TSTP Solution File: LCL558+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL558+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 : Wed May 31 12:19:36 EDT 2023
% Result : Theorem 88.53s 11.60s
% Output : CNFRefutation 92.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : LCL558+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 09:57:04 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 88.53/11.60 % Refutation found
% 88.53/11.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 88.53/11.60 % SZS output start CNFRefutation for theBenchmark
% 88.53/11.60 fof(f2,axiom,(
% 88.53/11.60 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f10,axiom,(
% 88.53/11.60 ( or_1<=> (! [X,Y] : is_a_theorem(implies(X,or(X,Y))) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f27,axiom,(
% 88.53/11.60 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f29,axiom,(
% 88.53/11.60 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f31,axiom,(
% 88.53/11.60 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f33,axiom,(
% 88.53/11.60 ( modus_ponens_strict_implies<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(strict_implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f34,axiom,(
% 88.53/11.60 ( adjunction<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(Y) )=> is_a_theorem(and(X,Y)) ) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f35,axiom,(
% 88.53/11.60 ( substitution_strict_equiv<=> (! [X,Y] :( is_a_theorem(strict_equiv(X,Y))=> X = Y ) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f45,axiom,(
% 88.53/11.60 ( axiom_m1<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f46,axiom,(
% 88.53/11.60 ( axiom_m2<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f47,axiom,(
% 88.53/11.60 ( axiom_m3<=> (! [X,Y,Z] : is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z)))) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f48,axiom,(
% 88.53/11.60 ( axiom_m4<=> (! [X] : is_a_theorem(strict_implies(X,and(X,X))) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f49,axiom,(
% 88.53/11.60 ( axiom_m5<=> (! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z))) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f57,axiom,(
% 88.53/11.60 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f58,axiom,(
% 88.53/11.60 ( op_strict_equiv=> (! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) )) ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f60,axiom,(
% 88.53/11.60 op_or ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f62,axiom,(
% 88.53/11.60 op_strict_implies ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f63,axiom,(
% 88.53/11.60 op_equiv ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f64,axiom,(
% 88.53/11.60 op_strict_equiv ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f65,axiom,(
% 88.53/11.60 modus_ponens_strict_implies ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f66,axiom,(
% 88.53/11.60 substitution_strict_equiv ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f67,axiom,(
% 88.53/11.60 adjunction ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f68,axiom,(
% 88.53/11.60 axiom_m1 ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f69,axiom,(
% 88.53/11.60 axiom_m2 ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f70,axiom,(
% 88.53/11.60 axiom_m3 ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f71,axiom,(
% 88.53/11.60 axiom_m4 ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f72,axiom,(
% 88.53/11.60 axiom_m5 ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f74,axiom,(
% 88.53/11.60 op_implies_and ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f76,axiom,(
% 88.53/11.60 substitution_of_equivalents ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.60 fof(f77,conjecture,(
% 88.53/11.60 or_1 ),
% 88.53/11.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 88.53/11.61 fof(f78,negated_conjecture,(
% 88.53/11.61 ~(or_1 )),
% 88.53/11.61 inference(negated_conjecture,[status(cth)],[f77])).
% 88.53/11.61 fof(f87,plain,(
% 88.53/11.61 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 88.53/11.61 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 88.53/11.61 fof(f88,plain,(
% 88.53/11.61 (~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)))),
% 88.53/11.61 inference(NNF_transformation,[status(esa)],[f87])).
% 88.53/11.61 fof(f89,plain,(
% 88.53/11.61 (~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))),
% 88.53/11.61 inference(skolemization,[status(esa)],[f88])).
% 88.53/11.61 fof(f90,plain,(
% 88.53/11.61 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f89])).
% 88.53/11.61 fof(f121,plain,(
% 88.53/11.61 (~or_1|(![X,Y]: is_a_theorem(implies(X,or(X,Y)))))&(or_1|(?[X,Y]: ~is_a_theorem(implies(X,or(X,Y)))))),
% 88.53/11.61 inference(NNF_transformation,[status(esa)],[f10])).
% 88.53/11.61 fof(f122,plain,(
% 88.53/11.61 (~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))))),
% 88.53/11.61 inference(skolemization,[status(esa)],[f121])).
% 88.53/11.61 fof(f124,plain,(
% 88.53/11.61 or_1|~is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20)))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f122])).
% 88.53/11.61 fof(f189,plain,(
% 88.53/11.61 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 88.53/11.61 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 88.53/11.61 fof(f190,plain,(
% 88.53/11.61 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f189])).
% 88.53/11.61 fof(f193,plain,(
% 88.53/11.61 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 88.53/11.61 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 88.53/11.61 fof(f194,plain,(
% 88.53/11.61 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f193])).
% 88.53/11.61 fof(f197,plain,(
% 88.53/11.61 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 88.53/11.61 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 88.53/11.61 fof(f198,plain,(
% 88.53/11.61 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f197])).
% 88.53/11.61 fof(f205,plain,(
% 88.53/11.61 modus_ponens_strict_implies<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y)))|is_a_theorem(Y)))),
% 88.53/11.61 inference(pre_NNF_transformation,[status(esa)],[f33])).
% 88.53/11.61 fof(f206,plain,(
% 88.53/11.61 (~modus_ponens_strict_implies|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y)))|is_a_theorem(Y))))&(modus_ponens_strict_implies|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(strict_implies(X,Y)))&~is_a_theorem(Y))))),
% 88.53/11.61 inference(NNF_transformation,[status(esa)],[f205])).
% 88.53/11.61 fof(f207,plain,(
% 88.53/11.61 (~modus_ponens_strict_implies|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens_strict_implies|(?[Y]: ((?[X]: (is_a_theorem(X)&is_a_theorem(strict_implies(X,Y))))&~is_a_theorem(Y))))),
% 88.53/11.61 inference(miniscoping,[status(esa)],[f206])).
% 88.53/11.61 fof(f208,plain,(
% 88.53/11.61 (~modus_ponens_strict_implies|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens_strict_implies|((is_a_theorem(sk0_57)&is_a_theorem(strict_implies(sk0_57,sk0_56)))&~is_a_theorem(sk0_56)))),
% 88.53/11.61 inference(skolemization,[status(esa)],[f207])).
% 88.53/11.61 fof(f209,plain,(
% 88.53/11.61 ![X0,X1]: (~modus_ponens_strict_implies|~is_a_theorem(X0)|~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(X1))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f208])).
% 88.53/11.61 fof(f213,plain,(
% 88.53/11.61 adjunction<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y))))),
% 88.53/11.61 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 88.53/11.61 fof(f214,plain,(
% 88.53/11.61 (~adjunction|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y)))))&(adjunction|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(Y))&~is_a_theorem(and(X,Y)))))),
% 88.53/11.61 inference(NNF_transformation,[status(esa)],[f213])).
% 88.53/11.61 fof(f215,plain,(
% 88.53/11.61 (~adjunction|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y)))))&(adjunction|((is_a_theorem(sk0_58)&is_a_theorem(sk0_59))&~is_a_theorem(and(sk0_58,sk0_59))))),
% 88.53/11.61 inference(skolemization,[status(esa)],[f214])).
% 88.53/11.61 fof(f216,plain,(
% 88.53/11.61 ![X0,X1]: (~adjunction|~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1)))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f215])).
