TSTP Solution File: LCL524+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL524+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:27:22 EDT 2024
% Result : Theorem 1.59s 0.57s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : LCL524+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Apr 29 20:16:02 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % Drodi V3.6.0
% 1.59/0.57 % Refutation found
% 1.59/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.59/0.57 % SZS output start CNFRefutation for theBenchmark
% 1.59/0.57 fof(f1,axiom,(
% 1.59/0.57 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f2,axiom,(
% 1.59/0.57 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f3,axiom,(
% 1.59/0.57 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f4,axiom,(
% 1.59/0.57 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f5,axiom,(
% 1.59/0.57 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f8,axiom,(
% 1.59/0.57 ( and_2<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f9,axiom,(
% 1.59/0.57 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f10,axiom,(
% 1.59/0.57 ( or_1<=> (! [X,Y] : is_a_theorem(implies(X,or(X,Y))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f12,axiom,(
% 1.59/0.57 ( or_3<=> (! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f21,axiom,(
% 1.59/0.57 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f27,axiom,(
% 1.59/0.57 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f29,axiom,(
% 1.59/0.57 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f31,axiom,(
% 1.59/0.57 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f32,axiom,(
% 1.59/0.57 op_or ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f33,axiom,(
% 1.59/0.57 op_implies_and ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f34,axiom,(
% 1.59/0.57 op_equiv ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f35,axiom,(
% 1.59/0.57 modus_ponens ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f36,axiom,(
% 1.59/0.57 modus_tollens ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f37,axiom,(
% 1.59/0.57 implies_1 ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f38,axiom,(
% 1.59/0.57 implies_2 ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f41,axiom,(
% 1.59/0.57 and_2 ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f42,axiom,(
% 1.59/0.57 and_3 ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f43,axiom,(
% 1.59/0.57 or_1 ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f45,axiom,(
% 1.59/0.57 or_3 ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f49,axiom,(
% 1.59/0.57 substitution_of_equivalents ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f55,axiom,(
% 1.59/0.57 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f57,axiom,(
% 1.59/0.57 ( axiom_B<=> (! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f58,axiom,(
% 1.59/0.57 ( axiom_5<=> (! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f73,axiom,(
% 1.59/0.57 ( op_possibly=> (! [X] : possibly(X) = not(necessarily(not(X))) )) ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f77,axiom,(
% 1.59/0.57 op_possibly ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.59/0.57 fof(f80,axiom,(
% 1.59/0.57 axiom_M ),
% 1.59/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.66/0.58 fof(f81,axiom,(
% 1.66/0.58 axiom_5 ),
% 1.66/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.66/0.58 fof(f82,conjecture,(
% 1.66/0.58 axiom_B ),
% 1.66/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.66/0.58 fof(f83,negated_conjecture,(
% 1.66/0.58 ~(axiom_B )),
% 1.66/0.58 inference(negated_conjecture,[status(cth)],[f82])).
% 1.66/0.58 fof(f84,plain,(
% 1.66/0.58 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 1.66/0.58 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 1.66/0.58 fof(f85,plain,(
% 1.66/0.58 (~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))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f84])).
% 1.66/0.58 fof(f86,plain,(
% 1.66/0.58 (~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))))),
% 1.66/0.58 inference(miniscoping,[status(esa)],[f85])).
% 1.66/0.58 fof(f87,plain,(
% 1.66/0.58 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|((is_a_theorem(sk0_1)&is_a_theorem(implies(sk0_1,sk0_0)))&~is_a_theorem(sk0_0)))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f86])).
% 1.66/0.58 fof(f88,plain,(
% 1.66/0.58 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f87])).
% 1.66/0.58 fof(f92,plain,(
% 1.66/0.58 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 1.66/0.58 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 1.66/0.58 fof(f93,plain,(
% 1.66/0.58 (~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)))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f92])).
% 1.66/0.58 fof(f94,plain,(
% 1.66/0.58 (~substitution_of_equivalents|(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y)))&(substitution_of_equivalents|(is_a_theorem(equiv(sk0_2,sk0_3))&~sk0_2=sk0_3))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f93])).
% 1.66/0.58 fof(f95,plain,(
% 1.66/0.58 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f94])).
% 1.66/0.58 fof(f98,plain,(
% 1.66/0.58 (~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)))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f3])).
% 1.66/0.58 fof(f99,plain,(
% 1.66/0.58 (~modus_tollens|(![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))))&(modus_tollens|~is_a_theorem(implies(implies(not(sk0_5),not(sk0_4)),implies(sk0_4,sk0_5))))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f98])).
% 1.66/0.58 fof(f100,plain,(
% 1.66/0.58 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f99])).
% 1.66/0.58 fof(f102,plain,(
% 1.66/0.58 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f4])).
% 1.66/0.58 fof(f103,plain,(
% 1.66/0.58 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|~is_a_theorem(implies(sk0_6,implies(sk0_7,sk0_6))))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f102])).
% 1.66/0.58 fof(f104,plain,(
% 1.66/0.58 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f103])).
