%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL523+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 : n007.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 21.35s 3.22s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL523+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 00:34:51 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.40 % Drodi V4.1.1
% 21.35/3.22 % Refutation found
% 21.35/3.22 % SZS status Theorem for theBenchmark: Theorem is valid
% 21.35/3.22 % SZS output start CNFRefutation for theBenchmark
% 21.35/3.22 fof(f1,axiom,(
% 21.35/3.22 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f2,axiom,(
% 21.35/3.22 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f4,axiom,(
% 21.35/3.22 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f5,axiom,(
% 21.35/3.22 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f6,axiom,(
% 21.35/3.22 ( implies_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f7,axiom,(
% 21.35/3.22 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f8,axiom,(
% 21.35/3.22 ( and_2<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f9,axiom,(
% 21.35/3.22 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f11,axiom,(
% 21.35/3.22 ( or_2<=> (! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f12,axiom,(
% 21.35/3.22 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f15,axiom,(
% 21.35/3.22 ( equivalence_3<=> (! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f21,axiom,(
% 21.35/3.22 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f27,axiom,(
% 21.35/3.22 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f29,axiom,(
% 21.35/3.22 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f32,axiom,(
% 21.35/3.22 op_or ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f33,axiom,(
% 21.35/3.22 op_implies_and ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f35,axiom,(
% 21.35/3.22 modus_ponens ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f37,axiom,(
% 21.35/3.22 implies_1 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f38,axiom,(
% 21.35/3.22 implies_2 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f39,axiom,(
% 21.35/3.22 implies_3 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f40,axiom,(
% 21.35/3.22 and_1 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f41,axiom,(
% 21.35/3.22 and_2 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f42,axiom,(
% 21.35/3.22 and_3 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f44,axiom,(
% 21.35/3.22 or_2 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f45,axiom,(
% 21.35/3.22 or_3 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f48,axiom,(
% 21.35/3.22 equivalence_3 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f49,axiom,(
% 21.35/3.22 substitution_of_equivalents ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f55,axiom,(
% 21.35/3.22 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f56,axiom,(
% 21.35/3.22 ( axiom_4<=> (! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f58,axiom,(
% 21.35/3.22 ( axiom_5<=> (! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f73,axiom,(
% 21.35/3.22 ( op_possibly=> (! [X] : possibly(X) = not(necessarily(not(X))) )) ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f77,axiom,(
% 21.35/3.22 op_possibly ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f80,axiom,(
% 21.35/3.22 axiom_M ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f81,axiom,(
% 21.35/3.22 axiom_5 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f82,conjecture,(
% 21.35/3.22 axiom_4 ),
% 21.35/3.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 21.35/3.22 fof(f83,negated_conjecture,(
% 21.35/3.22 ~(axiom_4 )),
% 21.35/3.22 inference(negated_conjecture,[status(cth)],[f82])).
% 21.35/3.22 fof(f84,plain,(
% 21.35/3.22 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 21.35/3.22 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 21.35/3.22 fof(f85,plain,(
% 21.35/3.22 (~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))))),
% 21.35/3.22 inference(NNF_transformation,[status(thm)],[f84])).
% 21.35/3.22 fof(f86,plain,(
% 21.35/3.22 (~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))))),
% 21.35/3.22 inference(miniscoping,[status(thm)],[f85])).
% 21.35/3.22 fof(f87,plain,(
% 21.35/3.22 (~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)))),
% 21.35/3.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f86])).
% 21.35/3.22 fof(f88,plain,(
% 21.35/3.22 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 21.35/3.22 inference(cnf_transformation,[status(thm)],[f87])).
% 21.35/3.22 fof(f92,plain,(
% 21.35/3.22 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 21.35/3.22 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 21.35/3.22 fof(f93,plain,(
% 21.35/3.22 (~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)))),
% 21.35/3.22 inference(NNF_transformation,[status(thm)],[f92])).
% 21.35/3.22 fof(f94,plain,(
% 21.35/3.22 (~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))),
% 21.35/3.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f93])).
% 21.35/3.22 fof(f95,plain,(
% 21.35/3.22 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 21.35/3.22 inference(cnf_transformation,[status(thm)],[f94])).
% 21.35/3.22 fof(f102,plain,(
% 21.35/3.22 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 21.35/3.22 inference(NNF_transformation,[status(thm)],[f4])).
% 21.35/3.22 fof(f103,plain,(
% 21.35/3.22 (~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))))),
% 21.35/3.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f102])).