% 88.53/11.61 fof(f220,plain,(
% 88.53/11.61 substitution_strict_equiv<=>(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y))),
% 88.53/11.61 inference(pre_NNF_transformation,[status(esa)],[f35])).
% 88.53/11.61 fof(f221,plain,(
% 88.53/11.61 (~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)))),
% 88.53/11.61 inference(NNF_transformation,[status(esa)],[f220])).
% 88.53/11.61 fof(f222,plain,(
% 88.53/11.61 (~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))),
% 88.53/11.61 inference(skolemization,[status(esa)],[f221])).
% 88.53/11.61 fof(f223,plain,(
% 88.53/11.61 ![X0,X1]: (~substitution_strict_equiv|~is_a_theorem(strict_equiv(X0,X1))|X0=X1)),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f222])).
% 88.53/11.61 fof(f262,plain,(
% 88.53/11.61 (~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)))))),
% 88.53/11.61 inference(NNF_transformation,[status(esa)],[f45])).
% 88.53/11.61 fof(f263,plain,(
% 88.53/11.61 (~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))))),
% 88.53/11.61 inference(skolemization,[status(esa)],[f262])).
% 88.53/11.61 fof(f264,plain,(
% 88.53/11.61 ![X0,X1]: (~axiom_m1|is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f263])).
% 88.53/11.61 fof(f266,plain,(
% 88.53/11.61 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|(?[X,Y]: ~is_a_theorem(strict_implies(and(X,Y),X))))),
% 88.53/11.61 inference(NNF_transformation,[status(esa)],[f46])).
% 88.53/11.61 fof(f267,plain,(
% 88.53/11.61 (~axiom_m2|(![X,Y]: is_a_theorem(strict_implies(and(X,Y),X))))&(axiom_m2|~is_a_theorem(strict_implies(and(sk0_78,sk0_79),sk0_78)))),
% 88.53/11.61 inference(skolemization,[status(esa)],[f266])).
% 88.53/11.61 fof(f268,plain,(
% 88.53/11.61 ![X0,X1]: (~axiom_m2|is_a_theorem(strict_implies(and(X0,X1),X0)))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f267])).
% 88.53/11.61 fof(f270,plain,(
% 88.53/11.61 (~axiom_m3|(![X,Y,Z]: is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))))&(axiom_m3|(?[X,Y,Z]: ~is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))))),
% 88.53/11.61 inference(NNF_transformation,[status(esa)],[f47])).
% 88.53/11.61 fof(f271,plain,(
% 88.53/11.61 (~axiom_m3|(![X,Y,Z]: is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))))&(axiom_m3|~is_a_theorem(strict_implies(and(and(sk0_80,sk0_81),sk0_82),and(sk0_80,and(sk0_81,sk0_82)))))),
% 88.53/11.61 inference(skolemization,[status(esa)],[f270])).
% 88.53/11.61 fof(f272,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~axiom_m3|is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f271])).
% 88.53/11.61 fof(f274,plain,(
% 88.53/11.61 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|(?[X]: ~is_a_theorem(strict_implies(X,and(X,X)))))),
% 88.53/11.61 inference(NNF_transformation,[status(esa)],[f48])).
% 88.53/11.61 fof(f275,plain,(
% 88.53/11.61 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|~is_a_theorem(strict_implies(sk0_83,and(sk0_83,sk0_83))))),
% 88.53/11.61 inference(skolemization,[status(esa)],[f274])).
% 88.53/11.61 fof(f276,plain,(
% 88.53/11.61 ![X0]: (~axiom_m4|is_a_theorem(strict_implies(X0,and(X0,X0))))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f275])).
% 88.53/11.61 fof(f278,plain,(
% 88.53/11.61 (~axiom_m5|(![X,Y,Z]: is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))))&(axiom_m5|(?[X,Y,Z]: ~is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))))),
% 88.53/11.61 inference(NNF_transformation,[status(esa)],[f49])).
% 88.53/11.61 fof(f279,plain,(
% 88.53/11.61 (~axiom_m5|(![X,Y,Z]: is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))))&(axiom_m5|~is_a_theorem(strict_implies(and(strict_implies(sk0_84,sk0_85),strict_implies(sk0_85,sk0_86)),strict_implies(sk0_84,sk0_86))))),
% 88.53/11.61 inference(skolemization,[status(esa)],[f278])).
% 88.53/11.61 fof(f280,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~axiom_m5|is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f279])).
% 88.53/11.61 fof(f306,plain,(
% 88.53/11.61 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 88.53/11.61 inference(pre_NNF_transformation,[status(esa)],[f57])).
% 88.53/11.61 fof(f307,plain,(
% 88.53/11.61 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f306])).
% 88.53/11.61 fof(f308,plain,(
% 88.53/11.61 ~op_strict_equiv|(![X,Y]: strict_equiv(X,Y)=and(strict_implies(X,Y),strict_implies(Y,X)))),
% 88.53/11.61 inference(pre_NNF_transformation,[status(esa)],[f58])).
% 88.53/11.61 fof(f309,plain,(
% 88.53/11.61 ![X0,X1]: (~op_strict_equiv|strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0)))),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f308])).
% 88.53/11.61 fof(f311,plain,(
% 88.53/11.61 op_or),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f60])).
% 88.53/11.61 fof(f313,plain,(
% 88.53/11.61 op_strict_implies),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f62])).
% 88.53/11.61 fof(f314,plain,(
% 88.53/11.61 op_equiv),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f63])).
% 88.53/11.61 fof(f315,plain,(
% 88.53/11.61 op_strict_equiv),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f64])).
% 88.53/11.61 fof(f316,plain,(
% 88.53/11.61 modus_ponens_strict_implies),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f65])).
% 88.53/11.61 fof(f317,plain,(
% 88.53/11.61 substitution_strict_equiv),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f66])).
% 88.53/11.61 fof(f318,plain,(
% 88.53/11.61 adjunction),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f67])).
% 88.53/11.61 fof(f319,plain,(
% 88.53/11.61 axiom_m1),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f68])).
% 88.53/11.61 fof(f320,plain,(
% 88.53/11.61 axiom_m2),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f69])).
% 88.53/11.61 fof(f321,plain,(
% 88.53/11.61 axiom_m3),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f70])).
% 88.53/11.61 fof(f322,plain,(
% 88.53/11.61 axiom_m4),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f71])).
% 88.53/11.61 fof(f323,plain,(
% 88.53/11.61 axiom_m5),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f72])).
% 88.53/11.61 fof(f325,plain,(
% 88.53/11.61 op_implies_and),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f74])).
% 88.53/11.61 fof(f327,plain,(
% 88.53/11.61 substitution_of_equivalents),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f76])).
% 88.53/11.61 fof(f328,plain,(
% 88.53/11.61 ~or_1),
% 88.53/11.61 inference(cnf_transformation,[status(esa)],[f78])).
% 88.53/11.61 fof(f348,plain,(
% 88.53/11.61 spl0_5 <=> substitution_of_equivalents),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f350,plain,(
% 88.53/11.61 ~substitution_of_equivalents|spl0_5),
% 88.53/11.61 inference(component_clause,[status(thm)],[f348])).