% 1.66/0.58 fof(f106,plain,(
% 1.66/0.58 (~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)))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f5])).
% 1.66/0.58 fof(f107,plain,(
% 1.66/0.58 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|~is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9))))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f106])).
% 1.66/0.58 fof(f108,plain,(
% 1.66/0.58 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f107])).
% 1.66/0.58 fof(f118,plain,(
% 1.66/0.58 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),Y))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f8])).
% 1.66/0.58 fof(f119,plain,(
% 1.66/0.58 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|~is_a_theorem(implies(and(sk0_15,sk0_16),sk0_16)))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f118])).
% 1.66/0.58 fof(f120,plain,(
% 1.66/0.58 ![X0,X1]: (~and_2|is_a_theorem(implies(and(X0,X1),X1)))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f119])).
% 1.66/0.58 fof(f122,plain,(
% 1.66/0.58 (~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))))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f9])).
% 1.66/0.58 fof(f123,plain,(
% 1.66/0.58 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|~is_a_theorem(implies(sk0_17,implies(sk0_18,and(sk0_17,sk0_18)))))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f122])).
% 1.66/0.58 fof(f124,plain,(
% 1.66/0.58 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f123])).
% 1.66/0.58 fof(f126,plain,(
% 1.66/0.58 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|(?[X,Y]: ~is_a_theorem(implies(X,or(X,Y)))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f10])).
% 1.66/0.58 fof(f127,plain,(
% 1.66/0.58 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|~is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20))))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f126])).
% 1.66/0.58 fof(f128,plain,(
% 1.66/0.58 ![X0,X1]: (~or_1|is_a_theorem(implies(X0,or(X0,X1))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f127])).
% 1.66/0.58 fof(f134,plain,(
% 1.66/0.58 (~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))))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f12])).
% 1.66/0.58 fof(f135,plain,(
% 1.66/0.58 (~or_3|(![X,Y,Z]: is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))))&(or_3|~is_a_theorem(implies(implies(sk0_23,sk0_25),implies(implies(sk0_24,sk0_25),implies(or(sk0_23,sk0_24),sk0_25)))))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f134])).
% 1.66/0.58 fof(f136,plain,(
% 1.66/0.58 ![X0,X1,X2]: (~or_3|is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f135])).
% 1.66/0.58 fof(f170,plain,(
% 1.66/0.58 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f21])).
% 1.66/0.58 fof(f171,plain,(
% 1.66/0.58 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43)))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f170])).
% 1.66/0.58 fof(f172,plain,(
% 1.66/0.58 ![X0]: (~cn3|is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f171])).
% 1.66/0.58 fof(f173,plain,(
% 1.66/0.58 cn3|~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f171])).
% 1.66/0.58 fof(f194,plain,(
% 1.66/0.58 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 1.66/0.58 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 1.66/0.58 fof(f195,plain,(
% 1.66/0.58 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f194])).
% 1.66/0.58 fof(f198,plain,(
% 1.66/0.58 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 1.66/0.58 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 1.66/0.58 fof(f199,plain,(
% 1.66/0.58 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f198])).
% 1.66/0.58 fof(f202,plain,(
% 1.66/0.58 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 1.66/0.58 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 1.66/0.58 fof(f203,plain,(
% 1.66/0.58 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f202])).
% 1.66/0.58 fof(f204,plain,(
% 1.66/0.58 op_or),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f32])).
% 1.66/0.58 fof(f205,plain,(
% 1.66/0.58 op_implies_and),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f33])).
% 1.66/0.58 fof(f206,plain,(
% 1.66/0.58 op_equiv),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f34])).
% 1.66/0.58 fof(f207,plain,(
% 1.66/0.58 modus_ponens),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f35])).
% 1.66/0.58 fof(f208,plain,(
% 1.66/0.58 modus_tollens),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f36])).
% 1.66/0.58 fof(f209,plain,(
% 1.66/0.58 implies_1),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f37])).
% 1.66/0.58 fof(f210,plain,(
% 1.66/0.58 implies_2),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f38])).
% 1.66/0.58 fof(f213,plain,(
% 1.66/0.58 and_2),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f41])).
% 1.66/0.58 fof(f214,plain,(
% 1.66/0.58 and_3),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f42])).
% 1.66/0.58 fof(f215,plain,(
% 1.66/0.58 or_1),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f43])).
% 1.66/0.58 fof(f217,plain,(
% 1.66/0.58 or_3),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f45])).
% 1.66/0.58 fof(f221,plain,(
% 1.66/0.58 substitution_of_equivalents),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f49])).
% 1.66/0.58 fof(f253,plain,(
% 1.66/0.58 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f55])).
% 1.66/0.58 fof(f254,plain,(
% 1.66/0.58 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sk0_64),sk0_64)))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f253])).
% 1.66/0.58 fof(f255,plain,(
% 1.66/0.58 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f254])).
% 1.66/0.58 fof(f261,plain,(
% 1.66/0.58 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|(?[X]: ~is_a_theorem(implies(X,necessarily(possibly(X))))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f57])).