% 21.35/3.22 fof(f104,plain,(
% 21.35/3.22 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 21.35/3.22 inference(cnf_transformation,[status(thm)],[f103])).
% 21.35/3.22 fof(f106,plain,(
% 21.35/3.22 (~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)))))),
% 21.35/3.22 inference(NNF_transformation,[status(thm)],[f5])).
% 21.35/3.22 fof(f107,plain,(
% 21.35/3.22 (~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))))),
% 21.35/3.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f106])).
% 21.35/3.22 fof(f108,plain,(
% 21.35/3.22 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 21.35/3.22 inference(cnf_transformation,[status(thm)],[f107])).
% 21.35/3.22 fof(f110,plain,(
% 21.35/3.22 (~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))))))),
% 21.35/3.22 inference(NNF_transformation,[status(thm)],[f6])).
% 21.35/3.22 fof(f111,plain,(
% 21.35/3.22 (~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)))))),
% 21.35/3.22 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)],[f110])).
% 21.35/3.22 fof(f112,plain,(
% 21.35/3.22 ![X0,X1,X2]: (~implies_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 21.35/3.22 inference(cnf_transformation,[status(thm)],[f111])).
% 21.35/3.22 fof(f114,plain,(
% 21.35/3.22 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 21.35/3.22 inference(NNF_transformation,[status(thm)],[f7])).
% 21.35/3.22 fof(f115,plain,(
% 21.35/3.22 (~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)))),
% 21.35/3.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f114])).
% 21.35/3.22 fof(f116,plain,(
% 21.35/3.22 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 21.35/3.22 inference(cnf_transformation,[status(thm)],[f115])).
% 21.35/3.22 fof(f118,plain,(
% 21.35/3.22 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),Y))))),
% 21.35/3.22 inference(NNF_transformation,[status(thm)],[f8])).
% 21.35/3.22 fof(f119,plain,(
% 21.35/3.22 (~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)))),
% 21.35/3.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(X,sK15_skl),skolemize(Y,sK16_skl)],[f118])).
% 21.35/3.22 fof(f120,plain,(
% 21.35/3.22 ![X0,X1]: (~and_2|is_a_theorem(implies(and(X0,X1),X1)))),
% 21.35/3.22 inference(cnf_transformation,[status(thm)],[f119])).
% 21.35/3.22 fof(f122,plain,(
% 21.35/3.22 (~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))))))),
% 21.35/3.22 inference(NNF_transformation,[status(thm)],[f9])).
% 21.35/3.23 fof(f123,plain,(
% 21.35/3.23 (~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)))))),
% 21.35/3.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f122])).
% 21.35/3.23 fof(f124,plain,(
% 21.35/3.23 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f123])).
% 21.35/3.23 fof(f130,plain,(
% 21.35/3.23 (~or_2|(![X,Y]: is_a_theorem(implies(Y,or(X,Y)))))&(or_2|(?[X,Y]: ~is_a_theorem(implies(Y,or(X,Y)))))),
% 21.35/3.23 inference(NNF_transformation,[status(thm)],[f11])).
% 21.35/3.23 fof(f131,plain,(
% 21.35/3.23 (~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))))),
% 21.35/3.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f130])).
% 21.35/3.23 fof(f132,plain,(
% 21.35/3.23 ![X0,X1]: (~or_2|is_a_theorem(implies(X0,or(X1,X0))))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f131])).
% 21.35/3.23 fof(f134,plain,(
% 21.35/3.23 (~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))))))),
% 21.35/3.23 inference(NNF_transformation,[status(thm)],[f12])).
% 21.35/3.23 fof(f135,plain,(
% 21.35/3.23 (~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)))))),
% 21.35/3.23 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)],[f134])).
% 21.35/3.23 fof(f136,plain,(
% 21.35/3.23 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f135])).
% 21.35/3.23 fof(f146,plain,(
% 21.35/3.23 (~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))))))),
% 21.35/3.23 inference(NNF_transformation,[status(thm)],[f15])).
% 21.35/3.23 fof(f147,plain,(
% 21.35/3.23 (~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)))))),
% 21.35/3.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(X,sK30_skl),skolemize(Y,sK31_skl)],[f146])).
% 21.35/3.23 fof(f148,plain,(
% 21.35/3.23 ![X0,X1]: (~equivalence_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f147])).
% 21.35/3.23 fof(f170,plain,(
% 21.35/3.23 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 21.35/3.23 inference(NNF_transformation,[status(thm)],[f21])).