% 88.53/11.61 fof(f351,plain,(
% 88.53/11.61 spl0_6 <=> ~is_a_theorem(equiv(X0,X1))|X0=X1),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f352,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~spl0_6)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f351])).
% 88.53/11.61 fof(f354,plain,(
% 88.53/11.61 ~spl0_5|spl0_6),
% 88.53/11.61 inference(split_clause,[status(thm)],[f90,f348,f351])).
% 88.53/11.61 fof(f410,plain,(
% 88.53/11.61 spl0_22 <=> is_a_theorem(implies(and(X0,X1),X0))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f411,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_22)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f410])).
% 88.53/11.61 fof(f440,plain,(
% 88.53/11.61 spl0_30 <=> or_1),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f441,plain,(
% 88.53/11.61 or_1|~spl0_30),
% 88.53/11.61 inference(component_clause,[status(thm)],[f440])).
% 88.53/11.61 fof(f443,plain,(
% 88.53/11.61 spl0_31 <=> is_a_theorem(implies(X0,or(X0,X1)))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f444,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_31)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f443])).
% 88.53/11.61 fof(f447,plain,(
% 88.53/11.61 spl0_32 <=> is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20)))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f449,plain,(
% 88.53/11.61 ~is_a_theorem(implies(sk0_19,or(sk0_19,sk0_20)))|spl0_32),
% 88.53/11.61 inference(component_clause,[status(thm)],[f447])).
% 88.53/11.61 fof(f450,plain,(
% 88.53/11.61 spl0_30|~spl0_32),
% 88.53/11.61 inference(split_clause,[status(thm)],[f124,f440,f447])).
% 88.53/11.61 fof(f618,plain,(
% 88.53/11.61 spl0_78 <=> op_or),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f620,plain,(
% 88.53/11.61 ~op_or|spl0_78),
% 88.53/11.61 inference(component_clause,[status(thm)],[f618])).
% 88.53/11.61 fof(f621,plain,(
% 88.53/11.61 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f622,plain,(
% 88.53/11.61 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f621])).
% 88.53/11.61 fof(f624,plain,(
% 88.53/11.61 ~spl0_78|spl0_79),
% 88.53/11.61 inference(split_clause,[status(thm)],[f190,f618,f621])).
% 88.53/11.61 fof(f632,plain,(
% 88.53/11.61 spl0_82 <=> op_implies_and),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f634,plain,(
% 88.53/11.61 ~op_implies_and|spl0_82),
% 88.53/11.61 inference(component_clause,[status(thm)],[f632])).
% 88.53/11.61 fof(f635,plain,(
% 88.53/11.61 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f636,plain,(
% 88.53/11.61 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f635])).
% 88.53/11.61 fof(f638,plain,(
% 88.53/11.61 ~spl0_82|spl0_83),
% 88.53/11.61 inference(split_clause,[status(thm)],[f194,f632,f635])).
% 88.53/11.61 fof(f646,plain,(
% 88.53/11.61 spl0_86 <=> op_equiv),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f648,plain,(
% 88.53/11.61 ~op_equiv|spl0_86),
% 88.53/11.61 inference(component_clause,[status(thm)],[f646])).
% 88.53/11.61 fof(f649,plain,(
% 88.53/11.61 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f650,plain,(
% 88.53/11.61 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f649])).
% 88.53/11.61 fof(f652,plain,(
% 88.53/11.61 ~spl0_86|spl0_87),
% 88.53/11.61 inference(split_clause,[status(thm)],[f198,f646,f649])).
% 88.53/11.61 fof(f668,plain,(
% 88.53/11.61 spl0_92 <=> modus_ponens_strict_implies),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f670,plain,(
% 88.53/11.61 ~modus_ponens_strict_implies|spl0_92),
% 88.53/11.61 inference(component_clause,[status(thm)],[f668])).
% 88.53/11.61 fof(f671,plain,(
% 88.53/11.61 spl0_93 <=> ~is_a_theorem(X0)|~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(X1)),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f672,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(X1)|~spl0_93)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f671])).
% 88.53/11.61 fof(f674,plain,(
% 88.53/11.61 ~spl0_92|spl0_93),
% 88.53/11.61 inference(split_clause,[status(thm)],[f209,f668,f671])).
% 88.53/11.61 fof(f687,plain,(
% 88.53/11.61 spl0_97 <=> adjunction),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f689,plain,(
% 88.53/11.61 ~adjunction|spl0_97),
% 88.53/11.61 inference(component_clause,[status(thm)],[f687])).
% 88.53/11.61 fof(f690,plain,(
% 88.53/11.61 spl0_98 <=> ~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f691,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))|~spl0_98)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f690])).
% 88.53/11.61 fof(f693,plain,(
% 88.53/11.61 ~spl0_97|spl0_98),
% 88.53/11.61 inference(split_clause,[status(thm)],[f216,f687,f690])).
% 88.53/11.61 fof(f706,plain,(
% 88.53/11.61 spl0_102 <=> substitution_strict_equiv),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f708,plain,(
% 88.53/11.61 ~substitution_strict_equiv|spl0_102),
% 88.53/11.61 inference(component_clause,[status(thm)],[f706])).
% 88.53/11.61 fof(f709,plain,(
% 88.53/11.61 spl0_103 <=> ~is_a_theorem(strict_equiv(X0,X1))|X0=X1),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f710,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_equiv(X0,X1))|X0=X1|~spl0_103)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f709])).
% 88.53/11.61 fof(f712,plain,(
% 88.53/11.61 ~spl0_102|spl0_103),
% 88.53/11.61 inference(split_clause,[status(thm)],[f223,f706,f709])).
% 88.53/11.61 fof(f820,plain,(
% 88.53/11.61 spl0_133 <=> axiom_m1),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f822,plain,(
% 88.53/11.61 ~axiom_m1|spl0_133),
% 88.53/11.61 inference(component_clause,[status(thm)],[f820])).
% 88.53/11.61 fof(f823,plain,(
% 88.53/11.61 spl0_134 <=> is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f824,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))|~spl0_134)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f823])).
% 88.53/11.61 fof(f826,plain,(
% 88.53/11.61 ~spl0_133|spl0_134),
% 88.53/11.61 inference(split_clause,[status(thm)],[f264,f820,f823])).
% 88.53/11.61 fof(f831,plain,(
% 88.53/11.61 spl0_136 <=> axiom_m2),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f833,plain,(
% 88.53/11.61 ~axiom_m2|spl0_136),
% 88.53/11.61 inference(component_clause,[status(thm)],[f831])).
% 88.53/11.61 fof(f834,plain,(
% 88.53/11.61 spl0_137 <=> is_a_theorem(strict_implies(and(X0,X1),X0))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f835,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),X0))|~spl0_137)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f834])).
% 88.53/11.61 fof(f837,plain,(
% 88.53/11.61 ~spl0_136|spl0_137),
% 88.53/11.61 inference(split_clause,[status(thm)],[f268,f831,f834])).
% 88.53/11.61 fof(f842,plain,(
% 88.53/11.61 spl0_139 <=> axiom_m3),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f844,plain,(
% 88.53/11.61 ~axiom_m3|spl0_139),
% 88.53/11.61 inference(component_clause,[status(thm)],[f842])).