% 1.66/0.58 fof(f262,plain,(
% 1.66/0.58 (~axiom_B|(![X]: is_a_theorem(implies(X,necessarily(possibly(X))))))&(axiom_B|~is_a_theorem(implies(sk0_66,necessarily(possibly(sk0_66)))))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f261])).
% 1.66/0.58 fof(f264,plain,(
% 1.66/0.58 axiom_B|~is_a_theorem(implies(sk0_66,necessarily(possibly(sk0_66))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f262])).
% 1.66/0.58 fof(f265,plain,(
% 1.66/0.58 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|(?[X]: ~is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))),
% 1.66/0.58 inference(NNF_transformation,[status(esa)],[f58])).
% 1.66/0.58 fof(f266,plain,(
% 1.66/0.58 (~axiom_5|(![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))))&(axiom_5|~is_a_theorem(implies(possibly(sk0_67),necessarily(possibly(sk0_67)))))),
% 1.66/0.58 inference(skolemization,[status(esa)],[f265])).
% 1.66/0.58 fof(f267,plain,(
% 1.66/0.58 ![X0]: (~axiom_5|is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f266])).
% 1.66/0.58 fof(f325,plain,(
% 1.66/0.58 ~op_possibly|(![X]: possibly(X)=not(necessarily(not(X))))),
% 1.66/0.58 inference(pre_NNF_transformation,[status(esa)],[f73])).
% 1.66/0.58 fof(f326,plain,(
% 1.66/0.58 ![X0]: (~op_possibly|possibly(X0)=not(necessarily(not(X0))))),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f325])).
% 1.66/0.58 fof(f333,plain,(
% 1.66/0.58 op_possibly),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f77])).
% 1.66/0.58 fof(f336,plain,(
% 1.66/0.58 axiom_M),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f80])).
% 1.66/0.58 fof(f337,plain,(
% 1.66/0.58 axiom_5),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f81])).
% 1.66/0.58 fof(f338,plain,(
% 1.66/0.58 ~axiom_B),
% 1.66/0.58 inference(cnf_transformation,[status(esa)],[f83])).
% 1.66/0.58 fof(f339,plain,(
% 1.66/0.58 spl0_0 <=> modus_ponens),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f341,plain,(
% 1.66/0.58 ~modus_ponens|spl0_0),
% 1.66/0.58 inference(component_clause,[status(thm)],[f339])).
% 1.66/0.58 fof(f342,plain,(
% 1.66/0.58 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f343,plain,(
% 1.66/0.58 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f342])).
% 1.66/0.58 fof(f345,plain,(
% 1.66/0.58 ~spl0_0|spl0_1),
% 1.66/0.58 inference(split_clause,[status(thm)],[f88,f339,f342])).
% 1.66/0.58 fof(f358,plain,(
% 1.66/0.58 spl0_5 <=> substitution_of_equivalents),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f360,plain,(
% 1.66/0.58 ~substitution_of_equivalents|spl0_5),
% 1.66/0.58 inference(component_clause,[status(thm)],[f358])).
% 1.66/0.58 fof(f361,plain,(
% 1.66/0.58 spl0_6 <=> ~is_a_theorem(equiv(X0,X1))|X0=X1),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f362,plain,(
% 1.66/0.58 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~spl0_6)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f361])).
% 1.66/0.58 fof(f364,plain,(
% 1.66/0.58 ~spl0_5|spl0_6),
% 1.66/0.58 inference(split_clause,[status(thm)],[f95,f358,f361])).
% 1.66/0.58 fof(f373,plain,(
% 1.66/0.58 spl0_9 <=> modus_tollens),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f375,plain,(
% 1.66/0.58 ~modus_tollens|spl0_9),
% 1.66/0.58 inference(component_clause,[status(thm)],[f373])).
% 1.66/0.58 fof(f376,plain,(
% 1.66/0.58 spl0_10 <=> is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f377,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))|~spl0_10)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f376])).
% 1.66/0.58 fof(f379,plain,(
% 1.66/0.58 ~spl0_9|spl0_10),
% 1.66/0.58 inference(split_clause,[status(thm)],[f100,f373,f376])).
% 1.66/0.58 fof(f384,plain,(
% 1.66/0.58 spl0_12 <=> implies_1),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f386,plain,(
% 1.66/0.58 ~implies_1|spl0_12),
% 1.66/0.58 inference(component_clause,[status(thm)],[f384])).
% 1.66/0.58 fof(f387,plain,(
% 1.66/0.58 spl0_13 <=> is_a_theorem(implies(X0,implies(X1,X0)))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f388,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~spl0_13)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f387])).
% 1.66/0.58 fof(f390,plain,(
% 1.66/0.58 ~spl0_12|spl0_13),
% 1.66/0.58 inference(split_clause,[status(thm)],[f104,f384,f387])).
% 1.66/0.58 fof(f395,plain,(
% 1.66/0.58 spl0_15 <=> implies_2),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f397,plain,(
% 1.66/0.58 ~implies_2|spl0_15),
% 1.66/0.58 inference(component_clause,[status(thm)],[f395])).