% 21.35/3.23 fof(f171,plain,(
% 21.35/3.23 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)))),
% 21.35/3.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f170])).
% 21.35/3.23 fof(f172,plain,(
% 21.35/3.23 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f171])).
% 21.35/3.23 fof(f173,plain,(
% 21.35/3.23 cn3|~is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f171])).
% 21.35/3.23 fof(f194,plain,(
% 21.35/3.23 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 21.35/3.23 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 21.35/3.23 fof(f195,plain,(
% 21.35/3.23 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f194])).
% 21.35/3.23 fof(f198,plain,(
% 21.35/3.23 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 21.35/3.23 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 21.35/3.23 fof(f199,plain,(
% 21.35/3.23 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f198])).
% 21.35/3.23 fof(f204,plain,(
% 21.35/3.23 op_or),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f32])).
% 21.35/3.23 fof(f205,plain,(
% 21.35/3.23 op_implies_and),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f33])).
% 21.35/3.23 fof(f207,plain,(
% 21.35/3.23 modus_ponens),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f35])).
% 21.35/3.23 fof(f209,plain,(
% 21.35/3.23 implies_1),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f37])).
% 21.35/3.23 fof(f210,plain,(
% 21.35/3.23 implies_2),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f38])).
% 21.35/3.23 fof(f211,plain,(
% 21.35/3.23 implies_3),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f39])).
% 21.35/3.23 fof(f212,plain,(
% 21.35/3.23 and_1),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f40])).
% 21.35/3.23 fof(f213,plain,(
% 21.35/3.23 and_2),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f41])).
% 21.35/3.23 fof(f214,plain,(
% 21.35/3.23 and_3),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f42])).
% 21.35/3.23 fof(f216,plain,(
% 21.35/3.23 or_2),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f44])).
% 21.35/3.23 fof(f217,plain,(
% 21.35/3.23 or_3),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f45])).
% 21.35/3.23 fof(f220,plain,(
% 21.35/3.23 equivalence_3),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f48])).
% 21.35/3.23 fof(f221,plain,(
% 21.35/3.23 substitution_of_equivalents),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f49])).
% 21.35/3.23 fof(f253,plain,(
% 21.35/3.23 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 21.35/3.23 inference(NNF_transformation,[status(thm)],[f55])).
% 21.35/3.23 fof(f254,plain,(
% 21.35/3.23 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sK64_skl),sK64_skl)))),
% 21.35/3.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f253])).
% 21.35/3.23 fof(f255,plain,(
% 21.35/3.23 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f254])).
% 21.35/3.23 fof(f257,plain,(
% 21.35/3.23 (~axiom_4|(![X]: is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))&(axiom_4|(?[X]: ~is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))))),
% 21.35/3.23 inference(NNF_transformation,[status(thm)],[f56])).
% 21.35/3.23 fof(f258,plain,(
% 21.35/3.23 (~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)))))),
% 21.35/3.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK65_skl]),skolemize(X,sK65_skl)],[f257])).
% 21.35/3.23 fof(f260,plain,(
% 21.35/3.23 axiom_4|~is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl))))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f258])).
% 21.35/3.23 fof(f265,plain,(
% 21.35/3.23 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|(?[X]: ~is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))),
% 21.35/3.23 inference(NNF_transformation,[status(thm)],[f58])).
% 21.35/3.23 fof(f266,plain,(
% 21.35/3.23 (~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)))))),
% 21.35/3.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK67_skl]),skolemize(X,sK67_skl)],[f265])).
% 21.35/3.23 fof(f267,plain,(
% 21.35/3.23 ![X0]: (~axiom_5|is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f266])).
% 21.35/3.23 fof(f325,plain,(
% 21.35/3.23 ~op_possibly|(![X]: possibly(X)=not(necessarily(not(X))))),
% 21.35/3.23 inference(pre_NNF_transformation,[status(thm)],[f73])).
% 21.35/3.23 fof(f326,plain,(
% 21.35/3.23 ![X0]: (~op_possibly|possibly(X0)=not(necessarily(not(X0))))),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f325])).
% 21.35/3.23 fof(f333,plain,(
% 21.35/3.23 op_possibly),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f77])).
% 21.35/3.23 fof(f336,plain,(
% 21.35/3.23 axiom_M),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f80])).
% 21.35/3.23 fof(f337,plain,(
% 21.35/3.23 axiom_5),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f81])).
