(implies(sK48_skl,or(sK48_skl,sK47_skl)))|r3),
% 188.88/24.23 inference(resolution,[status(thm)],[f932,f191])).
% 188.88/24.23 fof(f7944,plain,(
% 188.88/24.23 ~is_a_theorem(implies(sK48_skl,or(sK48_skl,sK47_skl)))|r3),
% 188.88/24.23 inference(forward_subsumption_resolution,[status(thm)],[f7929,f363])).
% 188.88/24.23 fof(f8060,plain,(
% 188.88/24.23 r3),
% 188.88/24.23 inference(resolution,[status(thm)],[f7944,f362])).
% 188.88/24.23 fof(f8063,plain,(
% 188.88/24.23 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 188.88/24.23 inference(backward_subsumption_resolution,[status(thm)],[f190,f8060])).
% 188.88/24.23 fof(f8065,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f8063,f354])).
% 188.88/24.23 fof(f8090,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(or(not(X0),X1))|is_a_theorem(strict_implies(X0,X1)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f8065,f2263])).
% 188.88/24.23 fof(f8091,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(or(not(X0),X1))|is_a_theorem(implies(X0,X1)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f8065,f572])).
% 188.88/24.23 fof(f8309,plain,(
% 188.88/24.23 ![X0]: (is_a_theorem(strict_implies(X0,not(not(X0)))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f8090,f851])).
% 188.88/24.23 fof(f8335,plain,(
% 188.88/24.23 ![X0]: (is_a_theorem(implies(X0,not(not(X0)))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f8309,f438])).
% 188.88/24.23 fof(f8776,plain,(
% 188.88/24.23 ![X0]: (is_a_theorem(or(X0,not(not(not(X0))))))),
% 188.88/24.23 inference(paramodulation,[status(thm)],[f377,f8335])).
% 188.88/24.23 fof(f13010,plain,(
% 188.88/24.23 ![X0]: (is_a_theorem(implies(X0,not(not(not(not(X0)))))))),
% 188.88/24.23 inference(resolution,[status(thm)],[f8091,f8776])).
% 188.88/24.23 fof(f14879,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|X0=X1)),
% 188.88/24.23 inference(resolution,[status(thm)],[f565,f368])).
% 188.88/24.23 fof(f19062,plain,(
% 188.88/24.23 ~is_a_theorem(or(not(not(not(and(sK76_skl,sK77_skl)))),and(sK77_skl,sK76_skl)))),
% 188.88/24.23 inference(resolution,[status(thm)],[f13010,f7571])).
% 188.88/24.23 fof(f20277,plain,(
% 188.88/24.23 ![X0,X1]: (~is_a_theorem(implies(or(X0,X1),or(X1,X0)))|or(X0,X1)=or(X1,X0))),
% 188.88/24.23 inference(resolution,[status(thm)],[f14879,f8063])).
% 188.88/24.23 fof(f20287,plain,(
% 188.88/24.23 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|X0=or(X0,X0))),
% 188.88/24.23 inference(resolution,[status(thm)],[f14879,f1207])).
% 188.88/24.23 fof(f20392,plain,(
% 188.88/24.23 ![X0]: (~is_a_theorem(implies(not(not(X0)),X0))|not(not(X0))=X0)),
% 188.88/24.23 inference(resolution,[status(thm)],[f14879,f8335])).
% 188.88/24.23 fof(f20401,plain,(
% 188.88/24.23 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|and(X0,X0)=X0)),
% 188.88/24.23 inference(resolution,[status(thm)],[f14879,f828])).
% 188.88/24.23 fof(f20756,plain,(
% 188.88/24.23 ~is_a_theorem(or(and(sK77_skl,sK76_skl),not(not(not(and(sK76_skl,sK77_skl))))))),
% 188.88/24.23 inference(backward_demodulation,[status(thm)],[f20818,f19062])).
% 188.88/24.23 fof(f20818,plain,(
% 188.88/24.23 ![X0,X1]: (or(X0,X1)=or(X1,X0))),
% 188.88/24.23 inference(forward_subsumption_resolution,[status(thm)],[f20277,f8063])).
% 188.88/24.23 fof(f21072,plain,(
% 188.88/24.23 ![X0]: (X0=or(X0,X0))),
% 188.88/24.23 inference(forward_subsumption_resolution,[status(thm)],[f20287,f363])).
% 188.88/24.23 fof(f22766,plain,(
% 188.88/24.23 ![X0]: (~is_a_theorem(or(not(X0),X0))|not(not(X0))=X0)),
% 188.88/24.23 inference(forward_demodulation,[status(thm)],[f377,f20392])).
