%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL524+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:10:13 PM UTC 2026
% Result : Theorem 1.01s 0.71s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL524+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:40:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 1.01/0.71 % Refutation found
% 1.01/0.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.01/0.71 % SZS output start CNFRefutation for theBenchmark
% 1.01/0.71 fof(f1,axiom,(
% 1.01/0.71 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f2,axiom,(
% 1.01/0.71 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f3,axiom,(
% 1.01/0.71 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f4,axiom,(
% 1.01/0.71 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f5,axiom,(
% 1.01/0.71 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f8,axiom,(
% 1.01/0.71 ( and_2<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f9,axiom,(
% 1.01/0.71 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f11,axiom,(
% 1.01/0.71 ( or_2<=> (! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f12,axiom,(
% 1.01/0.71 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f21,axiom,(
% 1.01/0.71 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f27,axiom,(
% 1.01/0.71 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f29,axiom,(
% 1.01/0.71 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f31,axiom,(
% 1.01/0.71 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f32,axiom,(
% 1.01/0.71 op_or ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f33,axiom,(
% 1.01/0.71 op_implies_and ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f34,axiom,(
% 1.01/0.71 op_equiv ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f35,axiom,(
% 1.01/0.71 modus_ponens ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f36,axiom,(
% 1.01/0.71 modus_tollens ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f37,axiom,(
% 1.01/0.71 implies_1 ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f38,axiom,(
% 1.01/0.71 implies_2 ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f41,axiom,(
% 1.01/0.71 and_2 ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f42,axiom,(
% 1.01/0.71 and_3 ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f44,axiom,(
% 1.01/0.71 or_2 ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f45,axiom,(
% 1.01/0.71 or_3 ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f49,axiom,(
% 1.01/0.71 substitution_of_equivalents ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f55,axiom,(
% 1.01/0.71 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f57,axiom,(
% 1.01/0.71 ( axiom_B<=> (! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f58,axiom,(
% 1.01/0.71 ( axiom_5<=> (! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f73,axiom,(
% 1.01/0.71 ( op_possibly=> (! [X] : possibly(X) = not(necessarily(not(X))) )) ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f77,axiom,(
% 1.01/0.71 op_possibly ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f80,axiom,(
% 1.01/0.71 axiom_M ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f81,axiom,(
% 1.01/0.71 axiom_5 ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f82,conjecture,(
% 1.01/0.71 axiom_B ),
% 1.01/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.71 fof(f83,negated_conjecture,(
% 1.01/0.71 ~(axiom_B )),
% 1.01/0.71 inference(negated_conjecture,[status(cth)],[f82])).
% 1.01/0.71 fof(f84,plain,(
% 1.01/0.71 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 1.01/0.71 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 1.01/0.71 fof(f85,plain,(
% 1.01/0.71 (~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))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f84])).
% 1.01/0.71 fof(f86,plain,(
% 1.01/0.71 (~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))))),
% 1.01/0.71 inference(miniscoping,[status(thm)],[f85])).
% 1.01/0.71 fof(f87,plain,(
% 1.01/0.71 (~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)))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f86])).
% 1.01/0.71 fof(f88,plain,(
% 1.01/0.71 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f87])).
% 1.01/0.71 fof(f92,plain,(
% 1.01/0.71 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 1.01/0.71 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 1.01/0.71 fof(f93,plain,(
% 1.01/0.71 (~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)))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f92])).
% 1.01/0.71 fof(f94,plain,(
% 1.01/0.71 (~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))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f93])).
% 1.01/0.71 fof(f95,plain,(
% 1.01/0.71 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f94])).
% 1.01/0.71 fof(f98,plain,(
% 1.01/0.71 (~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)))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f3])).
% 1.01/0.71 fof(f99,plain,(
% 1.01/0.71 (~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))))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f98])).
% 1.01/0.71 fof(f100,plain,(
% 1.01/0.71 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f99])).
% 1.01/0.71 fof(f102,plain,(
% 1.01/0.71 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f4])).