% 21.35/3.23 fof(f338,plain,(
% 21.35/3.23 ~axiom_4),
% 21.35/3.23 inference(cnf_transformation,[status(thm)],[f83])).
% 21.35/3.23 fof(f339,plain,(
% 21.35/3.23 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 21.35/3.23 inference(backward_subsumption_resolution,[status(thm)],[f88,f207])).
% 21.35/3.23 fof(f342,plain,(
% 21.35/3.23 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 21.35/3.23 inference(backward_subsumption_resolution,[status(thm)],[f104,f209])).
% 21.35/3.23 fof(f343,plain,(
% 21.35/3.23 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 21.35/3.23 inference(backward_subsumption_resolution,[status(thm)],[f108,f210])).
% 21.35/3.23 fof(f344,plain,(
% 21.35/3.23 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f112,f211])).
% 21.35/3.23 fof(f345,plain,(
% 21.35/3.23 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0)))),
% 21.35/3.23 inference(backward_subsumption_resolution,[status(thm)],[f116,f212])).
% 21.35/3.23 fof(f346,plain,(
% 21.35/3.23 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1)))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f120,f213])).
% 21.35/3.23 fof(f347,plain,(
% 21.35/3.23 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f124,f214])).
% 21.35/3.23 fof(f349,plain,(
% 21.35/3.23 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0))))),
% 21.35/3.23 inference(backward_subsumption_resolution,[status(thm)],[f132,f216])).
% 21.35/3.23 fof(f350,plain,(
% 21.35/3.23 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f136,f217])).
% 21.35/3.23 fof(f353,plain,(
% 21.35/3.23 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f148,f220])).
% 21.35/3.23 fof(f354,plain,(
% 21.35/3.23 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 21.35/3.23 inference(backward_subsumption_resolution,[status(thm)],[f95,f221])).
% 21.35/3.23 fof(f356,plain,(
% 21.35/3.23 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1))))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f195,f204])).
% 21.35/3.23 fof(f361,plain,(
% 21.35/3.23 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 21.35/3.23 inference(backward_demodulation,[status(thm)],[f362,f356])).
% 21.35/3.23 fof(f362,plain,(
% 21.35/3.23 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1))))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f199,f205])).
% 21.35/3.23 fof(f374,plain,(
% 21.35/3.23 ![X0]: (is_a_theorem(implies(necessarily(X0),X0)))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f255,f336])).
% 21.35/3.23 fof(f376,plain,(
% 21.35/3.23 ~is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl))))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f260,f338])).
% 21.35/3.23 fof(f377,plain,(
% 21.35/3.23 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f267,f337])).
% 21.35/3.23 fof(f378,plain,(
% 21.35/3.23 cn3|~is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl))),
% 21.35/3.23 inference(backward_demodulation,[status(thm)],[f361,f173])).
% 21.35/3.23 fof(f383,plain,(
% 21.35/3.23 ![X0]: (~cn3|is_a_theorem(implies(or(X0,X0),X0)))),
% 21.35/3.23 inference(backward_demodulation,[status(thm)],[f361,f172])).
% 21.35/3.23 fof(f410,plain,(
% 21.35/3.23 ![X0]: (possibly(X0)=not(necessarily(not(X0))))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f326,f333])).
% 21.35/3.23 fof(f411,plain,(
% 21.35/3.23 ![X0]: (possibly(necessarily(not(X0)))=not(necessarily(possibly(X0))))),
% 21.35/3.23 inference(paramodulation,[status(thm)],[f410,f410])).
% 21.35/3.23 fof(f412,plain,(
% 21.35/3.23 ![X0,X1]: (possibly(and(X0,not(X1)))=not(necessarily(implies(X0,X1))))),
% 21.35/3.23 inference(paramodulation,[status(thm)],[f362,f410])).
% 21.35/3.23 fof(f424,plain,(
% 21.35/3.23 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))))),
% 21.35/3.23 inference(resolution,[status(thm)],[f339,f353])).
% 21.35/3.23 fof(f426,plain,(
% 21.35/3.23 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X2),implies(X0,X2))))),
% 21.35/3.23 inference(resolution,[status(thm)],[f339,f344])).
% 21.35/3.23 fof(f429,plain,(
% 21.35/3.23 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,and(X0,X1))))),
% 21.35/3.23 inference(resolution,[status(thm)],[f339,f347])).
% 21.35/3.23 fof(f434,plain,(
% 21.35/3.23 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 21.35/3.23 inference(resolution,[status(thm)],[f343,f339])).