% 88.53/11.61 fof(f845,plain,(
% 88.53/11.61 spl0_140 <=> is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f846,plain,(
% 88.53/11.61 ![X0,X1,X2]: (is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))|~spl0_140)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f845])).
% 88.53/11.61 fof(f848,plain,(
% 88.53/11.61 ~spl0_139|spl0_140),
% 88.53/11.61 inference(split_clause,[status(thm)],[f272,f842,f845])).
% 88.53/11.61 fof(f853,plain,(
% 88.53/11.61 spl0_142 <=> axiom_m4),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f855,plain,(
% 88.53/11.61 ~axiom_m4|spl0_142),
% 88.53/11.61 inference(component_clause,[status(thm)],[f853])).
% 88.53/11.61 fof(f856,plain,(
% 88.53/11.61 spl0_143 <=> is_a_theorem(strict_implies(X0,and(X0,X0)))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f857,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(strict_implies(X0,and(X0,X0)))|~spl0_143)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f856])).
% 88.53/11.61 fof(f859,plain,(
% 88.53/11.61 ~spl0_142|spl0_143),
% 88.53/11.61 inference(split_clause,[status(thm)],[f276,f853,f856])).
% 88.53/11.61 fof(f864,plain,(
% 88.53/11.61 spl0_145 <=> axiom_m5),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f866,plain,(
% 88.53/11.61 ~axiom_m5|spl0_145),
% 88.53/11.61 inference(component_clause,[status(thm)],[f864])).
% 88.53/11.61 fof(f867,plain,(
% 88.53/11.61 spl0_146 <=> is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f868,plain,(
% 88.53/11.61 ![X0,X1,X2]: (is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))|~spl0_146)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f867])).
% 88.53/11.61 fof(f870,plain,(
% 88.53/11.61 ~spl0_145|spl0_146),
% 88.53/11.61 inference(split_clause,[status(thm)],[f280,f864,f867])).
% 88.53/11.61 fof(f944,plain,(
% 88.53/11.61 spl0_167 <=> op_strict_implies),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f946,plain,(
% 88.53/11.61 ~op_strict_implies|spl0_167),
% 88.53/11.61 inference(component_clause,[status(thm)],[f944])).
% 88.53/11.61 fof(f947,plain,(
% 88.53/11.61 spl0_168 <=> strict_implies(X0,X1)=necessarily(implies(X0,X1))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f948,plain,(
% 88.53/11.61 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1))|~spl0_168)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f947])).
% 88.53/11.61 fof(f950,plain,(
% 88.53/11.61 ~spl0_167|spl0_168),
% 88.53/11.61 inference(split_clause,[status(thm)],[f307,f944,f947])).
% 88.53/11.61 fof(f951,plain,(
% 88.53/11.61 spl0_169 <=> op_strict_equiv),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f953,plain,(
% 88.53/11.61 ~op_strict_equiv|spl0_169),
% 88.53/11.61 inference(component_clause,[status(thm)],[f951])).
% 88.53/11.61 fof(f954,plain,(
% 88.53/11.61 spl0_170 <=> strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))),
% 88.53/11.61 introduced(split_symbol_definition)).
% 88.53/11.61 fof(f955,plain,(
% 88.53/11.61 ![X0,X1]: (strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))|~spl0_170)),
% 88.53/11.61 inference(component_clause,[status(thm)],[f954])).
% 88.53/11.61 fof(f957,plain,(
% 88.53/11.61 ~spl0_169|spl0_170),
% 88.53/11.61 inference(split_clause,[status(thm)],[f309,f951,f954])).
% 88.53/11.61 fof(f958,plain,(
% 88.53/11.61 $false|spl0_169),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f953,f315])).
% 88.53/11.61 fof(f959,plain,(
% 88.53/11.61 spl0_169),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f958])).
% 88.53/11.61 fof(f960,plain,(
% 88.53/11.61 $false|spl0_97),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f689,f318])).
% 88.53/11.61 fof(f961,plain,(
% 88.53/11.61 spl0_97),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f960])).
% 88.53/11.61 fof(f962,plain,(
% 88.53/11.61 $false|spl0_92),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f670,f316])).
% 88.53/11.61 fof(f963,plain,(
% 88.53/11.61 spl0_92),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f962])).
% 88.53/11.61 fof(f964,plain,(
% 88.53/11.61 $false|spl0_102),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f708,f317])).
% 88.53/11.61 fof(f965,plain,(
% 88.53/11.61 spl0_102),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f964])).
% 88.53/11.61 fof(f966,plain,(
% 88.53/11.61 $false|spl0_5),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f350,f327])).
% 88.53/11.61 fof(f967,plain,(
% 88.53/11.61 spl0_5),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f966])).
% 88.53/11.61 fof(f968,plain,(
% 88.53/11.61 $false|spl0_167),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f946,f313])).
% 88.53/11.61 fof(f969,plain,(
% 88.53/11.61 spl0_167),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f968])).
% 88.53/11.61 fof(f972,plain,(
% 88.53/11.61 $false|spl0_86),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f648,f314])).
% 88.53/11.61 fof(f973,plain,(
% 88.53/11.61 spl0_86),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f972])).
% 88.53/11.61 fof(f974,plain,(
% 88.53/11.61 $false|spl0_82),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f634,f325])).
% 88.53/11.61 fof(f975,plain,(
% 88.53/11.61 spl0_82),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f974])).
% 88.53/11.61 fof(f976,plain,(
% 88.53/11.61 $false|spl0_78),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f620,f311])).
% 88.53/11.61 fof(f977,plain,(
% 88.53/11.61 spl0_78),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f976])).
% 88.53/11.61 fof(f989,plain,(
% 88.53/11.61 $false|spl0_142),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f855,f322])).
% 88.53/11.61 fof(f990,plain,(
% 88.53/11.61 spl0_142),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f989])).
% 88.53/11.61 fof(f993,plain,(
% 88.53/11.61 $false|spl0_136),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f833,f320])).
% 88.53/11.61 fof(f994,plain,(
% 88.53/11.61 spl0_136),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f993])).
% 88.53/11.61 fof(f1010,plain,(
% 88.53/11.61 $false|~spl0_31|spl0_32),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f449,f444])).
% 88.53/11.61 fof(f1011,plain,(
% 88.53/11.61 ~spl0_31|spl0_32),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f1010])).
% 88.53/11.61 fof(f1025,plain,(
% 88.53/11.61 $false|spl0_133),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f822,f319])).
% 88.53/11.61 fof(f1026,plain,(
% 88.53/11.61 spl0_133),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f1025])).
% 88.53/11.61 fof(f1055,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(and(X1,X0))|~spl0_134|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f824,f672])).
% 88.53/11.61 fof(f1069,plain,(
% 88.53/11.61 ![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)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f955,f691])).
% 88.53/11.61 fof(f1071,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X1)))|~spl0_137|~spl0_170)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f955,f835])).
% 88.53/11.61 fof(f1072,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(strict_implies(strict_implies(X0,X0),strict_equiv(X0,X0)))|~spl0_143|~spl0_170)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f955,f857])).
% 88.53/11.61 fof(f1103,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1))|~spl0_98|~spl0_87)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f650,f691])).
% 88.53/11.61 fof(f1118,plain,(
% 88.53/11.61 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f636,f622])).