% 1.01/0.71 fof(f103,plain,(
% 1.01/0.71 (~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))))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f102])).
% 1.01/0.71 fof(f104,plain,(
% 1.01/0.71 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f103])).
% 1.01/0.71 fof(f106,plain,(
% 1.01/0.71 (~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)))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f5])).
% 1.01/0.71 fof(f107,plain,(
% 1.01/0.71 (~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))))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f106])).
% 1.01/0.71 fof(f108,plain,(
% 1.01/0.71 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f107])).
% 1.01/0.71 fof(f118,plain,(
% 1.01/0.71 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),Y))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f8])).
% 1.01/0.71 fof(f119,plain,(
% 1.01/0.71 (~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)))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(X,sK15_skl),skolemize(Y,sK16_skl)],[f118])).
% 1.01/0.71 fof(f120,plain,(
% 1.01/0.71 ![X0,X1]: (~and_2|is_a_theorem(implies(and(X0,X1),X1)))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f119])).
% 1.01/0.71 fof(f122,plain,(
% 1.01/0.71 (~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))))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f9])).
% 1.01/0.71 fof(f123,plain,(
% 1.01/0.71 (~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)))))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f122])).
% 1.01/0.71 fof(f124,plain,(
% 1.01/0.71 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f123])).
% 1.01/0.71 fof(f130,plain,(
% 1.01/0.71 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|(?[X,Y]: ~is_a_theorem(implies(Y,or(X,Y)))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f11])).
% 1.01/0.71 fof(f131,plain,(
% 1.01/0.71 (~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))))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f130])).
% 1.01/0.71 fof(f132,plain,(
% 1.01/0.71 ![X0,X1]: (~or_2|is_a_theorem(implies(X0,or(X1,X0))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f131])).
% 1.01/0.71 fof(f134,plain,(
% 1.01/0.71 (~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))))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f12])).
% 1.01/0.71 fof(f135,plain,(
% 1.01/0.71 (~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)))))),
% 1.01/0.71 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)],[f134])).
% 1.01/0.71 fof(f136,plain,(
% 1.01/0.71 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f135])).
% 1.01/0.71 fof(f170,plain,(
% 1.01/0.71 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f21])).
% 1.01/0.71 fof(f171,plain,(
% 1.01/0.71 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f170])).
% 1.01/0.71 fof(f172,plain,(
% 1.01/0.71 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f171])).
% 1.01/0.71 fof(f173,plain,(
% 1.01/0.71 cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f171])).
% 1.01/0.71 fof(f194,plain,(
% 1.01/0.71 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 1.01/0.71 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 1.01/0.71 fof(f195,plain,(
% 1.01/0.71 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f194])).
% 1.01/0.71 fof(f198,plain,(
% 1.01/0.71 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 1.01/0.71 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 1.01/0.71 fof(f199,plain,(
% 1.01/0.71 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f198])).
% 1.01/0.71 fof(f202,plain,(
% 1.01/0.71 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 1.01/0.71 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 1.01/0.71 fof(f203,plain,(
% 1.01/0.71 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f202])).
% 1.01/0.71 fof(f204,plain,(
% 1.01/0.71 op_or),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f32])).
% 1.01/0.71 fof(f205,plain,(
% 1.01/0.71 op_implies_and),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f33])).
% 1.01/0.71 fof(f206,plain,(
% 1.01/0.71 op_equiv),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f34])).
% 1.01/0.71 fof(f207,plain,(
% 1.01/0.71 modus_ponens),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f35])).
% 1.01/0.71 fof(f208,plain,(
% 1.01/0.71 modus_tollens),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f36])).
% 1.01/0.71 fof(f209,plain,(
% 1.01/0.71 implies_1),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f37])).
% 1.01/0.71 fof(f210,plain,(
% 1.01/0.71 implies_2),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f38])).
% 1.01/0.71 fof(f213,plain,(
% 1.01/0.71 and_2),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f41])).
