TSTP Solution File: LCL541+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL541+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 20:27:24 EDT 2024
% Result : Theorem 9.84s 1.68s
% Output : CNFRefutation 10.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL541+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.07/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 20:29:56 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 9.84/1.68 % Refutation found
% 9.84/1.68 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.84/1.68 % SZS output start CNFRefutation for theBenchmark
% 9.84/1.68 fof(f1,axiom,(
% 9.84/1.68 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f2,axiom,(
% 9.84/1.68 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f3,axiom,(
% 9.84/1.68 ( modus_tollens<=> (! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f4,axiom,(
% 9.84/1.68 ( implies_1<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f5,axiom,(
% 9.84/1.68 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f7,axiom,(
% 9.84/1.68 ( and_1<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),X)) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f8,axiom,(
% 9.84/1.68 ( and_2<=> (! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f9,axiom,(
% 9.84/1.68 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f10,axiom,(
% 9.84/1.68 ( or_1<=> (! [X,Y] : is_a_theorem(implies(X,or(X,Y))) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f27,axiom,(
% 9.84/1.68 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f29,axiom,(
% 9.84/1.68 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f31,axiom,(
% 9.84/1.68 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f32,axiom,(
% 9.84/1.68 op_or ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f33,axiom,(
% 9.84/1.68 op_implies_and ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f34,axiom,(
% 9.84/1.68 op_equiv ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f35,axiom,(
% 9.84/1.68 modus_ponens ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f36,axiom,(
% 9.84/1.68 modus_tollens ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f37,axiom,(
% 9.84/1.68 implies_1 ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f38,axiom,(
% 9.84/1.68 implies_2 ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f40,axiom,(
% 9.84/1.68 and_1 ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f41,axiom,(
% 9.84/1.68 and_2 ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f42,axiom,(
% 9.84/1.68 and_3 ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f43,axiom,(
% 9.84/1.68 or_1 ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f49,axiom,(
% 9.84/1.68 substitution_of_equivalents ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f50,axiom,(
% 9.84/1.68 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f53,axiom,(
% 9.84/1.68 ( substitution_strict_equiv<=> (! [X,Y] :( is_a_theorem(strict_equiv(X,Y))=> X = Y ) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f55,axiom,(
% 9.84/1.68 ( axiom_M<=> (! [X] : is_a_theorem(implies(necessarily(X),X)) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f63,axiom,(
% 9.84/1.68 ( axiom_m1<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f75,axiom,(
% 9.84/1.68 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.84/1.68 fof(f76,axiom,(
% 9.84/1.68 ( op_strict_equiv=> (! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) )) ),
% 9.84/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.46/1.69 fof(f78,axiom,(
% 10.46/1.69 necessitation ),
% 10.46/1.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.46/1.69 fof(f80,axiom,(
% 10.46/1.69 axiom_M ),
% 10.46/1.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.46/1.69 fof(f86,axiom,(
% 10.46/1.69 op_strict_implies ),
% 10.46/1.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.46/1.69 fof(f88,axiom,(
% 10.46/1.69 op_strict_equiv ),
% 10.46/1.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.46/1.69 fof(f89,conjecture,(
% 10.46/1.69 axiom_m1 ),
% 10.46/1.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.46/1.69 fof(f90,negated_conjecture,(
% 10.46/1.69 ~(axiom_m1 )),
% 10.46/1.69 inference(negated_conjecture,[status(cth)],[f89])).
% 10.46/1.69 fof(f91,plain,(
% 10.46/1.69 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 10.46/1.69 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 10.46/1.69 fof(f92,plain,(
% 10.46/1.69 (~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))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f91])).
% 10.46/1.69 fof(f93,plain,(
% 10.46/1.69 (~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))))),
% 10.46/1.69 inference(miniscoping,[status(esa)],[f92])).
% 10.46/1.69 fof(f94,plain,(
% 10.46/1.69 (~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)))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f93])).
% 10.46/1.69 fof(f95,plain,(
% 10.46/1.69 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f94])).
% 10.46/1.69 fof(f99,plain,(
% 10.46/1.69 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 10.46/1.69 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 10.46/1.69 fof(f100,plain,(
% 10.46/1.69 (~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)))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f99])).
% 10.46/1.69 fof(f101,plain,(
% 10.46/1.69 (~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))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f100])).
% 10.46/1.69 fof(f102,plain,(
% 10.46/1.69 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f101])).
% 10.46/1.69 fof(f105,plain,(
% 10.46/1.69 (~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)))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f3])).
% 10.46/1.69 fof(f106,plain,(
% 10.46/1.69 (~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))))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f105])).
% 10.46/1.69 fof(f107,plain,(
% 10.46/1.69 ![X0,X1]: (~modus_tollens|is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f106])).
% 10.46/1.69 fof(f109,plain,(
% 10.46/1.69 (~implies_1|(![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))&(implies_1|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,X)))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f4])).
% 10.46/1.69 fof(f110,plain,(
% 10.46/1.69 (~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))))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f109])).
% 10.46/1.69 fof(f111,plain,(
% 10.46/1.69 ![X0,X1]: (~implies_1|is_a_theorem(implies(X0,implies(X1,X0))))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f110])).
% 10.46/1.69 fof(f113,plain,(
% 10.46/1.69 (~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)))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f5])).
% 10.46/1.69 fof(f114,plain,(
% 10.46/1.69 (~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))))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f113])).
% 10.46/1.69 fof(f115,plain,(
% 10.46/1.69 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f114])).
% 10.46/1.69 fof(f121,plain,(
% 10.46/1.69 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),X))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f7])).
% 10.46/1.69 fof(f122,plain,(
% 10.46/1.69 (~and_1|(![X,Y]: is_a_theorem(implies(and(X,Y),X))))&(and_1|~is_a_theorem(implies(and(sk0_13,sk0_14),sk0_13)))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f121])).
% 10.46/1.69 fof(f123,plain,(
% 10.46/1.69 ![X0,X1]: (~and_1|is_a_theorem(implies(and(X0,X1),X0)))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f122])).
% 10.46/1.69 fof(f125,plain,(
% 10.46/1.69 (~and_2|(![X,Y]: is_a_theorem(implies(and(X,Y),Y))))&(and_2|(?[X,Y]: ~is_a_theorem(implies(and(X,Y),Y))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f8])).
% 10.46/1.69 fof(f126,plain,(
% 10.46/1.69 (~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)))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f125])).