% 21.35/3.23 fof(f985,plain,(
% 21.35/3.23 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1)))),
% 21.35/3.23 inference(resolution,[status(thm)],[f424,f339])).
% 21.35/3.23 fof(f1013,plain,(
% 21.35/3.23 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X2))|is_a_theorem(implies(X0,X2)))),
% 21.35/3.23 inference(resolution,[status(thm)],[f426,f339])).
% 21.35/3.23 fof(f1034,plain,(
% 21.35/3.23 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))))),
% 21.35/3.23 inference(resolution,[status(thm)],[f434,f350])).
% 21.35/3.23 fof(f1037,plain,(
% 21.35/3.23 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 21.35/3.23 inference(resolution,[status(thm)],[f434,f347])).
% 21.35/3.23 fof(f1038,plain,(
% 21.35/3.23 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 21.35/3.23 inference(resolution,[status(thm)],[f434,f342])).
% 21.35/3.23 fof(f3715,plain,(
% 21.35/3.23 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1)))),
% 21.35/3.23 inference(resolution,[status(thm)],[f1034,f339])).
% 21.35/3.23 fof(f4624,plain,(
% 21.35/3.23 ~is_a_theorem(implies(sK43_skl,sK43_skl))|cn3),
% 21.35/3.23 inference(resolution,[status(thm)],[f3715,f378])).
% 21.35/3.23 fof(f4636,plain,(
% 21.35/3.23 cn3),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f4624,f1038])).
% 21.35/3.23 fof(f4647,plain,(
% 21.35/3.23 ![X0]: (is_a_theorem(implies(or(X0,X0),X0)))),
% 21.35/3.23 inference(backward_subsumption_resolution,[status(thm)],[f383,f4636])).
% 21.35/3.23 fof(f7648,plain,(
% 21.35/3.23 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|X0=X1)),
% 21.35/3.23 inference(resolution,[status(thm)],[f985,f354])).
% 21.35/3.23 fof(f7697,plain,(
% 21.35/3.23 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|X0=or(X0,X0))),
% 21.35/3.23 inference(resolution,[status(thm)],[f7648,f4647])).
% 21.35/3.23 fof(f7699,plain,(
% 21.35/3.23 ![X0]: (~is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0)))|necessarily(possibly(X0))=possibly(X0))),
% 21.35/3.23 inference(resolution,[status(thm)],[f7648,f377])).
% 21.35/3.23 fof(f7787,plain,(
% 21.35/3.23 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|and(X0,X0)=X0)),
% 21.35/3.23 inference(resolution,[status(thm)],[f7648,f1037])).
% 21.35/3.23 fof(f7788,plain,(
% 21.35/3.23 ![X0,X1]: (~is_a_theorem(implies(and(X0,X1),X1))|and(X0,X1)=X1|~is_a_theorem(X0))),
% 21.35/3.23 inference(resolution,[status(thm)],[f7648,f429])).
% 21.35/3.23 fof(f7801,plain,(
% 21.35/3.23 ![X0]: (X0=or(X0,X0))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f7697,f349])).
% 21.35/3.23 fof(f7802,plain,(
% 21.35/3.23 ![X0]: (necessarily(possibly(X0))=possibly(X0))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f7699,f374])).
% 21.35/3.23 fof(f7851,plain,(
% 21.35/3.23 ![X0]: (and(X0,X0)=X0)),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f7787,f345])).
% 21.35/3.23 fof(f7852,plain,(
% 21.35/3.23 ![X0,X1]: (and(X0,X1)=X1|~is_a_theorem(X0))),
% 21.35/3.23 inference(forward_subsumption_resolution,[status(thm)],[f7788,f346])).
% 21.35/3.23 fof(f8213,plain,(
% 21.35/3.23 ![X0]: (implies(not(X0),X0)=not(not(X0)))),
% 21.35/3.23 inference(paramodulation,[status(thm)],[f7851,f362])).
% 21.35/3.23 fof(f8370,plain,(
% 21.82/3.28 ![X0]: (or(X0,X0)=not(not(X0)))),
% 21.82/3.28 inference(forward_demodulation,[status(thm)],[f361,f8213])).
% 21.82/3.28 fof(f8371,plain,(
% 21.82/3.28 ![X0]: (X0=not(not(X0)))),
% 21.82/3.28 inference(forward_demodulation,[status(thm)],[f7801,f8370])).
% 21.82/3.28 fof(f8819,plain,(
% 21.82/3.28 ![X0]: (possibly(necessarily(not(X0)))=not(possibly(X0)))),
% 21.82/3.28 inference(backward_demodulation,[status(thm)],[f7802,f411])).