% 1.01/0.71 fof(f214,plain,(
% 1.01/0.71 and_3),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f42])).
% 1.01/0.71 fof(f216,plain,(
% 1.01/0.71 or_2),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f44])).
% 1.01/0.71 fof(f217,plain,(
% 1.01/0.71 or_3),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f45])).
% 1.01/0.71 fof(f221,plain,(
% 1.01/0.71 substitution_of_equivalents),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f49])).
% 1.01/0.71 fof(f253,plain,(
% 1.01/0.71 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f55])).
% 1.01/0.71 fof(f254,plain,(
% 1.01/0.71 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f253])).
% 1.01/0.71 fof(f255,plain,(
% 1.01/0.71 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f254])).
% 1.01/0.71 fof(f261,plain,(
% 1.01/0.71 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|(?[X]: ~is_a_theorem(implies(X,necessarily(possibly(X))))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f57])).
% 1.01/0.71 fof(f262,plain,(
% 1.01/0.71 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|~is_a_theorem(implies(sK66_skl,necessarily(possibly(sK66_skl)))))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl]),skolemize(X,sK66_skl)],[f261])).
% 1.01/0.71 fof(f264,plain,(
% 1.01/0.71 axiom_B|~is_a_theorem(implies(sK66_skl,necessarily(possibly(sK66_skl))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f262])).
% 1.01/0.71 fof(f265,plain,(
% 1.01/0.71 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|(?[X]: ~is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))),
% 1.01/0.71 inference(NNF_transformation,[status(thm)],[f58])).
% 1.01/0.71 fof(f266,plain,(
% 1.01/0.71 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|~is_a_theorem(implies(possibly(sK67_skl),necessarily(possibly(sK67_skl)))))),
% 1.01/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK67_skl]),skolemize(X,sK67_skl)],[f265])).
% 1.01/0.71 fof(f267,plain,(
% 1.01/0.71 ![X0]: (~axiom_5|is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f266])).
% 1.01/0.71 fof(f325,plain,(
% 1.01/0.71 ~op_possibly|(![X]: possibly(X)=not(necessarily(not(X))))),
% 1.01/0.71 inference(pre_NNF_transformation,[status(thm)],[f73])).
% 1.01/0.71 fof(f326,plain,(
% 1.01/0.71 ![X0]: (~op_possibly|possibly(X0)=not(necessarily(not(X0))))),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f325])).
% 1.01/0.71 fof(f333,plain,(
% 1.01/0.71 op_possibly),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f77])).
% 1.01/0.71 fof(f336,plain,(
% 1.01/0.71 axiom_M),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f80])).
% 1.01/0.71 fof(f337,plain,(
% 1.01/0.71 axiom_5),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f81])).
% 1.01/0.71 fof(f338,plain,(
% 1.01/0.71 ~axiom_B),
% 1.01/0.71 inference(cnf_transformation,[status(thm)],[f83])).
% 1.01/0.71 fof(f339,plain,(
% 1.01/0.71 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f195,f204])).
% 1.01/0.71 fof(f340,plain,(
% 1.01/0.71 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f199,f205])).
% 1.01/0.71 fof(f341,plain,(
% 1.01/0.71 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f203,f206])).
% 1.01/0.71 fof(f342,plain,(
% 1.01/0.71 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f88,f207])).
% 1.01/0.71 fof(f343,plain,(
% 1.01/0.71 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f100,f208])).
% 1.01/0.71 fof(f344,plain,(
% 1.01/0.71 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f104,f209])).
% 1.01/0.71 fof(f345,plain,(
% 1.01/0.71 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f108,f210])).
% 1.01/0.71 fof(f348,plain,(
% 1.01/0.71 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1)))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f120,f213])).
% 1.01/0.71 fof(f349,plain,(
% 1.01/0.71 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f124,f214])).
% 1.01/0.71 fof(f351,plain,(
% 1.01/0.71 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f132,f216])).