% 10.46/1.69 fof(f127,plain,(
% 10.46/1.69 ![X0,X1]: (~and_2|is_a_theorem(implies(and(X0,X1),X1)))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f126])).
% 10.46/1.69 fof(f129,plain,(
% 10.46/1.69 (~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))))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f9])).
% 10.46/1.69 fof(f130,plain,(
% 10.46/1.69 (~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)))))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f129])).
% 10.46/1.69 fof(f131,plain,(
% 10.46/1.69 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f130])).
% 10.46/1.69 fof(f133,plain,(
% 10.46/1.69 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|(?[X,Y]: ~is_a_theorem(implies(X,or(X,Y)))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f10])).
% 10.46/1.69 fof(f134,plain,(
% 10.46/1.69 (~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))))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f133])).
% 10.46/1.69 fof(f135,plain,(
% 10.46/1.69 ![X0,X1]: (~or_1|is_a_theorem(implies(X0,or(X0,X1))))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f134])).
% 10.46/1.69 fof(f201,plain,(
% 10.46/1.69 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 10.46/1.69 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 10.46/1.69 fof(f202,plain,(
% 10.46/1.69 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f201])).
% 10.46/1.69 fof(f205,plain,(
% 10.46/1.69 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 10.46/1.69 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 10.46/1.69 fof(f206,plain,(
% 10.46/1.69 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f205])).
% 10.46/1.69 fof(f209,plain,(
% 10.46/1.69 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 10.46/1.69 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 10.46/1.69 fof(f210,plain,(
% 10.46/1.69 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f209])).
% 10.46/1.69 fof(f211,plain,(
% 10.46/1.69 op_or),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f32])).
% 10.46/1.69 fof(f212,plain,(
% 10.46/1.69 op_implies_and),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f33])).
% 10.46/1.69 fof(f213,plain,(
% 10.46/1.69 op_equiv),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f34])).
% 10.46/1.69 fof(f214,plain,(
% 10.46/1.69 modus_ponens),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f35])).
% 10.46/1.69 fof(f215,plain,(
% 10.46/1.69 modus_tollens),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f36])).
% 10.46/1.69 fof(f216,plain,(
% 10.46/1.69 implies_1),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f37])).
% 10.46/1.69 fof(f217,plain,(
% 10.46/1.69 implies_2),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f38])).
% 10.46/1.69 fof(f219,plain,(
% 10.46/1.69 and_1),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f40])).
% 10.46/1.69 fof(f220,plain,(
% 10.46/1.69 and_2),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f41])).
% 10.46/1.69 fof(f221,plain,(
% 10.46/1.69 and_3),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f42])).
% 10.46/1.69 fof(f222,plain,(
% 10.46/1.69 or_1),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f43])).
% 10.46/1.69 fof(f228,plain,(
% 10.46/1.69 substitution_of_equivalents),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f49])).
% 10.46/1.69 fof(f229,plain,(
% 10.46/1.69 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 10.46/1.69 inference(pre_NNF_transformation,[status(esa)],[f50])).
% 10.46/1.69 fof(f230,plain,(
% 10.46/1.69 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f229])).
% 10.46/1.69 fof(f231,plain,(
% 10.46/1.69 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sk0_55)&~is_a_theorem(necessarily(sk0_55))))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f230])).
% 10.46/1.69 fof(f232,plain,(
% 10.46/1.69 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f231])).
% 10.46/1.69 fof(f250,plain,(
% 10.46/1.69 substitution_strict_equiv<=>(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y))),
% 10.46/1.69 inference(pre_NNF_transformation,[status(esa)],[f53])).
% 10.46/1.69 fof(f251,plain,(
% 10.46/1.69 (~substitution_strict_equiv|(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y)))&(substitution_strict_equiv|(?[X,Y]: (is_a_theorem(strict_equiv(X,Y))&~X=Y)))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f250])).
% 10.46/1.69 fof(f252,plain,(
% 10.46/1.69 (~substitution_strict_equiv|(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y)))&(substitution_strict_equiv|(is_a_theorem(strict_equiv(sk0_60,sk0_61))&~sk0_60=sk0_61))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f251])).
% 10.46/1.69 fof(f253,plain,(
% 10.46/1.69 ![X0,X1]: (~substitution_strict_equiv|~is_a_theorem(strict_equiv(X0,X1))|X0=X1)),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f252])).
% 10.46/1.69 fof(f254,plain,(
% 10.46/1.69 substitution_strict_equiv|is_a_theorem(strict_equiv(sk0_60,sk0_61))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f252])).
% 10.46/1.69 fof(f255,plain,(
% 10.46/1.69 substitution_strict_equiv|~sk0_60=sk0_61),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f252])).
% 10.46/1.69 fof(f260,plain,(
% 10.46/1.69 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|(?[X]: ~is_a_theorem(implies(necessarily(X),X))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f55])).
% 10.46/1.69 fof(f261,plain,(
% 10.46/1.69 (~axiom_M|(![X]: is_a_theorem(implies(necessarily(X),X))))&(axiom_M|~is_a_theorem(implies(necessarily(sk0_64),sk0_64)))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f260])).
% 10.46/1.69 fof(f262,plain,(
% 10.46/1.69 ![X0]: (~axiom_M|is_a_theorem(implies(necessarily(X0),X0)))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f261])).
% 10.46/1.69 fof(f292,plain,(
% 10.46/1.69 (~axiom_m1|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))&(axiom_m1|(?[X,Y]: ~is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))),
% 10.46/1.69 inference(NNF_transformation,[status(esa)],[f63])).
% 10.46/1.69 fof(f293,plain,(
% 10.46/1.69 (~axiom_m1|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),and(Y,X)))))&(axiom_m1|~is_a_theorem(strict_implies(and(sk0_76,sk0_77),and(sk0_77,sk0_76))))),
% 10.46/1.69 inference(skolemization,[status(esa)],[f292])).
% 10.46/1.69 fof(f295,plain,(
% 10.46/1.69 axiom_m1|~is_a_theorem(strict_implies(and(sk0_76,sk0_77),and(sk0_77,sk0_76)))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f293])).
% 10.46/1.69 fof(f336,plain,(
% 10.46/1.69 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 10.46/1.69 inference(pre_NNF_transformation,[status(esa)],[f75])).
% 10.46/1.69 fof(f337,plain,(
% 10.46/1.69 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f336])).
% 10.46/1.69 fof(f338,plain,(
% 10.46/1.69 ~op_strict_equiv|(![X,Y]: strict_equiv(X,Y)=and(strict_implies(X,Y),strict_implies(Y,X)))),
% 10.46/1.69 inference(pre_NNF_transformation,[status(esa)],[f76])).