% 1.66/0.58 fof(f398,plain,(
% 1.66/0.58 spl0_16 <=> is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f399,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))|~spl0_16)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f398])).
% 1.66/0.58 fof(f401,plain,(
% 1.66/0.58 ~spl0_15|spl0_16),
% 1.66/0.58 inference(split_clause,[status(thm)],[f108,f395,f398])).
% 1.66/0.58 fof(f428,plain,(
% 1.66/0.58 spl0_24 <=> and_2),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f430,plain,(
% 1.66/0.58 ~and_2|spl0_24),
% 1.66/0.58 inference(component_clause,[status(thm)],[f428])).
% 1.66/0.58 fof(f431,plain,(
% 1.66/0.58 spl0_25 <=> is_a_theorem(implies(and(X0,X1),X1))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f432,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1))|~spl0_25)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f431])).
% 1.66/0.58 fof(f434,plain,(
% 1.66/0.58 ~spl0_24|spl0_25),
% 1.66/0.58 inference(split_clause,[status(thm)],[f120,f428,f431])).
% 1.66/0.58 fof(f439,plain,(
% 1.66/0.58 spl0_27 <=> and_3),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f441,plain,(
% 1.66/0.58 ~and_3|spl0_27),
% 1.66/0.58 inference(component_clause,[status(thm)],[f439])).
% 1.66/0.58 fof(f442,plain,(
% 1.66/0.58 spl0_28 <=> is_a_theorem(implies(X0,implies(X1,and(X0,X1))))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f443,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1))))|~spl0_28)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f442])).
% 1.66/0.58 fof(f445,plain,(
% 1.66/0.58 ~spl0_27|spl0_28),
% 1.66/0.58 inference(split_clause,[status(thm)],[f124,f439,f442])).
% 1.66/0.58 fof(f450,plain,(
% 1.66/0.58 spl0_30 <=> or_1),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f452,plain,(
% 1.66/0.58 ~or_1|spl0_30),
% 1.66/0.58 inference(component_clause,[status(thm)],[f450])).
% 1.66/0.58 fof(f453,plain,(
% 1.66/0.58 spl0_31 <=> is_a_theorem(implies(X0,or(X0,X1)))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f454,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_31)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f453])).
% 1.66/0.58 fof(f456,plain,(
% 1.66/0.58 ~spl0_30|spl0_31),
% 1.66/0.58 inference(split_clause,[status(thm)],[f128,f450,f453])).
% 1.66/0.58 fof(f472,plain,(
% 1.66/0.58 spl0_36 <=> or_3),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f474,plain,(
% 1.66/0.58 ~or_3|spl0_36),
% 1.66/0.58 inference(component_clause,[status(thm)],[f472])).
% 1.66/0.58 fof(f475,plain,(
% 1.66/0.58 spl0_37 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f476,plain,(
% 1.66/0.58 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))|~spl0_37)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f475])).
% 1.66/0.58 fof(f478,plain,(
% 1.66/0.58 ~spl0_36|spl0_37),
% 1.66/0.58 inference(split_clause,[status(thm)],[f136,f472,f475])).
% 1.66/0.58 fof(f519,plain,(
% 1.66/0.58 spl0_49 <=> is_a_theorem(implies(X0,and(X0,X0)))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f520,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_49)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f519])).
% 1.66/0.58 fof(f565,plain,(
% 1.66/0.58 spl0_61 <=> cn3),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f568,plain,(
% 1.66/0.58 spl0_62 <=> is_a_theorem(implies(implies(not(X0),X0),X0))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f569,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0))|~spl0_62)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f568])).
% 1.66/0.58 fof(f571,plain,(
% 1.66/0.58 ~spl0_61|spl0_62),
% 1.66/0.58 inference(split_clause,[status(thm)],[f172,f565,f568])).
% 1.66/0.58 fof(f572,plain,(
% 1.66/0.58 spl0_63 <=> is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f574,plain,(
% 1.66/0.58 ~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))|spl0_63),
% 1.66/0.58 inference(component_clause,[status(thm)],[f572])).
% 1.66/0.58 fof(f575,plain,(
% 1.66/0.58 spl0_61|~spl0_63),
% 1.66/0.58 inference(split_clause,[status(thm)],[f173,f565,f572])).
% 1.66/0.58 fof(f598,plain,(
% 1.66/0.58 spl0_70 <=> is_a_theorem(implies(or(X0,X1),or(X1,X0)))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f599,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_70)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f598])).
% 1.66/0.58 fof(f628,plain,(
% 1.66/0.58 spl0_78 <=> op_or),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f630,plain,(
% 1.66/0.58 ~op_or|spl0_78),
% 1.66/0.58 inference(component_clause,[status(thm)],[f628])).
% 1.66/0.58 fof(f631,plain,(
% 1.66/0.58 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f632,plain,(
% 1.66/0.58 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f631])).
% 1.66/0.58 fof(f634,plain,(
% 1.66/0.58 ~spl0_78|spl0_79),
% 1.66/0.58 inference(split_clause,[status(thm)],[f195,f628,f631])).