% 88.53/11.61 fof(f1120,plain,(
% 88.53/11.61 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~spl0_79|~spl0_83)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f636,f1118])).
% 88.53/11.61 fof(f1125,plain,(
% 88.53/11.61 ![X0,X1]: (equiv(X0,not(X1))=and(implies(X0,not(X1)),or(X1,X0))|~spl0_87|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1118,f650])).
% 88.53/11.61 fof(f1127,plain,(
% 88.53/11.61 ![X0,X1]: (strict_implies(not(X0),X1)=necessarily(or(X0,X1))|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1118,f948])).
% 88.53/11.61 fof(f1131,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(necessarily(or(X0,and(not(X0),not(X0)))))|~spl0_143|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1127,f857])).
% 88.53/11.61 fof(f1133,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(strict_equiv(not(X0),X1),necessarily(or(X0,X1))))|~spl0_137|~spl0_170|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1127,f1071])).
% 88.53/11.61 fof(f1211,plain,(
% 88.53/11.61 $false|spl0_145),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f866,f323])).
% 88.53/11.61 fof(f1212,plain,(
% 88.53/11.61 spl0_145),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f1211])).
% 88.53/11.61 fof(f1213,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~is_a_theorem(and(strict_implies(X0,X1),strict_implies(X1,X2)))|is_a_theorem(strict_implies(X0,X2))|~spl0_146|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f868,f672])).
% 88.53/11.61 fof(f1214,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X0)))|~spl0_146|~spl0_170)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f955,f868])).
% 88.53/11.61 fof(f1222,plain,(
% 88.53/11.61 $false|spl0_139),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f844,f321])).
% 88.53/11.61 fof(f1223,plain,(
% 88.53/11.61 spl0_139),
% 88.53/11.61 inference(contradiction_clause,[status(thm)],[f1222])).
% 88.53/11.61 fof(f1323,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(strict_implies(X1,X0))|X0=X1|~spl0_98|~spl0_170|~spl0_103)),
% 88.53/11.61 inference(resolution,[status(thm)],[f1069,f710])).
% 88.53/11.61 fof(f1331,plain,(
% 88.53/11.61 ![X0]: (~is_a_theorem(strict_implies(strict_equiv(X0,X0),strict_implies(X0,X0)))|strict_equiv(X0,X0)=strict_implies(X0,X0)|~spl0_98|~spl0_103|~spl0_143|~spl0_170)),
% 88.53/11.61 inference(resolution,[status(thm)],[f1323,f1072])).
% 88.53/11.61 fof(f1332,plain,(
% 88.53/11.61 ![X0]: (strict_equiv(X0,X0)=strict_implies(X0,X0)|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170)),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f1331,f1214])).
% 88.53/11.61 fof(f1338,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))|and(X0,X1)=and(X1,X0)|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(resolution,[status(thm)],[f1323,f824])).
% 88.53/11.61 fof(f1339,plain,(
% 88.53/11.61 ![X0,X1]: (and(X0,X1)=and(X1,X0)|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f1338,f824])).
% 88.53/11.61 fof(f1340,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_implies(X0,and(X0,X1)))|X0=and(X0,X1)|~spl0_98|~spl0_170|~spl0_103|~spl0_137)),
% 88.53/11.61 inference(resolution,[status(thm)],[f1323,f835])).
% 88.53/11.61 fof(f1341,plain,(
% 88.53/11.61 ![X0]: (~is_a_theorem(strict_implies(and(X0,X0),X0))|and(X0,X0)=X0|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(resolution,[status(thm)],[f1323,f857])).
% 88.53/11.61 fof(f1342,plain,(
% 88.53/11.61 ![X0]: (and(X0,X0)=X0|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f1341,f835])).
% 88.53/11.61 fof(f1344,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(necessarily(or(X0,not(X0))))|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(backward_demodulation,[status(thm)],[f1342,f1131])).
% 88.53/11.61 fof(f1348,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(strict_implies(X0,X0))|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(backward_demodulation,[status(thm)],[f1342,f857])).
% 88.53/11.61 fof(f1359,plain,(
% 88.53/11.61 ![X0]: (implies(not(X0),X0)=not(not(X0))|~spl0_83|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1342,f636])).
% 88.53/11.61 fof(f1360,plain,(
% 88.53/11.61 ![X0]: (or(X0,X0)=not(not(X0))|~spl0_79|~spl0_83|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1118,f1359])).
% 88.53/11.61 fof(f1452,plain,(
% 88.53/11.61 ![X0,X1,X2]: (or(and(not(X0),X1),X2)=implies(implies(X1,X0),X2)|~spl0_79|~spl0_83|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1339,f1120])).
% 88.53/11.61 fof(f1454,plain,(
% 88.53/11.61 ![X0,X1]: (implies(X0,X1)=not(and(not(X1),X0))|~spl0_83|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1339,f636])).
% 88.53/11.61 fof(f1458,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),X1))|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1339,f835])).
% 88.53/11.61 fof(f1527,plain,(
% 88.53/11.61 ![X0,X1]: (implies(not(X0),X1)=implies(not(X1),X0)|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f636,f1454])).
% 88.53/11.61 fof(f1528,plain,(
% 88.53/11.61 ![X0,X1]: (or(X0,X1)=implies(not(X1),X0)|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1118,f1527])).
% 88.53/11.61 fof(f1529,plain,(
% 88.53/11.61 ![X0,X1]: (or(X0,X1)=or(X1,X0)|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1118,f1528])).
% 88.53/11.61 fof(f1575,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(strict_equiv(not(X0),X1),necessarily(or(X1,X0))))|~spl0_137|~spl0_168|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1529,f1133])).
% 88.53/11.61 fof(f1605,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_implies(X0,and(X1,X0)))|X0=and(X0,X1)|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1339,f1340])).
% 88.53/11.61 fof(f1675,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),and(X0,and(X0,X1))))|~spl0_140|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1342,f846])).
% 88.53/11.61 fof(f1981,plain,(
% 88.53/11.61 ![X0,X1]: (and(X0,X1)=and(and(X0,X1),X0)|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(resolution,[status(thm)],[f1675,f1605])).
% 88.53/11.61 fof(f2016,plain,(
% 88.53/11.61 ![X0,X1]: (and(X0,X1)=and(and(X1,X0),X0)|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1339,f1981])).
% 88.53/11.61 fof(f2107,plain,(
% 88.53/11.61 ![X0,X1]: (implies(and(X0,not(X1)),X1)=not(and(not(X1),X0))|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f2016,f636])).
% 88.53/11.61 fof(f2108,plain,(
% 88.53/11.61 ![X0,X1]: (implies(and(X0,not(X1)),X1)=implies(X0,X1)|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1454,f2107])).
% 88.53/11.61 fof(f2221,plain,(
% 88.53/11.61 ![X0,X1]: (strict_implies(and(X0,not(X1)),X1)=necessarily(implies(X0,X1))|~spl0_168|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f2108,f948])).
% 88.53/11.61 fof(f2222,plain,(
% 88.53/11.61 ![X0,X1]: (strict_implies(and(X0,not(X1)),X1)=strict_implies(X0,X1)|~spl0_168|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f948,f2221])).