% 10.46/1.69 fof(f339,plain,(
% 10.46/1.69 ![X0,X1]: (~op_strict_equiv|strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0)))),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f338])).
% 10.46/1.69 fof(f341,plain,(
% 10.46/1.69 necessitation),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f78])).
% 10.46/1.69 fof(f343,plain,(
% 10.46/1.69 axiom_M),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f80])).
% 10.46/1.69 fof(f349,plain,(
% 10.46/1.69 op_strict_implies),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f86])).
% 10.46/1.69 fof(f351,plain,(
% 10.46/1.69 op_strict_equiv),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f88])).
% 10.46/1.69 fof(f352,plain,(
% 10.46/1.69 ~axiom_m1),
% 10.46/1.69 inference(cnf_transformation,[status(esa)],[f90])).
% 10.46/1.69 fof(f353,plain,(
% 10.46/1.69 spl0_0 <=> modus_ponens),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f355,plain,(
% 10.46/1.69 ~modus_ponens|spl0_0),
% 10.46/1.69 inference(component_clause,[status(thm)],[f353])).
% 10.46/1.69 fof(f356,plain,(
% 10.46/1.69 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f357,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f356])).
% 10.46/1.69 fof(f359,plain,(
% 10.46/1.69 ~spl0_0|spl0_1),
% 10.46/1.69 inference(split_clause,[status(thm)],[f95,f353,f356])).
% 10.46/1.69 fof(f372,plain,(
% 10.46/1.69 spl0_5 <=> substitution_of_equivalents),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f374,plain,(
% 10.46/1.69 ~substitution_of_equivalents|spl0_5),
% 10.46/1.69 inference(component_clause,[status(thm)],[f372])).
% 10.46/1.69 fof(f375,plain,(
% 10.46/1.69 spl0_6 <=> ~is_a_theorem(equiv(X0,X1))|X0=X1),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f376,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~spl0_6)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f375])).
% 10.46/1.69 fof(f378,plain,(
% 10.46/1.69 ~spl0_5|spl0_6),
% 10.46/1.69 inference(split_clause,[status(thm)],[f102,f372,f375])).
% 10.46/1.69 fof(f387,plain,(
% 10.46/1.69 spl0_9 <=> modus_tollens),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f389,plain,(
% 10.46/1.69 ~modus_tollens|spl0_9),
% 10.46/1.69 inference(component_clause,[status(thm)],[f387])).
% 10.46/1.69 fof(f390,plain,(
% 10.46/1.69 spl0_10 <=> is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f391,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))|~spl0_10)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f390])).
% 10.46/1.69 fof(f393,plain,(
% 10.46/1.69 ~spl0_9|spl0_10),
% 10.46/1.69 inference(split_clause,[status(thm)],[f107,f387,f390])).
% 10.46/1.69 fof(f398,plain,(
% 10.46/1.69 spl0_12 <=> implies_1),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f400,plain,(
% 10.46/1.69 ~implies_1|spl0_12),
% 10.46/1.69 inference(component_clause,[status(thm)],[f398])).
% 10.46/1.69 fof(f401,plain,(
% 10.46/1.69 spl0_13 <=> is_a_theorem(implies(X0,implies(X1,X0)))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f402,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~spl0_13)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f401])).
% 10.46/1.69 fof(f404,plain,(
% 10.46/1.69 ~spl0_12|spl0_13),
% 10.46/1.69 inference(split_clause,[status(thm)],[f111,f398,f401])).
% 10.46/1.69 fof(f409,plain,(
% 10.46/1.69 spl0_15 <=> implies_2),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f411,plain,(
% 10.46/1.69 ~implies_2|spl0_15),
% 10.46/1.69 inference(component_clause,[status(thm)],[f409])).
% 10.46/1.69 fof(f412,plain,(
% 10.46/1.69 spl0_16 <=> is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f413,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))|~spl0_16)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f412])).
% 10.46/1.69 fof(f415,plain,(
% 10.46/1.69 ~spl0_15|spl0_16),
% 10.46/1.69 inference(split_clause,[status(thm)],[f115,f409,f412])).
% 10.46/1.69 fof(f431,plain,(
% 10.46/1.69 spl0_21 <=> and_1),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f433,plain,(
% 10.46/1.69 ~and_1|spl0_21),
% 10.46/1.69 inference(component_clause,[status(thm)],[f431])).
% 10.46/1.69 fof(f434,plain,(
% 10.46/1.69 spl0_22 <=> is_a_theorem(implies(and(X0,X1),X0))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f435,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_22)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f434])).
% 10.46/1.69 fof(f437,plain,(
% 10.46/1.69 ~spl0_21|spl0_22),
% 10.46/1.69 inference(split_clause,[status(thm)],[f123,f431,f434])).
% 10.46/1.69 fof(f442,plain,(
% 10.46/1.69 spl0_24 <=> and_2),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f444,plain,(
% 10.46/1.69 ~and_2|spl0_24),
% 10.46/1.69 inference(component_clause,[status(thm)],[f442])).
% 10.46/1.69 fof(f445,plain,(
% 10.46/1.69 spl0_25 <=> is_a_theorem(implies(and(X0,X1),X1))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f446,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X1))|~spl0_25)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f445])).
% 10.46/1.69 fof(f448,plain,(
% 10.46/1.69 ~spl0_24|spl0_25),
% 10.46/1.69 inference(split_clause,[status(thm)],[f127,f442,f445])).
% 10.46/1.69 fof(f453,plain,(
% 10.46/1.69 spl0_27 <=> and_3),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f455,plain,(
% 10.46/1.69 ~and_3|spl0_27),
% 10.46/1.69 inference(component_clause,[status(thm)],[f453])).
% 10.46/1.69 fof(f456,plain,(
% 10.46/1.69 spl0_28 <=> is_a_theorem(implies(X0,implies(X1,and(X0,X1))))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f457,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1))))|~spl0_28)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f456])).
% 10.46/1.69 fof(f459,plain,(
% 10.46/1.69 ~spl0_27|spl0_28),
% 10.46/1.69 inference(split_clause,[status(thm)],[f131,f453,f456])).
% 10.46/1.69 fof(f464,plain,(
% 10.46/1.69 spl0_30 <=> or_1),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f466,plain,(
% 10.46/1.69 ~or_1|spl0_30),
% 10.46/1.69 inference(component_clause,[status(thm)],[f464])).