% 1.01/0.71 fof(f352,plain,(
% 1.01/0.71 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f136,f217])).
% 1.01/0.71 fof(f356,plain,(
% 1.01/0.71 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f95,f221])).
% 1.01/0.71 fof(f357,plain,(
% 1.01/0.71 ![X0]: (possibly(X0)=not(necessarily(not(X0))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f326,f333])).
% 1.01/0.71 fof(f360,plain,(
% 1.01/0.71 ![X0]: (is_a_theorem(implies(necessarily(X0),X0)))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f255,f336])).
% 1.01/0.71 fof(f361,plain,(
% 1.01/0.71 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f267,f337])).
% 1.01/0.71 fof(f362,plain,(
% 1.01/0.71 ~is_a_theorem(implies(sK66_skl,necessarily(possibly(sK66_skl))))),
% 1.01/0.71 inference(backward_subsumption_resolution,[status(thm)],[f264,f338])).
% 1.01/0.71 fof(f363,plain,(
% 1.01/0.71 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 1.01/0.71 inference(backward_demodulation,[status(thm)],[f340,f339])).
% 1.01/0.71 fof(f367,plain,(
% 1.01/0.71 cn3|~is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl))),
% 1.01/0.71 inference(backward_demodulation,[status(thm)],[f363,f173])).
% 1.01/0.71 fof(f371,plain,(
% 1.01/0.71 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 1.01/0.71 inference(backward_demodulation,[status(thm)],[f363,f343])).
% 1.01/0.71 fof(f372,plain,(
% 1.01/0.71 ![X0]: (~cn3|is_a_theorem(implies(or(X0,X0),X0)))),
% 1.01/0.71 inference(backward_demodulation,[status(thm)],[f363,f172])).
% 1.01/0.71 fof(f377,plain,(
% 1.01/0.71 ![X0,X1]: (or(necessarily(not(X0)),X1)=implies(possibly(X0),X1))),
% 1.01/0.71 inference(paramodulation,[status(thm)],[f357,f363])).
% 1.01/0.71 fof(f390,plain,(
% 1.01/0.71 ![X0,X1]: (implies(X0,necessarily(not(X1)))=not(and(X0,possibly(X1))))),
% 1.01/0.71 inference(paramodulation,[status(thm)],[f357,f340])).
% 1.01/0.71 fof(f394,plain,(
% 1.01/0.71 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2))),
% 1.01/0.71 inference(paramodulation,[status(thm)],[f340,f363])).
% 1.01/0.71 fof(f422,plain,(
% 1.01/0.71 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,and(X0,X1))))),
% 1.01/0.71 inference(resolution,[status(thm)],[f349,f342])).
% 1.01/0.71 fof(f433,plain,(
% 1.01/0.71 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1)))),
% 1.01/0.71 inference(resolution,[status(thm)],[f422,f342])).
% 1.01/0.71 fof(f444,plain,(
% 1.01/0.71 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1)))),
% 1.01/0.71 inference(paramodulation,[status(thm)],[f341,f433])).
% 1.01/0.71 fof(f455,plain,(
% 1.01/0.71 ![X0,X1]: (is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))))),
% 1.01/0.71 inference(paramodulation,[status(thm)],[f363,f371])).
% 1.01/0.71 fof(f540,plain,(
% 1.01/0.71 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 1.01/0.71 inference(resolution,[status(thm)],[f345,f342])).
% 1.01/0.71 fof(f567,plain,(
% 1.01/0.71 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 1.01/0.73 inference(resolution,[status(thm)],[f540,f349])).
% 1.01/0.73 fof(f568,plain,(
% 1.01/0.73 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 1.01/0.73 inference(resolution,[status(thm)],[f540,f344])).
% 1.01/0.73 fof(f794,plain,(
% 1.01/0.73 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))))),
% 1.01/0.73 inference(resolution,[status(thm)],[f352,f540])).
% 1.01/0.73 fof(f804,plain,(
% 1.01/0.73 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1)))),
% 1.01/0.73 inference(resolution,[status(thm)],[f794,f342])).