% 1.66/0.58 fof(f642,plain,(
% 1.66/0.58 spl0_82 <=> op_implies_and),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f644,plain,(
% 1.66/0.58 ~op_implies_and|spl0_82),
% 1.66/0.58 inference(component_clause,[status(thm)],[f642])).
% 1.66/0.58 fof(f645,plain,(
% 1.66/0.58 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f646,plain,(
% 1.66/0.58 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f645])).
% 1.66/0.58 fof(f648,plain,(
% 1.66/0.58 ~spl0_82|spl0_83),
% 1.66/0.58 inference(split_clause,[status(thm)],[f199,f642,f645])).
% 1.66/0.58 fof(f656,plain,(
% 1.66/0.58 spl0_86 <=> op_equiv),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f658,plain,(
% 1.66/0.58 ~op_equiv|spl0_86),
% 1.66/0.58 inference(component_clause,[status(thm)],[f656])).
% 1.66/0.58 fof(f659,plain,(
% 1.66/0.58 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f660,plain,(
% 1.66/0.58 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f659])).
% 1.66/0.58 fof(f662,plain,(
% 1.66/0.58 ~spl0_86|spl0_87),
% 1.66/0.58 inference(split_clause,[status(thm)],[f203,f656,f659])).
% 1.66/0.58 fof(f742,plain,(
% 1.66/0.58 spl0_109 <=> axiom_M),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f744,plain,(
% 1.66/0.58 ~axiom_M|spl0_109),
% 1.66/0.58 inference(component_clause,[status(thm)],[f742])).
% 1.66/0.58 fof(f745,plain,(
% 1.66/0.58 spl0_110 <=> is_a_theorem(implies(necessarily(X0),X0))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f746,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(implies(necessarily(X0),X0))|~spl0_110)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f745])).
% 1.66/0.58 fof(f748,plain,(
% 1.66/0.58 ~spl0_109|spl0_110),
% 1.66/0.58 inference(split_clause,[status(thm)],[f255,f742,f745])).
% 1.66/0.58 fof(f764,plain,(
% 1.66/0.58 spl0_115 <=> axiom_B),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f765,plain,(
% 1.66/0.58 axiom_B|~spl0_115),
% 1.66/0.58 inference(component_clause,[status(thm)],[f764])).
% 1.66/0.58 fof(f771,plain,(
% 1.66/0.58 spl0_117 <=> is_a_theorem(implies(sk0_66,necessarily(possibly(sk0_66))))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f773,plain,(
% 1.66/0.58 ~is_a_theorem(implies(sk0_66,necessarily(possibly(sk0_66))))|spl0_117),
% 1.66/0.58 inference(component_clause,[status(thm)],[f771])).
% 1.66/0.58 fof(f774,plain,(
% 1.66/0.58 spl0_115|~spl0_117),
% 1.66/0.58 inference(split_clause,[status(thm)],[f264,f764,f771])).
% 1.66/0.58 fof(f775,plain,(
% 1.66/0.58 spl0_118 <=> axiom_5),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f777,plain,(
% 1.66/0.58 ~axiom_5|spl0_118),
% 1.66/0.58 inference(component_clause,[status(thm)],[f775])).
% 1.66/0.58 fof(f778,plain,(
% 1.66/0.58 spl0_119 <=> is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f779,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))|~spl0_119)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f778])).
% 1.66/0.58 fof(f781,plain,(
% 1.66/0.58 ~spl0_118|spl0_119),
% 1.66/0.58 inference(split_clause,[status(thm)],[f267,f775,f778])).
% 1.66/0.58 fof(f940,plain,(
% 1.66/0.58 spl0_163 <=> op_possibly),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f942,plain,(
% 1.66/0.58 ~op_possibly|spl0_163),
% 1.66/0.58 inference(component_clause,[status(thm)],[f940])).
% 1.66/0.58 fof(f943,plain,(
% 1.66/0.58 spl0_164 <=> possibly(X0)=not(necessarily(not(X0)))),
% 1.66/0.58 introduced(split_symbol_definition)).
% 1.66/0.58 fof(f944,plain,(
% 1.66/0.58 ![X0]: (possibly(X0)=not(necessarily(not(X0)))|~spl0_164)),
% 1.66/0.58 inference(component_clause,[status(thm)],[f943])).
% 1.66/0.58 fof(f946,plain,(
% 1.66/0.58 ~spl0_163|spl0_164),
% 1.66/0.58 inference(split_clause,[status(thm)],[f326,f940,f943])).
% 1.66/0.58 fof(f968,plain,(
% 1.66/0.58 $false|spl0_163),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f942,f333])).
% 1.66/0.58 fof(f969,plain,(
% 1.66/0.58 spl0_163),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f968])).
% 1.66/0.58 fof(f970,plain,(
% 1.66/0.58 $false|spl0_0),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f341,f207])).
% 1.66/0.58 fof(f971,plain,(
% 1.66/0.58 spl0_0),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f970])).
% 1.66/0.58 fof(f974,plain,(
% 1.66/0.58 $false|spl0_5),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f360,f221])).