% 10.46/1.69 fof(f467,plain,(
% 10.46/1.69 spl0_31 <=> is_a_theorem(implies(X0,or(X0,X1)))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f468,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_31)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f467])).
% 10.46/1.69 fof(f470,plain,(
% 10.46/1.69 ~spl0_30|spl0_31),
% 10.46/1.69 inference(split_clause,[status(thm)],[f135,f464,f467])).
% 10.46/1.69 fof(f533,plain,(
% 10.46/1.69 spl0_49 <=> is_a_theorem(implies(X0,and(X0,X0)))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f534,plain,(
% 10.46/1.69 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_49)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f533])).
% 10.46/1.69 fof(f642,plain,(
% 10.46/1.69 spl0_78 <=> op_or),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f644,plain,(
% 10.46/1.69 ~op_or|spl0_78),
% 10.46/1.69 inference(component_clause,[status(thm)],[f642])).
% 10.46/1.69 fof(f645,plain,(
% 10.46/1.69 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f646,plain,(
% 10.46/1.69 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f645])).
% 10.46/1.69 fof(f648,plain,(
% 10.46/1.69 ~spl0_78|spl0_79),
% 10.46/1.69 inference(split_clause,[status(thm)],[f202,f642,f645])).
% 10.46/1.69 fof(f656,plain,(
% 10.46/1.69 spl0_82 <=> op_implies_and),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f658,plain,(
% 10.46/1.69 ~op_implies_and|spl0_82),
% 10.46/1.69 inference(component_clause,[status(thm)],[f656])).
% 10.46/1.69 fof(f659,plain,(
% 10.46/1.69 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f660,plain,(
% 10.46/1.69 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f659])).
% 10.46/1.69 fof(f662,plain,(
% 10.46/1.69 ~spl0_82|spl0_83),
% 10.46/1.69 inference(split_clause,[status(thm)],[f206,f656,f659])).
% 10.46/1.69 fof(f670,plain,(
% 10.46/1.69 spl0_86 <=> op_equiv),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f672,plain,(
% 10.46/1.69 ~op_equiv|spl0_86),
% 10.46/1.69 inference(component_clause,[status(thm)],[f670])).
% 10.46/1.69 fof(f673,plain,(
% 10.46/1.69 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f674,plain,(
% 10.46/1.69 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f673])).
% 10.46/1.69 fof(f676,plain,(
% 10.46/1.69 ~spl0_86|spl0_87),
% 10.46/1.69 inference(split_clause,[status(thm)],[f210,f670,f673])).
% 10.46/1.69 fof(f677,plain,(
% 10.46/1.69 spl0_88 <=> necessitation),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f679,plain,(
% 10.46/1.69 ~necessitation|spl0_88),
% 10.46/1.69 inference(component_clause,[status(thm)],[f677])).
% 10.46/1.69 fof(f680,plain,(
% 10.46/1.69 spl0_89 <=> ~is_a_theorem(X0)|is_a_theorem(necessarily(X0))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f681,plain,(
% 10.46/1.69 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0))|~spl0_89)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f680])).
% 10.46/1.69 fof(f683,plain,(
% 10.46/1.69 ~spl0_88|spl0_89),
% 10.46/1.69 inference(split_clause,[status(thm)],[f232,f677,f680])).
% 10.46/1.69 fof(f714,plain,(
% 10.46/1.69 spl0_98 <=> ~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f715,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))|~spl0_98)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f714])).
% 10.46/1.69 fof(f730,plain,(
% 10.46/1.69 spl0_102 <=> substitution_strict_equiv),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f733,plain,(
% 10.46/1.69 spl0_103 <=> ~is_a_theorem(strict_equiv(X0,X1))|X0=X1),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f734,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(strict_equiv(X0,X1))|X0=X1|~spl0_103)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f733])).
% 10.46/1.69 fof(f736,plain,(
% 10.46/1.69 ~spl0_102|spl0_103),
% 10.46/1.69 inference(split_clause,[status(thm)],[f253,f730,f733])).
% 10.46/1.69 fof(f737,plain,(
% 10.46/1.69 spl0_104 <=> is_a_theorem(strict_equiv(sk0_60,sk0_61))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f738,plain,(
% 10.46/1.69 is_a_theorem(strict_equiv(sk0_60,sk0_61))|~spl0_104),
% 10.46/1.69 inference(component_clause,[status(thm)],[f737])).
% 10.46/1.69 fof(f740,plain,(
% 10.46/1.69 spl0_102|spl0_104),
% 10.46/1.69 inference(split_clause,[status(thm)],[f254,f730,f737])).
% 10.46/1.69 fof(f741,plain,(
% 10.46/1.69 spl0_105 <=> sk0_60=sk0_61),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f744,plain,(
% 10.46/1.69 spl0_102|~spl0_105),
% 10.46/1.69 inference(split_clause,[status(thm)],[f255,f730,f741])).
% 10.46/1.69 fof(f756,plain,(
% 10.46/1.69 spl0_109 <=> axiom_M),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f758,plain,(
% 10.46/1.69 ~axiom_M|spl0_109),
% 10.46/1.69 inference(component_clause,[status(thm)],[f756])).
% 10.46/1.69 fof(f759,plain,(
% 10.46/1.69 spl0_110 <=> is_a_theorem(implies(necessarily(X0),X0))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f760,plain,(
% 10.46/1.69 ![X0]: (is_a_theorem(implies(necessarily(X0),X0))|~spl0_110)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f759])).
% 10.46/1.69 fof(f762,plain,(
% 10.46/1.69 ~spl0_109|spl0_110),
% 10.46/1.69 inference(split_clause,[status(thm)],[f262,f756,f759])).
% 10.46/1.69 fof(f844,plain,(
% 10.46/1.69 spl0_133 <=> axiom_m1),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f845,plain,(
% 10.46/1.69 axiom_m1|~spl0_133),
% 10.46/1.69 inference(component_clause,[status(thm)],[f844])).
% 10.46/1.69 fof(f851,plain,(
% 10.46/1.69 spl0_135 <=> is_a_theorem(strict_implies(and(sk0_76,sk0_77),and(sk0_77,sk0_76)))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f853,plain,(
% 10.46/1.69 ~is_a_theorem(strict_implies(and(sk0_76,sk0_77),and(sk0_77,sk0_76)))|spl0_135),
% 10.46/1.69 inference(component_clause,[status(thm)],[f851])).