% 1.01/0.73 fof(f810,plain,(
% 1.01/0.73 ~is_a_theorem(implies(sK43_skl,sK43_skl))|cn3),
% 1.01/0.73 inference(resolution,[status(thm)],[f804,f367])).
% 1.01/0.73 fof(f816,plain,(
% 1.01/0.73 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 1.01/0.73 inference(backward_subsumption_resolution,[status(thm)],[f372,f817])).
% 1.01/0.73 fof(f817,plain,(
% 1.01/0.73 cn3),
% 1.01/0.73 inference(forward_subsumption_resolution,[status(thm)],[f810,f568])).
% 1.01/0.73 fof(f989,plain,(
% 1.01/0.73 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|X0=X1)),
% 1.01/0.73 inference(resolution,[status(thm)],[f444,f356])).
% 1.01/0.73 fof(f998,plain,(
% 1.01/0.73 ![X0,X1]: (~is_a_theorem(implies(or(X0,X1),or(X1,not(not(X0)))))|or(X0,X1)=or(X1,not(not(X0))))),
% 1.01/0.73 inference(resolution,[status(thm)],[f989,f455])).
% 1.01/0.73 fof(f1000,plain,(
% 1.01/0.73 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|X0=or(X0,X0))),
% 1.01/0.73 inference(resolution,[status(thm)],[f989,f816])).
% 1.01/0.73 fof(f1002,plain,(
% 1.01/0.73 ![X0]: (~is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0)))|necessarily(possibly(X0))=possibly(X0))),
% 1.01/0.73 inference(resolution,[status(thm)],[f989,f361])).
% 1.01/0.73 fof(f1015,plain,(
% 1.01/0.73 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|and(X0,X0)=X0)),
% 1.01/0.73 inference(resolution,[status(thm)],[f989,f567])).
% 1.01/0.73 fof(f1046,plain,(
% 1.01/0.73 ![X0]: (X0=or(X0,X0))),
% 1.01/0.73 inference(forward_subsumption_resolution,[status(thm)],[f1000,f351])).
% 1.01/0.73 fof(f1051,plain,(
% 1.01/0.73 ~is_a_theorem(implies(sK66_skl,possibly(sK66_skl)))),
% 1.01/0.73 inference(backward_demodulation,[status(thm)],[f1059,f362])).
% 1.01/0.73 fof(f1059,plain,(
% 1.01/0.73 ![X0]: (necessarily(possibly(X0))=possibly(X0))),
% 1.01/0.73 inference(forward_subsumption_resolution,[status(thm)],[f1002,f360])).
% 1.01/0.73 fof(f1075,plain,(
% 1.01/0.73 ![X0]: (and(X0,X0)=X0)),
% 1.01/0.73 inference(forward_subsumption_resolution,[status(thm)],[f1015,f348])).
% 1.01/0.73 fof(f1084,plain,(
% 1.01/0.73 ![X0]: (necessarily(not(X0))=implies(possibly(X0),necessarily(not(X0))))),
% 1.01/0.73 inference(paramodulation,[status(thm)],[f377,f1046])).
% 1.01/0.73 fof(f1117,plain,(
% 1.01/0.73 ![X0]: (implies(possibly(X0),necessarily(not(X0)))=not(possibly(X0)))),
% 1.01/0.73 inference(paramodulation,[status(thm)],[f1075,f390])).
% 1.01/0.73 fof(f1122,plain,(
% 1.01/0.73 ![X0,X1]: (or(not(X0),X1)=implies(implies(not(X0),X0),X1))),
% 1.01/0.73 inference(paramodulation,[status(thm)],[f1075,f394])).
% 1.01/0.73 fof(f1125,plain,(
% 1.01/0.73 ![X0]: (implies(not(X0),X0)=not(not(X0)))),
% 1.01/0.73 inference(paramodulation,[status(thm)],[f1075,f340])).