% 1.66/0.58 fof(f975,plain,(
% 1.66/0.58 spl0_5),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f974])).
% 1.66/0.58 fof(f976,plain,(
% 1.66/0.58 $false|spl0_86),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f658,f206])).
% 1.66/0.58 fof(f977,plain,(
% 1.66/0.58 spl0_86),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f976])).
% 1.66/0.58 fof(f978,plain,(
% 1.66/0.58 $false|spl0_82),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f644,f205])).
% 1.66/0.58 fof(f979,plain,(
% 1.66/0.58 spl0_82),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f978])).
% 1.66/0.58 fof(f980,plain,(
% 1.66/0.58 $false|spl0_78),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f630,f204])).
% 1.66/0.58 fof(f981,plain,(
% 1.66/0.58 spl0_78),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f980])).
% 1.66/0.58 fof(f986,plain,(
% 1.66/0.58 $false|spl0_109),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f744,f336])).
% 1.66/0.58 fof(f987,plain,(
% 1.66/0.58 spl0_109),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f986])).
% 1.66/0.58 fof(f1013,plain,(
% 1.66/0.58 $false|spl0_30),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f452,f215])).
% 1.66/0.58 fof(f1014,plain,(
% 1.66/0.58 spl0_30),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f1013])).
% 1.66/0.58 fof(f1017,plain,(
% 1.66/0.58 $false|spl0_24),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f430,f213])).
% 1.66/0.58 fof(f1018,plain,(
% 1.66/0.58 spl0_24),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f1017])).
% 1.66/0.58 fof(f1021,plain,(
% 1.66/0.58 $false|spl0_12),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f386,f209])).
% 1.66/0.58 fof(f1022,plain,(
% 1.66/0.58 spl0_12),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f1021])).
% 1.66/0.58 fof(f1033,plain,(
% 1.66/0.58 $false|spl0_118),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f777,f337])).
% 1.66/0.58 fof(f1034,plain,(
% 1.66/0.58 spl0_118),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f1033])).
% 1.66/0.58 fof(f1045,plain,(
% 1.66/0.58 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,and(X0,X1)))|~spl0_1|~spl0_28)),
% 1.66/0.58 inference(resolution,[status(thm)],[f343,f443])).
% 1.66/0.58 fof(f1146,plain,(
% 1.66/0.58 $false|spl0_27),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f441,f214])).
% 1.66/0.58 fof(f1147,plain,(
% 1.66/0.58 spl0_27),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f1146])).
% 1.66/0.58 fof(f1156,plain,(
% 1.66/0.58 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))|~spl0_28|~spl0_1)),
% 1.66/0.58 inference(resolution,[status(thm)],[f1045,f343])).
% 1.66/0.58 fof(f1251,plain,(
% 1.66/0.58 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1))|~spl0_28|~spl0_1|~spl0_87)),
% 1.66/0.58 inference(paramodulation,[status(thm)],[f660,f1156])).
% 1.66/0.58 fof(f1256,plain,(
% 1.66/0.58 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 1.66/0.58 inference(forward_demodulation,[status(thm)],[f646,f632])).
% 1.66/0.58 fof(f1260,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0)))|~spl0_83|~spl0_79|~spl0_10)),
% 1.66/0.58 inference(backward_demodulation,[status(thm)],[f1256,f377])).
% 1.66/0.58 fof(f1262,plain,(
% 1.66/0.58 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~spl0_79|~spl0_83)),
% 1.66/0.58 inference(paramodulation,[status(thm)],[f646,f1256])).
% 1.66/0.58 fof(f1302,plain,(
% 1.66/0.58 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1))|~spl0_1|~spl0_16)),
% 1.66/0.58 inference(resolution,[status(thm)],[f343,f399])).
% 1.66/0.58 fof(f1349,plain,(
% 1.66/0.58 ~is_a_theorem(implies(or(sk0_43,sk0_43),sk0_43))|~spl0_83|~spl0_79|spl0_63),
% 1.66/0.58 inference(forward_demodulation,[status(thm)],[f1256,f574])).
% 1.66/0.58 fof(f1360,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0)))|~spl0_10|~spl0_83|~spl0_79)),
% 1.66/0.58 inference(paramodulation,[status(thm)],[f1256,f1260])).
% 1.66/0.58 fof(f1446,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1)))|~spl0_1|~spl0_16|~spl0_37)),
% 1.66/0.58 inference(resolution,[status(thm)],[f1302,f476])).
% 1.66/0.58 fof(f1448,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_1|~spl0_16|~spl0_28)),
% 1.66/0.58 inference(resolution,[status(thm)],[f1302,f443])).
% 1.66/0.58 fof(f1449,plain,(
% 1.66/0.58 spl0_49|~spl0_1|~spl0_16|~spl0_28),
% 1.66/0.58 inference(split_clause,[status(thm)],[f1448,f519,f342,f398,f442])).
% 1.66/0.58 fof(f1450,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_1|~spl0_16|~spl0_13)),
% 1.66/0.58 inference(resolution,[status(thm)],[f1302,f388])).