% 10.46/1.69 fof(f854,plain,(
% 10.46/1.69 spl0_133|~spl0_135),
% 10.46/1.69 inference(split_clause,[status(thm)],[f295,f844,f851])).
% 10.46/1.69 fof(f880,plain,(
% 10.46/1.69 spl0_143 <=> is_a_theorem(strict_implies(X0,and(X0,X0)))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f881,plain,(
% 10.46/1.69 ![X0]: (is_a_theorem(strict_implies(X0,and(X0,X0)))|~spl0_143)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f880])).
% 10.46/1.69 fof(f968,plain,(
% 10.46/1.69 spl0_167 <=> op_strict_implies),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f970,plain,(
% 10.46/1.69 ~op_strict_implies|spl0_167),
% 10.46/1.69 inference(component_clause,[status(thm)],[f968])).
% 10.46/1.69 fof(f971,plain,(
% 10.46/1.69 spl0_168 <=> strict_implies(X0,X1)=necessarily(implies(X0,X1))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f972,plain,(
% 10.46/1.69 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1))|~spl0_168)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f971])).
% 10.46/1.69 fof(f974,plain,(
% 10.46/1.69 ~spl0_167|spl0_168),
% 10.46/1.69 inference(split_clause,[status(thm)],[f337,f968,f971])).
% 10.46/1.69 fof(f975,plain,(
% 10.46/1.69 spl0_169 <=> op_strict_equiv),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f977,plain,(
% 10.46/1.69 ~op_strict_equiv|spl0_169),
% 10.46/1.69 inference(component_clause,[status(thm)],[f975])).
% 10.46/1.69 fof(f978,plain,(
% 10.46/1.69 spl0_170 <=> strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f979,plain,(
% 10.46/1.69 ![X0,X1]: (strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))|~spl0_170)),
% 10.46/1.69 inference(component_clause,[status(thm)],[f978])).
% 10.46/1.69 fof(f981,plain,(
% 10.46/1.69 ~spl0_169|spl0_170),
% 10.46/1.69 inference(split_clause,[status(thm)],[f339,f975,f978])).
% 10.46/1.69 fof(f982,plain,(
% 10.46/1.69 $false|spl0_169),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f977,f351])).
% 10.46/1.69 fof(f983,plain,(
% 10.46/1.69 spl0_169),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f982])).
% 10.46/1.69 fof(f984,plain,(
% 10.46/1.69 $false|spl0_0),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f355,f214])).
% 10.46/1.69 fof(f985,plain,(
% 10.46/1.69 spl0_0),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f984])).
% 10.46/1.69 fof(f986,plain,(
% 10.46/1.69 $false|spl0_88),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f679,f341])).
% 10.46/1.69 fof(f987,plain,(
% 10.46/1.69 spl0_88),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f986])).
% 10.46/1.69 fof(f988,plain,(
% 10.46/1.69 $false|spl0_5),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f374,f228])).
% 10.46/1.69 fof(f989,plain,(
% 10.46/1.69 spl0_5),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f988])).
% 10.46/1.69 fof(f990,plain,(
% 10.46/1.69 $false|spl0_167),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f970,f349])).
% 10.46/1.69 fof(f991,plain,(
% 10.46/1.69 spl0_167),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f990])).
% 10.46/1.69 fof(f994,plain,(
% 10.46/1.69 $false|spl0_86),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f672,f213])).
% 10.46/1.69 fof(f995,plain,(
% 10.46/1.69 spl0_86),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f994])).
% 10.46/1.69 fof(f996,plain,(
% 10.46/1.69 $false|spl0_82),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f658,f212])).
% 10.46/1.69 fof(f997,plain,(
% 10.46/1.69 spl0_82),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f996])).
% 10.46/1.69 fof(f998,plain,(
% 10.46/1.69 $false|spl0_78),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f644,f211])).
% 10.46/1.69 fof(f999,plain,(
% 10.46/1.69 spl0_78),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f998])).
% 10.46/1.69 fof(f1013,plain,(
% 10.46/1.69 $false|spl0_109),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f758,f343])).
% 10.46/1.69 fof(f1014,plain,(
% 10.46/1.69 spl0_109),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f1013])).
% 10.46/1.69 fof(f1016,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1))|~spl0_89|~spl0_168)),
% 10.46/1.69 inference(paramodulation,[status(thm)],[f972,f681])).
% 10.46/1.69 fof(f1038,plain,(
% 10.46/1.69 $false|spl0_21),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f433,f219])).
% 10.46/1.69 fof(f1039,plain,(
% 10.46/1.69 spl0_21),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f1038])).
% 10.46/1.69 fof(f1052,plain,(
% 10.46/1.69 $false|spl0_30),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f466,f222])).
% 10.46/1.69 fof(f1053,plain,(
% 10.46/1.69 spl0_30),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f1052])).
% 10.46/1.69 fof(f1056,plain,(
% 10.46/1.69 $false|spl0_24),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f444,f220])).
% 10.46/1.69 fof(f1057,plain,(
% 10.46/1.69 spl0_24),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f1056])).
% 10.46/1.69 fof(f1061,plain,(
% 10.46/1.69 $false|spl0_12),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f400,f216])).
% 10.46/1.69 fof(f1062,plain,(
% 10.46/1.69 spl0_12),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f1061])).
% 10.46/1.69 fof(f1080,plain,(
% 10.46/1.69 ![X0]: (~is_a_theorem(necessarily(X0))|is_a_theorem(X0)|~spl0_1|~spl0_110)),
% 10.46/1.69 inference(resolution,[status(thm)],[f357,f760])).
% 10.46/1.69 fof(f1081,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(X1)|~spl0_1|~spl0_25)),
% 10.46/1.69 inference(resolution,[status(thm)],[f357,f446])).
% 10.46/1.69 fof(f1082,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(X0)|~spl0_1|~spl0_22)),
% 10.46/1.69 inference(resolution,[status(thm)],[f357,f435])).
% 10.46/1.69 fof(f1085,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,and(X0,X1)))|~spl0_1|~spl0_28)),
% 10.46/1.69 inference(resolution,[status(thm)],[f357,f457])).
% 10.46/1.69 fof(f1119,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(X0,X1))|~spl0_1|~spl0_110|~spl0_168)),
% 10.46/1.69 inference(paramodulation,[status(thm)],[f972,f1080])).
% 10.46/1.69 fof(f1120,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1))|~spl0_89|~spl0_168)),
% 10.46/1.69 inference(paramodulation,[status(thm)],[f972,f681])).