% 188.88/24.23 fof(f22767,plain,(
% 188.88/24.23 ![X0]: (~is_a_theorem(or(X0,not(X0)))|not(not(X0))=X0)),
% 188.88/24.23 inference(forward_demodulation,[status(thm)],[f20818,f22766])).
% 188.88/24.38 fof(f22996,plain,(
% 188.88/24.38 ![X0]: (not(not(X0))=X0)),
% 188.88/24.38 inference(forward_subsumption_resolution,[status(thm)],[f22767,f851])).
% 188.88/24.38 fof(f23143,plain,(
% 188.88/24.38 ![X0]: (and(X0,X0)=X0)),
% 188.88/24.38 inference(forward_subsumption_resolution,[status(thm)],[f20401,f360])).
% 188.88/24.38 fof(f23468,plain,(
% 188.88/24.38 ~is_a_theorem(or(and(sK77_skl,sK76_skl),not(and(sK76_skl,sK77_skl))))),
% 188.88/24.38 inference(forward_demodulation,[status(thm)],[f22996,f20756])).
% 188.88/24.38 fof(f25775,plain,(
% 188.88/24.38 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,or(X1,X1))))),
% 188.88/24.38 inference(paramodulation,[status(thm)],[f23143,f642])).
% 188.88/24.38 fof(f25879,plain,(
% 188.88/24.38 ![X0,X1]: (is_a_theorem(implies(implies(implies(not(X0),X0),not(X1)),implies(X1,not(X0)))))),
% 188.88/24.38 inference(paramodulation,[status(thm)],[f23143,f684])).
% 188.88/24.38 fof(f25881,plain,(
% 188.88/24.38 ![X0,X1,X2]: (or(and(X0,implies(not(X1),X1)),X2)=implies(implies(X0,not(X1)),X2))),
% 188.88/24.38 inference(paramodulation,[status(thm)],[f23143,f654])).
% 188.88/24.38 fof(f26251,plain,(
% 188.88/24.38 ~is_a_theorem(or(and(sK77_skl,sK76_skl),implies(sK76_skl,not(sK77_skl))))),
% 188.88/24.38 inference(backward_demodulation,[status(thm)],[f26353,f23468])).
% 188.88/24.38 fof(f26353,plain,(
% 188.88/24.38 ![X0,X1]: (implies(X0,not(X1))=not(and(X0,X1)))),
% 188.88/24.38 inference(forward_demodulation,[status(thm)],[f21072,f25775])).
% 188.88/24.38 fof(f26556,plain,(
% 188.88/24.38 ![X0,X1]: (is_a_theorem(implies(implies(or(X0,X0),not(X1)),implies(X1,not(X0)))))),
% 188.88/24.38 inference(forward_demodulation,[status(thm)],[f377,f25879])).
% 188.88/24.38 fof(f26557,plain,(
% 188.88/24.38 ![X0,X1]: (is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))))),
% 188.88/24.38 inference(forward_demodulation,[status(thm)],[f21072,f26556])).
% 188.88/24.38 fof(f26565,plain,(
% 188.88/24.38 ![X0,X1,X2]: (or(and(X0,or(X1,X1)),X2)=implies(implies(X0,not(X1)),X2))),
% 188.88/24.38 inference(forward_demodulation,[status(thm)],[f377,f25881])).
% 188.88/24.38 fof(f26628,plain,(
% 188.88/24.38 ![X0,X1]: (is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))))),
% 188.88/24.38 inference(backward_demodulation,[status(thm)],[f26650,f26557])).
% 188.88/24.38 fof(f26650,plain,(
% 188.88/24.38 ![X0,X1,X2]: (or(and(X0,X1),X2)=implies(implies(X0,not(X1)),X2))),
% 188.88/24.38 inference(forward_demodulation,[status(thm)],[f21072,f26565])).
% 188.88/24.38 fof(f28318,plain,(
% 188.88/24.38 $false),
% 188.88/24.38 inference(backward_subsumption_resolution,[status(thm)],[f26251,f26628])).
% 188.88/24.38 % SZS output end CNFRefutation for theBenchmark.p
% 12.01/24.59 % Elapsed time: 24.180617 seconds
% 12.01/24.59 % CPU time: 191.074691 seconds
% 12.01/24.59 % Total memory used: 2.265 GB
% 12.01/24.59 % Net memory used: 2.122 GB
%------------------------------------------------------------------------------