% 1.66/0.58 fof(f1457,plain,(
% 1.66/0.58 $false|spl0_15),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f397,f210])).
% 1.66/0.58 fof(f1458,plain,(
% 1.66/0.58 spl0_15),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f1457])).
% 1.66/0.58 fof(f1550,plain,(
% 1.66/0.58 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X0,X0),X1))|~spl0_16|~spl0_37|~spl0_1)),
% 1.66/0.58 inference(resolution,[status(thm)],[f1446,f343])).
% 1.66/0.58 fof(f1559,plain,(
% 1.66/0.58 ~is_a_theorem(implies(sk0_43,sk0_43))|~spl0_16|~spl0_37|~spl0_1|~spl0_83|~spl0_79|spl0_63),
% 1.66/0.58 inference(resolution,[status(thm)],[f1550,f1349])).
% 1.66/0.58 fof(f1560,plain,(
% 1.66/0.58 $false|~spl0_13|~spl0_16|~spl0_37|~spl0_1|~spl0_83|~spl0_79|spl0_63),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f1559,f1450])).
% 1.66/0.58 fof(f1561,plain,(
% 1.66/0.58 ~spl0_13|~spl0_16|~spl0_37|~spl0_1|~spl0_83|~spl0_79|spl0_63),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f1560])).
% 1.66/0.58 fof(f1564,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(implies(or(X0,X0),X0))|~spl0_83|~spl0_79|~spl0_62)),
% 1.66/0.58 inference(forward_demodulation,[status(thm)],[f1256,f569])).
% 1.66/0.58 fof(f1566,plain,(
% 1.66/0.58 $false|spl0_36),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f474,f217])).
% 1.66/0.58 fof(f1567,plain,(
% 1.66/0.58 spl0_36),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f1566])).
% 1.66/0.58 fof(f1583,plain,(
% 1.66/0.58 $false|spl0_9),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f375,f208])).
% 1.66/0.58 fof(f1584,plain,(
% 1.66/0.58 spl0_9),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f1583])).
% 1.66/0.58 fof(f1908,plain,(
% 1.66/0.58 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|X0=X1|~spl0_28|~spl0_1|~spl0_87|~spl0_6)),
% 1.66/0.58 inference(resolution,[status(thm)],[f1251,f362])).
% 1.66/0.58 fof(f1909,plain,(
% 1.66/0.58 ![X0]: (~is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0)))|necessarily(possibly(X0))=possibly(X0)|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_119)),
% 1.66/0.58 inference(resolution,[status(thm)],[f1908,f779])).
% 1.66/0.58 fof(f1910,plain,(
% 1.66/0.58 ![X0]: (necessarily(possibly(X0))=possibly(X0)|~spl0_110|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_119)),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f1909,f746])).
% 1.66/0.58 fof(f1921,plain,(
% 1.66/0.58 ![X0]: (~is_a_theorem(implies(X0,or(X0,X0)))|X0=or(X0,X0)|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_83|~spl0_79|~spl0_62)),
% 1.66/0.58 inference(resolution,[status(thm)],[f1908,f1564])).
% 1.66/0.58 fof(f1922,plain,(
% 1.66/0.58 ![X0]: (X0=or(X0,X0)|~spl0_31|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_83|~spl0_79|~spl0_62)),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f1921,f454])).
% 1.66/0.58 fof(f1940,plain,(
% 1.66/0.58 ![X0]: (~is_a_theorem(implies(and(X0,X0),X0))|and(X0,X0)=X0|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49)),
% 1.66/0.58 inference(resolution,[status(thm)],[f1908,f520])).
% 1.66/0.58 fof(f1941,plain,(
% 1.66/0.58 ![X0]: (and(X0,X0)=X0|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49)),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f1940,f432])).
% 1.66/0.58 fof(f1989,plain,(
% 1.66/0.58 ![X0,X1]: (or(not(X0),X1)=implies(implies(not(X0),X0),X1)|~spl0_79|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49)),
% 1.66/0.58 inference(paramodulation,[status(thm)],[f1941,f1262])).
% 1.66/0.58 fof(f1990,plain,(
% 1.66/0.58 ![X0,X1]: (or(not(X0),X1)=implies(or(X0,X0),X1)|~spl0_79|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49)),
% 1.66/0.58 inference(forward_demodulation,[status(thm)],[f1256,f1989])).
% 1.66/0.58 fof(f1991,plain,(
% 1.66/0.58 ![X0,X1]: (or(not(X0),X1)=implies(X0,X1)|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49)),
% 1.66/0.58 inference(forward_demodulation,[status(thm)],[f1922,f1990])).
% 1.66/0.58 fof(f1996,plain,(
% 1.66/0.58 ![X0]: (implies(not(X0),X0)=not(not(X0))|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49)),
% 1.66/0.58 inference(paramodulation,[status(thm)],[f1941,f646])).
% 1.66/0.58 fof(f1997,plain,(
% 1.66/0.58 ![X0]: (or(X0,X0)=not(not(X0))|~spl0_79|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49)),
% 1.66/0.58 inference(forward_demodulation,[status(thm)],[f1256,f1996])).