% 10.46/1.69 fof(f1161,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),X1))|~spl0_89|~spl0_168|~spl0_25)),
% 10.46/1.69 inference(resolution,[status(thm)],[f1016,f446])).
% 10.46/1.69 fof(f1297,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(strict_equiv(X0,X1))|is_a_theorem(strict_implies(X0,X1))|~spl0_1|~spl0_22|~spl0_170)),
% 10.46/1.69 inference(paramodulation,[status(thm)],[f979,f1082])).
% 10.46/1.69 fof(f1298,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(strict_equiv(X0,X1))|is_a_theorem(strict_implies(X1,X0))|~spl0_1|~spl0_25|~spl0_170)),
% 10.46/1.69 inference(paramodulation,[status(thm)],[f979,f1081])).
% 10.46/1.69 fof(f1302,plain,(
% 10.46/1.69 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 10.46/1.69 inference(forward_demodulation,[status(thm)],[f660,f646])).
% 10.46/1.69 fof(f1304,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0)))|~spl0_83|~spl0_79|~spl0_10)),
% 10.46/1.69 inference(backward_demodulation,[status(thm)],[f1302,f391])).
% 10.46/1.69 fof(f1374,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(or(X0,or(not(X0),X1)))|~spl0_31|~spl0_83|~spl0_79)),
% 10.46/1.69 inference(paramodulation,[status(thm)],[f1302,f468])).
% 10.46/1.69 fof(f1593,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(strict_implies(X1,X0))|is_a_theorem(strict_equiv(X0,X1))|~spl0_98|~spl0_170)),
% 10.46/1.69 inference(paramodulation,[status(thm)],[f979,f715])).
% 10.46/1.69 fof(f1594,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1))|~spl0_98|~spl0_87)),
% 10.46/1.69 inference(paramodulation,[status(thm)],[f674,f715])).
% 10.46/1.69 fof(f1619,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1))|~spl0_1|~spl0_16)),
% 10.46/1.69 inference(resolution,[status(thm)],[f357,f413])).
% 10.46/1.69 fof(f1644,plain,(
% 10.46/1.69 $false|spl0_27),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f455,f221])).
% 10.46/1.69 fof(f1645,plain,(
% 10.46/1.69 spl0_27),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f1644])).
% 10.46/1.69 fof(f1683,plain,(
% 10.46/1.69 is_a_theorem(strict_implies(sk0_60,sk0_61))|~spl0_1|~spl0_22|~spl0_170|~spl0_104),
% 10.46/1.69 inference(resolution,[status(thm)],[f1297,f738])).
% 10.46/1.69 fof(f1696,plain,(
% 10.46/1.69 is_a_theorem(strict_implies(sk0_61,sk0_60))|~spl0_1|~spl0_25|~spl0_170|~spl0_104),
% 10.46/1.69 inference(resolution,[status(thm)],[f1298,f738])).
% 10.46/1.69 fof(f1748,plain,(
% 10.46/1.69 $false|spl0_15),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f411,f217])).
% 10.46/1.69 fof(f1749,plain,(
% 10.46/1.69 spl0_15),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f1748])).
% 10.46/1.69 fof(f1837,plain,(
% 10.46/1.69 $false|spl0_9),
% 10.46/1.69 inference(forward_subsumption_resolution,[status(thm)],[f389,f215])).
% 10.46/1.69 fof(f1838,plain,(
% 10.46/1.69 spl0_9),
% 10.46/1.69 inference(contradiction_clause,[status(thm)],[f1837])).
% 10.46/1.69 fof(f1841,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(or(X0,not(X1)))|is_a_theorem(implies(X1,X0))|~spl0_83|~spl0_79|~spl0_10|~spl0_1)),
% 10.46/1.69 inference(resolution,[status(thm)],[f1304,f357])).
% 10.46/1.69 fof(f1842,plain,(
% 10.46/1.69 ![X0,X1]: (is_a_theorem(strict_implies(or(X0,not(X1)),implies(X1,X0)))|~spl0_83|~spl0_79|~spl0_10|~spl0_89|~spl0_168)),
% 10.46/1.69 inference(resolution,[status(thm)],[f1304,f1120])).
% 10.46/1.69 fof(f2328,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(strict_implies(X1,X0))|is_a_theorem(strict_equiv(X0,X1))|~spl0_98|~spl0_170)),
% 10.46/1.69 inference(paramodulation,[status(thm)],[f979,f715])).
% 10.46/1.69 fof(f2329,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1))|~spl0_98|~spl0_87)),
% 10.46/1.69 inference(paramodulation,[status(thm)],[f674,f715])).
% 10.46/1.69 fof(f3301,plain,(
% 10.46/1.69 spl0_193 <=> is_a_theorem(strict_implies(sk0_61,sk0_60))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f3302,plain,(
% 10.46/1.69 is_a_theorem(strict_implies(sk0_61,sk0_60))|~spl0_193),
% 10.46/1.69 inference(component_clause,[status(thm)],[f3301])).
% 10.46/1.69 fof(f3316,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(strict_implies(X0,and(X1,X0)))|is_a_theorem(strict_equiv(X0,and(X1,X0)))|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25)),
% 10.46/1.69 inference(resolution,[status(thm)],[f1593,f1161])).
% 10.46/1.69 fof(f3662,plain,(
% 10.46/1.69 is_a_theorem(implies(sk0_61,sk0_60))|~spl0_193|~spl0_1|~spl0_110|~spl0_168),
% 10.46/1.69 inference(resolution,[status(thm)],[f3302,f1119])).
% 10.46/1.69 fof(f3670,plain,(
% 10.46/1.69 spl0_195 <=> is_a_theorem(implies(sk0_60,sk0_61))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f3673,plain,(
% 10.46/1.69 spl0_196 <=> is_a_theorem(equiv(sk0_60,sk0_61))),
% 10.46/1.69 introduced(split_symbol_definition)).
% 10.46/1.69 fof(f3674,plain,(
% 10.46/1.69 is_a_theorem(equiv(sk0_60,sk0_61))|~spl0_196),
% 10.46/1.69 inference(component_clause,[status(thm)],[f3673])).
% 10.46/1.69 fof(f3676,plain,(
% 10.46/1.69 ~is_a_theorem(implies(sk0_60,sk0_61))|is_a_theorem(equiv(sk0_60,sk0_61))|~spl0_193|~spl0_1|~spl0_110|~spl0_168|~spl0_98|~spl0_87),
% 10.46/1.69 inference(resolution,[status(thm)],[f3662,f1594])).