% 21.82/3.28 fof(f9057,plain,(
% 21.82/3.28 ![X0,X1]: (and(implies(X0,X0),X1)=X1)),
% 21.82/3.28 inference(resolution,[status(thm)],[f7852,f1038])).
% 21.82/3.28 fof(f9078,plain,(
% 21.82/3.28 ![X0,X1]: (possibly(necessarily(implies(X0,X1)))=not(possibly(and(X0,not(X1)))))),
% 21.82/3.28 inference(paramodulation,[status(thm)],[f362,f8819])).
% 21.82/3.28 fof(f9138,plain,(
% 21.82/3.28 ![X0,X1]: (possibly(necessarily(implies(X0,X1)))=not(not(necessarily(implies(X0,X1)))))),
% 21.82/3.28 inference(forward_demodulation,[status(thm)],[f412,f9078])).
% 21.82/3.28 fof(f9139,plain,(
% 21.82/3.28 ![X0,X1]: (possibly(necessarily(implies(X0,X1)))=necessarily(implies(X0,X1)))),
% 21.82/3.28 inference(forward_demodulation,[status(thm)],[f8371,f9138])).
% 21.82/3.28 fof(f9485,plain,(
% 21.82/3.28 ![X0]: (~is_a_theorem(implies(necessarily(sK65_skl),X0))|~is_a_theorem(implies(X0,necessarily(necessarily(sK65_skl)))))),
% 21.82/3.28 inference(resolution,[status(thm)],[f1013,f376])).
% 21.82/3.28 fof(f9531,plain,(
% 21.82/3.28 ~is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(necessarily(sK65_skl)))))),
% 21.82/3.28 inference(resolution,[status(thm)],[f9485,f374])).
% 21.82/3.28 fof(f10148,plain,(
% 21.82/3.28 ![X0,X1]: (implies(implies(X0,X0),X1)=not(not(X1)))),
% 21.82/3.28 inference(paramodulation,[status(thm)],[f9057,f362])).
% 21.82/3.28 fof(f10202,plain,(
% 21.82/3.28 ![X0,X1]: (implies(implies(X0,X0),X1)=X1)),
% 21.82/3.28 inference(forward_demodulation,[status(thm)],[f8371,f10148])).
% 21.82/3.28 fof(f13755,plain,(
% 21.82/3.28 ![X0,X1]: (possibly(necessarily(X0))=necessarily(implies(implies(X1,X1),X0)))),
% 21.82/3.28 inference(paramodulation,[status(thm)],[f10202,f9139])).
% 21.82/3.28 fof(f13846,plain,(
% 21.82/3.28 ![X0]: (possibly(necessarily(X0))=necessarily(X0))),
% 21.82/3.28 inference(forward_demodulation,[status(thm)],[f10202,f13755])).
% 21.82/3.28 fof(f14163,plain,(
% 21.82/3.28 ![X0]: (necessarily(necessarily(X0))=possibly(necessarily(X0)))),
% 21.82/3.28 inference(paramodulation,[status(thm)],[f13846,f7802])).
% 21.82/3.28 fof(f14232,plain,(
% 21.82/3.28 ![X0]: (necessarily(necessarily(X0))=necessarily(X0))),
% 21.82/3.28 inference(forward_demodulation,[status(thm)],[f13846,f14163])).
% 21.82/3.28 fof(f14257,plain,(
% 21.82/3.28 ~is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl))))),
% 21.82/3.28 inference(backward_demodulation,[status(thm)],[f14232,f9531])).
% 21.82/3.28 fof(f14320,plain,(
% 21.82/3.28 ~is_a_theorem(implies(necessarily(sK65_skl),necessarily(sK65_skl)))),
% 21.82/3.28 inference(forward_demodulation,[status(thm)],[f14232,f14257])).
% 21.82/3.28 fof(f14321,plain,(
% 21.82/3.28 $false),
% 21.82/3.28 inference(forward_subsumption_resolution,[status(thm)],[f14320,f1038])).
% 21.82/3.28 % SZS output end CNFRefutation for theBenchmark.p
% 21.82/3.32 % Elapsed time: 2.925376 seconds
% 21.82/3.32 % CPU time: 22.694228 seconds
% 21.82/3.32 % Total memory used: 323.050 MB
% 21.82/3.32 % Net memory used: 301.572 MB
%------------------------------------------------------------------------------