% 88.53/11.61 fof(f2234,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(implies(X0,not(X1)))|~is_a_theorem(or(X1,X0))|is_a_theorem(equiv(X0,not(X1)))|~spl0_98|~spl0_87|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1118,f1103])).
% 88.53/11.61 fof(f2675,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~is_a_theorem(and(strict_implies(X0,not(X1)),necessarily(or(X1,X2))))|is_a_theorem(strict_implies(X0,X2))|~spl0_146|~spl0_93|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1127,f1213])).
% 88.53/11.61 fof(f2676,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~is_a_theorem(and(necessarily(or(X0,X1)),strict_implies(X2,not(X0))))|is_a_theorem(strict_implies(X2,X1))|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_146|~spl0_93|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1339,f2675])).
% 88.53/11.61 fof(f3197,plain,(
% 88.53/11.61 ![X0,X1,X2]: (implies(implies(not(X0),X1),X2)=implies(implies(not(X1),X0),X2)|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_79|~spl0_83)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1120,f1452])).
% 88.53/11.61 fof(f3198,plain,(
% 88.53/11.61 ![X0,X1,X2]: (implies(or(X0,X1),X2)=implies(implies(not(X1),X0),X2)|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_79|~spl0_83)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1118,f3197])).
% 88.53/11.61 fof(f3199,plain,(
% 88.53/11.61 ![X0,X1,X2]: (implies(or(X0,X1),X2)=implies(or(X1,X0),X2)|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_79|~spl0_83)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1118,f3198])).
% 88.53/11.61 fof(f3201,plain,(
% 88.53/11.61 ![X0,X1,X2]: (or(X0,and(not(X1),X2))=implies(implies(X2,X1),X0)|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1529,f1452])).
% 88.53/11.61 fof(f3274,plain,(
% 88.53/11.61 ![X0,X1,X2]: (strict_implies(or(X0,X1),X2)=necessarily(implies(or(X1,X0),X2))|~spl0_168|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_79|~spl0_83)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f3199,f948])).
% 88.53/11.61 fof(f3275,plain,(
% 88.53/11.61 ![X0,X1,X2]: (strict_implies(or(X0,X1),X2)=strict_implies(or(X1,X0),X2)|~spl0_168|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_79|~spl0_83)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f948,f3274])).
% 88.53/11.61 fof(f3322,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(or(X0,X1),or(X1,X0)))|~spl0_137|~spl0_143|~spl0_168|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_79|~spl0_83)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f3275,f1348])).
% 88.53/11.61 fof(f3354,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0))|~spl0_137|~spl0_143|~spl0_168|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_79|~spl0_83|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f3322,f672])).
% 88.53/11.61 fof(f3444,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_equiv(not(X0),X1))|is_a_theorem(necessarily(or(X1,X0)))|~spl0_137|~spl0_168|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f1575,f672])).
% 88.53/11.61 fof(f3840,plain,(
% 88.53/11.61 ![X0]: (~is_a_theorem(strict_implies(not(X0),not(X0)))|is_a_theorem(necessarily(or(not(X0),X0)))|~spl0_137|~spl0_168|~spl0_79|~spl0_134|~spl0_83|~spl0_93|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1332,f3444])).
% 88.53/11.61 fof(f3841,plain,(
% 88.53/11.61 ![X0]: (~is_a_theorem(necessarily(or(X0,not(X0))))|is_a_theorem(necessarily(or(not(X0),X0)))|~spl0_137|~spl0_168|~spl0_79|~spl0_134|~spl0_83|~spl0_93|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1127,f3840])).
% 88.53/11.61 fof(f3842,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(necessarily(or(not(X0),X0)))|~spl0_137|~spl0_168|~spl0_79|~spl0_134|~spl0_83|~spl0_93|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170)),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f3841,f1344])).
% 88.53/11.61 fof(f8001,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~is_a_theorem(X0)|is_a_theorem(and(X0,strict_implies(and(X1,X2),X2)))|~spl0_137|~spl0_170|~spl0_103|~spl0_134|~spl0_98)),
% 88.53/11.61 inference(resolution,[status(thm)],[f1458,f691])).
% 88.53/11.61 fof(f8059,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(and(X0,necessarily(or(not(X1),X1))))|~spl0_137|~spl0_168|~spl0_79|~spl0_134|~spl0_83|~spl0_93|~spl0_146|~spl0_103|~spl0_143|~spl0_170|~spl0_98)),
% 88.53/11.61 inference(resolution,[status(thm)],[f3842,f691])).
% 88.53/11.61 fof(f8060,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_implies(necessarily(or(not(X0),X0)),X1))|is_a_theorem(X1)|~spl0_137|~spl0_168|~spl0_79|~spl0_134|~spl0_83|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f3842,f672])).
% 88.53/11.61 fof(f10547,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~is_a_theorem(strict_implies(X0,and(X1,X2)))|is_a_theorem(strict_implies(X0,X2))|~spl0_137|~spl0_170|~spl0_103|~spl0_134|~spl0_98|~spl0_146|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f8001,f1213])).
% 88.53/11.61 fof(f10549,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~is_a_theorem(X0)|is_a_theorem(and(strict_implies(and(X1,X2),X2),X0))|~spl0_137|~spl0_170|~spl0_103|~spl0_98|~spl0_134|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f8001,f1055])).
% 88.53/11.61 fof(f10949,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~is_a_theorem(strict_implies(X0,and(X1,X2)))|is_a_theorem(strict_implies(X0,X1))|~spl0_146|~spl0_93|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f2016,f10547])).
% 88.53/11.61 fof(f11103,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(strict_implies(and(X2,X0),X1))|~spl0_137|~spl0_170|~spl0_103|~spl0_98|~spl0_134|~spl0_146|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f10549,f1213])).
% 88.53/11.61 fof(f12466,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_implies(not(X0),X0))|is_a_theorem(strict_implies(X1,X0))|~spl0_146|~spl0_93|~spl0_168|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f2222,f11103])).
% 88.53/11.61 fof(f12467,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(necessarily(or(X0,X0)))|is_a_theorem(strict_implies(X1,X0))|~spl0_79|~spl0_146|~spl0_93|~spl0_168|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1127,f12466])).
% 88.53/11.61 fof(f12468,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(necessarily(not(not(X0))))|is_a_theorem(strict_implies(X1,X0))|~spl0_79|~spl0_146|~spl0_93|~spl0_168|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1360,f12467])).
% 88.53/11.61 fof(f16385,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(and(necessarily(or(not(X1),X1)),X0))|~spl0_137|~spl0_168|~spl0_79|~spl0_83|~spl0_146|~spl0_103|~spl0_143|~spl0_170|~spl0_98|~spl0_134|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f8059,f1055])).
% 88.53/11.61 fof(f17687,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_implies(X0,not(not(X1))))|is_a_theorem(strict_implies(X0,X1))|~spl0_137|~spl0_143|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_146|~spl0_93|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(resolution,[status(thm)],[f16385,f2676])).
% 88.53/11.61 fof(f17929,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(and(not(not(X0)),X1),X0))|~spl0_143|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_146|~spl0_93|~spl0_168|~spl0_83|~spl0_79|~spl0_137)),
% 88.53/11.61 inference(resolution,[status(thm)],[f17687,f835])).