% 1.66/0.58 fof(f1998,plain,(
% 1.66/0.58 ![X0]: (X0=not(not(X0))|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49)),
% 1.66/0.58 inference(forward_demodulation,[status(thm)],[f1922,f1997])).
% 1.66/0.58 fof(f2001,plain,(
% 1.66/0.58 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_31|~spl0_62|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49|~spl0_10|~spl0_83|~spl0_79)),
% 1.66/0.58 inference(backward_demodulation,[status(thm)],[f1998,f1360])).
% 1.66/0.58 fof(f2002,plain,(
% 1.66/0.58 spl0_70|~spl0_31|~spl0_62|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49|~spl0_10|~spl0_83|~spl0_79),
% 1.66/0.58 inference(split_clause,[status(thm)],[f2001,f598,f453,f568,f431,f442,f342,f659,f361,f519,f376,f645,f631])).
% 1.66/0.58 fof(f2006,plain,(
% 1.66/0.58 ![X0]: (necessarily(not(X0))=not(possibly(X0))|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49|~spl0_164)),
% 1.66/0.58 inference(paramodulation,[status(thm)],[f944,f1998])).
% 1.66/0.58 fof(f2042,plain,(
% 1.66/0.58 ~is_a_theorem(implies(sk0_66,possibly(sk0_66)))|~spl0_110|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_119|spl0_117),
% 1.66/0.58 inference(backward_demodulation,[status(thm)],[f1910,f773])).
% 1.66/0.58 fof(f2685,plain,(
% 1.66/0.58 ![X0,X1]: (~is_a_theorem(implies(or(X0,X1),or(X1,X0)))|or(X0,X1)=or(X1,X0)|~spl0_70|~spl0_28|~spl0_1|~spl0_87|~spl0_6)),
% 1.66/0.58 inference(resolution,[status(thm)],[f599,f1908])).
% 1.66/0.58 fof(f2686,plain,(
% 1.66/0.58 ![X0,X1]: (or(X0,X1)=or(X1,X0)|~spl0_70|~spl0_28|~spl0_1|~spl0_87|~spl0_6)),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f2685,f599])).
% 1.66/0.58 fof(f3898,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(implies(not(possibly(X0)),not(X0)))|~spl0_110|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49|~spl0_164)),
% 1.66/0.58 inference(paramodulation,[status(thm)],[f2006,f746])).
% 1.66/0.58 fof(f3899,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(or(possibly(X0),not(X0)))|~spl0_110|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49|~spl0_164)),
% 1.66/0.58 inference(forward_demodulation,[status(thm)],[f1256,f3898])).
% 1.66/0.58 fof(f3900,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(or(not(X0),possibly(X0)))|~spl0_70|~spl0_110|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49|~spl0_164)),
% 1.66/0.58 inference(forward_demodulation,[status(thm)],[f2686,f3899])).
% 1.66/0.58 fof(f3901,plain,(
% 1.66/0.58 ![X0]: (is_a_theorem(implies(X0,possibly(X0)))|~spl0_70|~spl0_110|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_49|~spl0_164)),
% 1.66/0.58 inference(forward_demodulation,[status(thm)],[f1991,f3900])).
% 1.66/0.58 fof(f3904,plain,(
% 1.66/0.58 $false|~spl0_70|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_49|~spl0_164|~spl0_110|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_119|spl0_117),
% 1.66/0.58 inference(backward_subsumption_resolution,[status(thm)],[f2042,f3901])).
% 1.66/0.58 fof(f3905,plain,(
% 1.66/0.58 ~spl0_70|~spl0_31|~spl0_62|~spl0_79|~spl0_83|~spl0_25|~spl0_49|~spl0_164|~spl0_110|~spl0_28|~spl0_1|~spl0_87|~spl0_6|~spl0_119|spl0_117),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f3904])).
% 1.66/0.58 fof(f3916,plain,(
% 1.66/0.58 $false|~spl0_115),
% 1.66/0.58 inference(forward_subsumption_resolution,[status(thm)],[f765,f338])).
% 1.66/0.58 fof(f3917,plain,(
% 1.66/0.58 ~spl0_115),
% 1.66/0.58 inference(contradiction_clause,[status(thm)],[f3916])).
% 1.66/0.58 fof(f3918,plain,(
% 1.66/0.58 $false),
% 1.66/0.58 inference(sat_refutation,[status(thm)],[f345,f364,f379,f390,f401,f434,f445,f456,f478,f571,f575,f634,f648,f662,f748,f774,f781,f946,f969,f971,f975,f977,f979,f981,f987,f1014,f1018,f1022,f1034,f1147,f1449,f1458,f1561,f1567,f1584,f2002,f3905,f3917])).
% 1.66/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 1.66/0.58 % Elapsed time: 0.227500 seconds
% 1.66/0.58 % CPU time: 1.671103 seconds
% 1.66/0.58 % Total memory used: 86.270 MB
% 1.66/0.58 % Net memory used: 84.807 MB
%------------------------------------------------------------------------------