% 10.46/1.69 fof(f3677,plain,(
% 10.46/1.69 ~spl0_195|spl0_196|~spl0_193|~spl0_1|~spl0_110|~spl0_168|~spl0_98|~spl0_87),
% 10.46/1.69 inference(split_clause,[status(thm)],[f3676,f3670,f3673,f3301,f356,f759,f971,f714,f673])).
% 10.46/1.69 fof(f3698,plain,(
% 10.46/1.69 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))|~spl0_28|~spl0_1)),
% 10.46/1.69 inference(resolution,[status(thm)],[f1085,f357])).
% 10.46/1.69 fof(f3699,plain,(
% 10.46/1.69 spl0_98|~spl0_28|~spl0_1),
% 10.46/1.69 inference(split_clause,[status(thm)],[f3698,f714,f456,f356])).
% 10.46/1.69 fof(f3823,plain,(
% 10.46/1.69 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_1|~spl0_16|~spl0_28)),
% 10.46/1.69 inference(resolution,[status(thm)],[f1619,f457])).
% 10.46/1.69 fof(f3824,plain,(
% 10.46/1.69 spl0_49|~spl0_1|~spl0_16|~spl0_28),
% 10.46/1.69 inference(split_clause,[status(thm)],[f3823,f533,f356,f412,f456])).
% 10.46/1.69 fof(f3825,plain,(
% 10.46/1.69 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_1|~spl0_16|~spl0_13)),
% 10.46/1.69 inference(resolution,[status(thm)],[f1619,f402])).
% 10.46/1.69 fof(f3834,plain,(
% 10.46/1.69 ![X0]: (is_a_theorem(strict_implies(X0,and(X0,X0)))|~spl0_49|~spl0_89|~spl0_168)),
% 10.46/1.69 inference(resolution,[status(thm)],[f534,f1120])).
% 10.46/1.69 fof(f3835,plain,(
% 10.46/1.69 spl0_143|~spl0_49|~spl0_89|~spl0_168),
% 10.46/1.69 inference(split_clause,[status(thm)],[f3834,f880,f533,f680,f971])).
% 10.46/1.69 fof(f3861,plain,(
% 10.46/1.69 ![X0]: (is_a_theorem(strict_equiv(X0,and(X0,X0)))|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143)),
% 10.46/1.69 inference(resolution,[status(thm)],[f3316,f881])).
% 10.46/1.69 fof(f4264,plain,(
% 10.46/1.69 ![X0]: (is_a_theorem(strict_implies(X0,X0))|~spl0_1|~spl0_16|~spl0_13|~spl0_89|~spl0_168)),
% 10.46/1.69 inference(resolution,[status(thm)],[f3825,f1120])).
% 10.46/1.69 fof(f4292,plain,(
% 10.46/1.69 ![X0]: (X0=and(X0,X0)|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103)),
% 10.46/1.70 inference(resolution,[status(thm)],[f3861,f734])).
% 10.46/1.70 fof(f4314,plain,(
% 10.46/1.70 ![X0]: (implies(not(X0),X0)=not(not(X0))|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103)),
% 10.46/1.70 inference(paramodulation,[status(thm)],[f4292,f660])).
% 10.46/1.70 fof(f4315,plain,(
% 10.46/1.70 ![X0]: (or(X0,X0)=not(not(X0))|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103)),
% 10.46/1.70 inference(forward_demodulation,[status(thm)],[f1302,f4314])).
% 10.46/1.70 fof(f4559,plain,(
% 10.46/1.70 ![X0]: (is_a_theorem(or(X0,not(not(not(X0)))))|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103)),
% 10.46/1.70 inference(paramodulation,[status(thm)],[f4315,f1374])).
% 10.46/1.70 fof(f4609,plain,(
% 10.46/1.70 ![X0]: (is_a_theorem(implies(X0,not(not(X0))))|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103)),
% 10.46/1.70 inference(paramodulation,[status(thm)],[f4315,f468])).
% 10.46/1.70 fof(f4843,plain,(
% 10.46/1.70 ![X0]: (is_a_theorem(implies(not(not(X0)),X0))|~spl0_31|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_83|~spl0_79|~spl0_10|~spl0_1)),
% 10.46/1.70 inference(resolution,[status(thm)],[f4559,f1841])).
% 10.46/1.70 fof(f4844,plain,(
% 10.46/1.70 ![X0]: (is_a_theorem(or(not(X0),X0))|~spl0_31|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_83|~spl0_79|~spl0_10|~spl0_1)),
% 10.46/1.70 inference(forward_demodulation,[status(thm)],[f1302,f4843])).
% 10.46/1.70 fof(f4870,plain,(
% 10.46/1.70 spl0_193|~spl0_1|~spl0_25|~spl0_170|~spl0_104),
% 10.46/1.70 inference(split_clause,[status(thm)],[f1696,f3301,f356,f445,f978,f737])).
% 10.46/1.70 fof(f4919,plain,(
% 10.46/1.70 is_a_theorem(implies(sk0_60,sk0_61))|~spl0_22|~spl0_170|~spl0_104|~spl0_1|~spl0_110|~spl0_168),
% 10.46/1.70 inference(resolution,[status(thm)],[f1683,f1119])).
% 10.46/1.70 fof(f4920,plain,(
% 10.46/1.70 spl0_195|~spl0_22|~spl0_170|~spl0_104|~spl0_1|~spl0_110|~spl0_168),
% 10.46/1.70 inference(split_clause,[status(thm)],[f4919,f3670,f434,f978,f737,f356,f759,f971])).
% 10.46/1.70 fof(f4923,plain,(
% 10.46/1.70 sk0_60=sk0_61|~spl0_196|~spl0_6),
% 10.46/1.70 inference(resolution,[status(thm)],[f3674,f376])).
% 10.46/1.70 fof(f4924,plain,(
% 10.46/1.70 spl0_105|~spl0_196|~spl0_6),
% 10.46/1.70 inference(split_clause,[status(thm)],[f4923,f741,f3673,f375])).
% 10.46/1.70 fof(f6041,plain,(
% 10.46/1.70 ![X0]: (~is_a_theorem(implies(not(not(X0)),X0))|is_a_theorem(equiv(not(not(X0)),X0))|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103)),
% 10.46/1.70 inference(resolution,[status(thm)],[f2329,f4609])).