% 88.53/11.61 fof(f18072,plain,(
% 88.53/11.61 ![X0,X1,X2]: (is_a_theorem(strict_implies(and(not(not(and(X0,X1))),X2),X0))|~spl0_168|~spl0_83|~spl0_79|~spl0_146|~spl0_93|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(resolution,[status(thm)],[f17929,f10949])).
% 88.53/11.61 fof(f18329,plain,(
% 88.53/11.61 ![X0,X1,X2]: (is_a_theorem(strict_implies(and(not(not(and(not(not(X0)),X1))),X2),X0))|~spl0_140|~spl0_137|~spl0_143|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_146|~spl0_93|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(resolution,[status(thm)],[f18072,f17687])).
% 88.53/11.61 fof(f18330,plain,(
% 88.53/11.61 ![X0,X1,X2]: (is_a_theorem(strict_implies(and(not(implies(X0,not(X1))),X2),X1))|~spl0_140|~spl0_137|~spl0_143|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_146|~spl0_93|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1454,f18329])).
% 88.53/11.61 fof(f18354,plain,(
% 88.53/11.61 ![X0,X1,X2]: (is_a_theorem(strict_implies(and(not(implies(X0,X1)),X2),X0))|~spl0_168|~spl0_79|~spl0_146|~spl0_93|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f636,f18072])).
% 88.53/11.61 fof(f20917,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(not(implies(X0,not(X1))),X1))|~spl0_146|~spl0_93|~spl0_79|~spl0_168|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f2222,f18330])).
% 88.53/11.61 fof(f20918,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(necessarily(or(implies(X0,not(X1)),X1)))|~spl0_146|~spl0_93|~spl0_79|~spl0_168|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1127,f20917])).
% 88.53/11.61 fof(f20993,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(necessarily(or(X0,implies(X1,not(X0)))))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_143|~spl0_137|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1529,f20918])).
% 88.53/11.61 fof(f21003,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(necessarily(or(or(X0,not(X1)),X1)))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1118,f20918])).
% 88.53/11.61 fof(f21242,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(necessarily(or(X0,or(X1,not(X0)))))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1118,f20993])).
% 88.53/11.61 fof(f21312,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(necessarily(or(not(not(not(X0))),X0)))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_134|~spl0_79|~spl0_83|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1360,f21003])).
% 88.53/11.61 fof(f21484,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(necessarily(or(X0,not(not(not(X0))))))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_134|~spl0_79|~spl0_83|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1360,f21242])).
% 88.53/11.61 fof(f21912,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(necessarily(implies(implies(X0,X1),not(not(not(and(not(X1),X0)))))))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_137|~spl0_143|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f3201,f21312])).
% 88.53/11.61 fof(f21913,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(implies(X0,X1),not(not(not(and(not(X1),X0))))))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_137|~spl0_143|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f948,f21912])).
% 88.53/11.61 fof(f21914,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(strict_implies(implies(X0,X1),not(not(implies(X0,X1)))))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_137|~spl0_143|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1454,f21913])).
% 88.53/11.61 fof(f28015,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_implies(not(not(implies(X0,X1))),implies(X0,X1)))|not(not(implies(X0,X1)))=implies(X0,X1)|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_137|~spl0_143|~spl0_79|~spl0_134|~spl0_83|~spl0_98|~spl0_170|~spl0_103)),
% 88.53/11.61 inference(resolution,[status(thm)],[f21914,f1323])).
% 88.53/11.61 fof(f28016,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(necessarily(or(not(implies(X0,X1)),implies(X0,X1))))|not(not(implies(X0,X1)))=implies(X0,X1)|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_137|~spl0_143|~spl0_79|~spl0_134|~spl0_83|~spl0_98|~spl0_170|~spl0_103)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1127,f28015])).
% 88.53/11.61 fof(f28017,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(necessarily(or(implies(X0,X1),not(implies(X0,X1)))))|not(not(implies(X0,X1)))=implies(X0,X1)|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_137|~spl0_143|~spl0_79|~spl0_134|~spl0_83|~spl0_98|~spl0_170|~spl0_103)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1529,f28016])).
% 88.53/11.61 fof(f28018,plain,(
% 88.53/11.61 ![X0,X1]: (not(not(implies(X0,X1)))=implies(X0,X1)|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_137|~spl0_143|~spl0_79|~spl0_134|~spl0_83|~spl0_98|~spl0_170|~spl0_103)),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f28017,f1344])).
% 88.53/11.61 fof(f28150,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~is_a_theorem(necessarily(implies(X0,X1)))|is_a_theorem(strict_implies(X2,implies(X0,X1)))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_137|~spl0_143|~spl0_79|~spl0_134|~spl0_83|~spl0_98|~spl0_170|~spl0_103)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f28018,f12468])).
% 88.53/11.61 fof(f28151,plain,(
% 88.53/11.61 ![X0,X1,X2]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(strict_implies(X2,implies(X0,X1)))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_137|~spl0_143|~spl0_79|~spl0_134|~spl0_83|~spl0_98|~spl0_170|~spl0_103)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f948,f28150])).
% 88.53/11.61 fof(f29656,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(implies(X0,X1))|~spl0_140|~spl0_137|~spl0_168|~spl0_79|~spl0_134|~spl0_83|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f28151,f8060])).
% 88.53/11.61 fof(f29985,plain,(
% 88.53/11.61 ![X0,X1,X2]: (is_a_theorem(implies(and(not(implies(X0,X1)),X2),X0))|~spl0_168|~spl0_79|~spl0_146|~spl0_93|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 88.53/11.61 inference(resolution,[status(thm)],[f29656,f18354])).
% 88.53/11.61 fof(f30059,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_140|~spl0_168|~spl0_79|~spl0_134|~spl0_83|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170|~spl0_93|~spl0_137)),
% 88.53/11.61 inference(resolution,[status(thm)],[f29656,f835])).
% 88.53/11.61 fof(f30060,plain,(
% 88.53/11.61 spl0_22|~spl0_140|~spl0_168|~spl0_79|~spl0_134|~spl0_83|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170|~spl0_93|~spl0_137),
% 88.53/11.61 inference(split_clause,[status(thm)],[f30059,f410,f845,f947,f621,f823,f635,f867,f690,f709,f856,f954,f671,f834])).
% 88.53/11.61 fof(f30065,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_140|~spl0_168|~spl0_79|~spl0_134|~spl0_83|~spl0_146|~spl0_93|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(resolution,[status(thm)],[f29656,f1348])).
% 88.53/11.61 fof(f30078,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(necessarily(or(X0,X1)))|is_a_theorem(implies(not(X0),X1))|~spl0_140|~spl0_137|~spl0_134|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170|~spl0_93|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1127,f29656])).
% 88.53/11.61 fof(f30079,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(necessarily(or(X0,X1)))|is_a_theorem(or(X0,X1))|~spl0_140|~spl0_137|~spl0_134|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170|~spl0_93|~spl0_168|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1118,f30078])).
% 88.53/11.61 fof(f30099,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(or(X0,not(X0)))|~spl0_140|~spl0_168|~spl0_134|~spl0_146|~spl0_93|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1118,f30065])).