% 1.01/0.73 fof(f1137,plain,(
% 1.01/0.73 ![X0]: (necessarily(not(X0))=not(possibly(X0)))),
% 1.01/0.73 inference(backward_demodulation,[status(thm)],[f1117,f1084])).
% 1.01/0.73 fof(f1149,plain,(
% 1.01/0.73 ![X0,X1]: (or(not(X0),X1)=implies(or(X0,X0),X1))),
% 1.01/0.73 inference(forward_demodulation,[status(thm)],[f363,f1122])).
% 1.01/0.73 fof(f1154,plain,(
% 1.01/0.73 ![X0,X1]: (or(not(X0),X1)=implies(X0,X1))),
% 1.01/0.73 inference(forward_demodulation,[status(thm)],[f1046,f1149])).
% 1.01/0.73 fof(f1157,plain,(
% 1.01/0.73 ![X0]: (or(X0,X0)=not(not(X0)))),
% 1.01/0.73 inference(forward_demodulation,[status(thm)],[f363,f1125])).
% 1.01/0.73 fof(f1160,plain,(
% 1.01/0.73 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 1.01/0.73 inference(backward_demodulation,[status(thm)],[f1168,f455])).
% 1.01/0.73 fof(f1162,plain,(
% 1.01/0.73 ![X0,X1]: (~is_a_theorem(implies(or(X0,X1),or(X1,not(not(X0)))))|or(X0,X1)=or(X1,X0))),
% 1.01/0.73 inference(backward_demodulation,[status(thm)],[f1168,f998])).
% 1.01/0.73 fof(f1168,plain,(
% 1.01/0.73 ![X0]: (X0=not(not(X0)))),
% 1.01/0.73 inference(forward_demodulation,[status(thm)],[f1046,f1157])).
% 1.01/0.73 fof(f1296,plain,(
% 1.01/0.73 ![X0,X1]: (~is_a_theorem(implies(or(X0,X1),or(X1,X0)))|or(X0,X1)=or(X1,X0))),
% 1.01/0.73 inference(forward_demodulation,[status(thm)],[f1168,f1162])).
% 1.01/0.73 fof(f1298,plain,(
% 1.01/0.73 ![X0,X1]: (or(X0,X1)=or(X1,X0))),
% 1.01/0.73 inference(forward_subsumption_resolution,[status(thm)],[f1296,f1160])).
% 1.01/0.73 fof(f1640,plain,(
% 1.01/0.73 ![X0]: (is_a_theorem(implies(not(possibly(X0)),not(X0))))),
% 1.01/0.73 inference(paramodulation,[status(thm)],[f1137,f360])).
% 1.01/0.73 fof(f1645,plain,(
% 1.01/0.73 ![X0]: (is_a_theorem(or(possibly(X0),not(X0))))),
% 1.01/0.74 inference(forward_demodulation,[status(thm)],[f363,f1640])).
% 1.01/0.74 fof(f1646,plain,(
% 1.01/0.74 ![X0]: (is_a_theorem(or(not(X0),possibly(X0))))),
% 1.01/0.74 inference(forward_demodulation,[status(thm)],[f1298,f1645])).
% 1.01/0.74 fof(f1648,plain,(
% 1.01/0.74 ![X0]: (is_a_theorem(implies(X0,possibly(X0))))),
% 1.01/0.74 inference(forward_demodulation,[status(thm)],[f1154,f1646])).
% 1.01/0.74 fof(f1649,plain,(
% 1.01/0.74 $false),
% 1.01/0.74 inference(backward_subsumption_resolution,[status(thm)],[f1051,f1648])).
% 1.01/0.74 % SZS output end CNFRefutation for theBenchmark.p
% 0.84/0.75 % Elapsed time: 0.370440 seconds
% 0.84/0.75 % CPU time: 2.626814 seconds
% 0.84/0.75 % Total memory used: 137.209 MB
% 0.84/0.75 % Net memory used: 132.563 MB
%------------------------------------------------------------------------------