% 10.46/1.70 fof(f6042,plain,(
% 10.46/1.70 ![X0]: (~is_a_theorem(or(not(X0),X0))|is_a_theorem(equiv(not(not(X0)),X0))|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103)),
% 10.46/1.70 inference(forward_demodulation,[status(thm)],[f1302,f6041])).
% 10.46/1.70 fof(f6043,plain,(
% 10.46/1.70 ![X0]: (is_a_theorem(equiv(not(not(X0)),X0))|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103)),
% 10.46/1.70 inference(forward_subsumption_resolution,[status(thm)],[f6042,f4844])).
% 10.46/1.70 fof(f6110,plain,(
% 10.46/1.70 ![X0]: (not(not(X0))=X0|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6)),
% 10.46/1.70 inference(resolution,[status(thm)],[f6043,f376])).
% 10.46/1.70 fof(f6132,plain,(
% 10.46/1.70 ![X0,X1]: (not(implies(X0,X1))=and(X0,not(X1))|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6|~spl0_83)),
% 10.46/1.70 inference(paramodulation,[status(thm)],[f660,f6110])).
% 10.46/1.70 fof(f6179,plain,(
% 10.46/1.70 ![X0,X1]: (is_a_theorem(strict_implies(or(X0,X1),implies(not(X1),X0)))|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6)),
% 10.46/1.70 inference(paramodulation,[status(thm)],[f6110,f1842])).
% 10.46/1.70 fof(f6180,plain,(
% 10.46/1.70 ![X0,X1]: (is_a_theorem(strict_implies(or(X0,X1),or(X1,X0)))|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6)),
% 10.46/1.70 inference(forward_demodulation,[status(thm)],[f1302,f6179])).
% 10.46/1.70 fof(f6203,plain,(
% 10.46/1.70 ![X0,X1]: (or(not(X0),X1)=implies(X0,X1)|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6)),
% 10.46/1.72 inference(paramodulation,[status(thm)],[f6110,f1302])).
% 10.46/1.72 fof(f6206,plain,(
% 10.46/1.72 ![X0,X1]: (~is_a_theorem(strict_implies(or(X0,X1),or(X1,X0)))|is_a_theorem(strict_equiv(or(X0,X1),or(X1,X0)))|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6|~spl0_98|~spl0_170)),
% 10.46/1.72 inference(resolution,[status(thm)],[f6180,f2328])).
% 10.46/1.72 fof(f6207,plain,(
% 10.46/1.72 ![X0,X1]: (is_a_theorem(strict_equiv(or(X0,X1),or(X1,X0)))|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6|~spl0_98|~spl0_170)),
% 10.46/1.72 inference(forward_subsumption_resolution,[status(thm)],[f6206,f6180])).
% 10.46/1.72 fof(f6992,plain,(
% 10.46/1.72 ![X0,X1]: (not(implies(X0,not(X1)))=and(X0,X1)|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6)),
% 10.46/1.72 inference(paramodulation,[status(thm)],[f6110,f6132])).
% 10.46/1.72 fof(f7130,plain,(
% 10.46/1.72 ![X0,X1]: (or(X0,X1)=or(X1,X0)|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_6|~spl0_98|~spl0_170|~spl0_103)),
% 10.46/1.72 inference(resolution,[status(thm)],[f6207,f734])).
% 10.46/1.72 fof(f7141,plain,(
% 10.46/1.72 ![X0,X1]: (implies(X0,X1)=or(X1,not(X0))|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6)),
% 10.46/1.72 inference(paramodulation,[status(thm)],[f6203,f7130])).
% 10.46/1.72 fof(f7341,plain,(
% 10.46/1.72 ![X0,X1]: (implies(X0,not(X1))=implies(X1,not(X0))|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6)),
% 10.46/1.72 inference(paramodulation,[status(thm)],[f6203,f7141])).
% 10.46/1.72 fof(f7911,plain,(
% 10.46/1.72 ![X0,X1]: (not(implies(X0,not(X1)))=and(X1,X0)|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6)),
% 10.46/1.72 inference(paramodulation,[status(thm)],[f7341,f6992])).
% 10.46/1.72 fof(f7912,plain,(
% 10.46/1.72 ![X0,X1]: (and(X0,X1)=and(X1,X0)|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6)),
% 10.46/1.72 inference(forward_demodulation,[status(thm)],[f6992,f7911])).
% 10.46/1.72 fof(f8136,plain,(
% 10.46/1.72 ~is_a_theorem(strict_implies(and(sk0_76,sk0_77),and(sk0_76,sk0_77)))|spl0_135|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6),
% 10.46/1.72 inference(paramodulation,[status(thm)],[f7912,f853])).
% 10.46/1.72 fof(f8137,plain,(
% 10.46/1.72 $false|~spl0_16|~spl0_13|spl0_135|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6),
% 10.46/1.72 inference(forward_subsumption_resolution,[status(thm)],[f8136,f4264])).
% 10.46/1.72 fof(f8138,plain,(
% 10.46/1.72 ~spl0_16|~spl0_13|spl0_135|~spl0_10|~spl0_1|~spl0_87|~spl0_31|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_89|~spl0_168|~spl0_25|~spl0_143|~spl0_103|~spl0_6),
% 10.46/1.72 inference(contradiction_clause,[status(thm)],[f8137])).
% 10.46/1.72 fof(f8209,plain,(
% 10.46/1.72 $false|~spl0_133),
% 10.46/1.72 inference(forward_subsumption_resolution,[status(thm)],[f845,f352])).
% 10.46/1.72 fof(f8210,plain,(
% 10.46/1.72 ~spl0_133),
% 10.46/1.72 inference(contradiction_clause,[status(thm)],[f8209])).
% 10.46/1.72 fof(f8211,plain,(
% 10.46/1.72 $false),
% 10.46/1.72 inference(sat_refutation,[status(thm)],[f359,f378,f393,f404,f415,f437,f448,f459,f470,f648,f662,f676,f683,f736,f740,f744,f762,f854,f974,f981,f983,f985,f987,f989,f991,f995,f997,f999,f1014,f1039,f1053,f1057,f1062,f1645,f1749,f1838,f3677,f3699,f3824,f3835,f4870,f4920,f4924,f8138,f8210])).
% 10.46/1.72 % SZS output end CNFRefutation for theBenchmark.p
% 10.46/1.75 % Elapsed time: 1.391186 seconds
% 10.46/1.75 % CPU time: 10.776118 seconds
% 10.46/1.75 % Total memory used: 275.818 MB
% 10.46/1.75 % Net memory used: 267.573 MB
%------------------------------------------------------------------------------