% 88.53/11.61 fof(f30106,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(or(not(X0),X0))|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_79|~spl0_83|~spl0_93)),
% 88.53/11.61 inference(resolution,[status(thm)],[f30099,f3354])).
% 88.53/11.61 fof(f30222,plain,(
% 88.53/11.61 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(and(X0,or(not(X1),X1)))|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_170|~spl0_103|~spl0_134|~spl0_79|~spl0_83|~spl0_93|~spl0_98)),
% 88.53/11.61 inference(resolution,[status(thm)],[f30106,f691])).
% 88.53/11.61 fof(f37128,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(implies(not(implies(X0,X1)),X0))|~spl0_168|~spl0_79|~spl0_146|~spl0_93|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f2108,f29985])).
% 88.53/11.61 fof(f37129,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(or(implies(X0,X1),X0))|~spl0_168|~spl0_79|~spl0_146|~spl0_93|~spl0_83|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1118,f37128])).
% 88.53/11.61 fof(f37189,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(or(or(X0,X1),not(X0)))|~spl0_168|~spl0_146|~spl0_93|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1118,f37129])).
% 88.53/11.61 fof(f37190,plain,(
% 88.53/11.61 ![X0,X1]: (is_a_theorem(or(not(X0),or(X0,X1)))|~spl0_168|~spl0_146|~spl0_93|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1529,f37189])).
% 88.53/11.61 fof(f37986,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(or(X0,not(not(not(X0)))))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_134|~spl0_79|~spl0_83|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(resolution,[status(thm)],[f30079,f21484])).
% 88.53/11.61 fof(f39652,plain,(
% 88.53/11.61 ![X0]: (~is_a_theorem(implies(not(not(not(X0))),not(X0)))|is_a_theorem(equiv(not(not(not(X0))),not(X0)))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_134|~spl0_137|~spl0_170|~spl0_103|~spl0_143|~spl0_98|~spl0_87|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(resolution,[status(thm)],[f37986,f2234])).
% 88.53/11.61 fof(f39653,plain,(
% 88.53/11.61 ![X0]: (~is_a_theorem(or(not(not(X0)),not(X0)))|is_a_theorem(equiv(not(not(not(X0))),not(X0)))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_134|~spl0_137|~spl0_170|~spl0_103|~spl0_143|~spl0_98|~spl0_87|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1118,f39652])).
% 88.53/11.61 fof(f39654,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(equiv(not(not(not(X0))),not(X0)))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_134|~spl0_137|~spl0_170|~spl0_103|~spl0_143|~spl0_98|~spl0_87|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f39653,f30106])).
% 88.53/11.61 fof(f46573,plain,(
% 88.53/11.61 ![X0]: (not(not(not(X0)))=not(X0)|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_134|~spl0_137|~spl0_170|~spl0_103|~spl0_143|~spl0_98|~spl0_87|~spl0_83|~spl0_79|~spl0_6)),
% 88.53/11.61 inference(resolution,[status(thm)],[f39654,f352])).
% 88.53/11.61 fof(f47141,plain,(
% 88.53/11.61 ![X0,X1]: (implies(X0,not(not(X1)))=not(and(not(X1),X0))|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_134|~spl0_137|~spl0_170|~spl0_103|~spl0_143|~spl0_98|~spl0_87|~spl0_83|~spl0_79|~spl0_6)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f46573,f1454])).
% 88.53/11.61 fof(f47142,plain,(
% 88.53/11.61 ![X0,X1]: (implies(X0,not(not(X1)))=implies(X0,X1)|~spl0_146|~spl0_93|~spl0_168|~spl0_140|~spl0_134|~spl0_137|~spl0_170|~spl0_103|~spl0_143|~spl0_98|~spl0_87|~spl0_83|~spl0_79|~spl0_6)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f1454,f47141])).
% 88.53/11.61 fof(f63832,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_22|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1342,f411])).
% 88.53/11.61 fof(f80082,plain,(
% 88.53/11.61 ![X0]: (~is_a_theorem(implies(X0,not(not(X0))))|is_a_theorem(equiv(X0,not(not(X0))))|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_170|~spl0_103|~spl0_134|~spl0_93|~spl0_98|~spl0_87|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(paramodulation,[status(thm)],[f1125,f30222])).
% 88.53/11.61 fof(f80083,plain,(
% 88.53/11.61 ![X0]: (~is_a_theorem(implies(X0,X0))|is_a_theorem(equiv(X0,not(not(X0))))|~spl0_6|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_170|~spl0_103|~spl0_134|~spl0_93|~spl0_98|~spl0_87|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(forward_demodulation,[status(thm)],[f47142,f80082])).
% 88.53/11.61 fof(f80084,plain,(
% 88.53/11.61 ![X0]: (is_a_theorem(equiv(X0,not(not(X0))))|~spl0_22|~spl0_6|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_170|~spl0_103|~spl0_134|~spl0_93|~spl0_98|~spl0_87|~spl0_83|~spl0_79)),
% 88.53/11.61 inference(forward_subsumption_resolution,[status(thm)],[f80083,f63832])).
% 88.53/11.61 fof(f80150,plain,(
% 88.53/11.61 ![X0]: (X0=not(not(X0))|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_170|~spl0_103|~spl0_134|~spl0_93|~spl0_98|~spl0_87|~spl0_83|~spl0_79|~spl0_6)),
% 88.53/11.61 inference(resolution,[status(thm)],[f80084,f352])).
% 88.53/11.61 fof(f80381,plain,(
% 88.53/11.61 ![X0,X1]: (or(not(X0),X1)=implies(X0,X1)|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_170|~spl0_103|~spl0_134|~spl0_93|~spl0_98|~spl0_87|~spl0_83|~spl0_79|~spl0_6)),
% 92.97/12.99 inference(paramodulation,[status(thm)],[f80150,f1118])).
% 92.97/12.99 fof(f80878,plain,(
% 92.97/12.99 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_22|~spl0_87|~spl0_6|~spl0_168|~spl0_146|~spl0_93|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83|~spl0_79)),
% 92.97/12.99 inference(backward_demodulation,[status(thm)],[f80381,f37190])).
% 92.97/12.99 fof(f80879,plain,(
% 92.97/12.99 spl0_31|~spl0_22|~spl0_87|~spl0_6|~spl0_168|~spl0_146|~spl0_93|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83|~spl0_79),
% 92.97/12.99 inference(split_clause,[status(thm)],[f80878,f443,f410,f649,f351,f947,f867,f671,f845,f856,f834,f690,f954,f709,f823,f635,f621])).
% 92.97/12.99 fof(f81116,plain,(
% 92.97/12.99 $false|~spl0_30),
% 92.97/12.99 inference(forward_subsumption_resolution,[status(thm)],[f441,f328])).
% 92.97/12.99 fof(f81117,plain,(
% 92.97/12.99 ~spl0_30),
% 92.97/12.99 inference(contradiction_clause,[status(thm)],[f81116])).
% 92.97/12.99 fof(f81118,plain,(
% 92.97/12.99 $false),
% 92.97/12.99 inference(sat_refutation,[status(thm)],[f354,f450,f624,f638,f652,f674,f693,f712,f826,f837,f848,f859,f870,f950,f957,f959,f961,f963,f965,f967,f969,f973,f975,f977,f990,f994,f1011,f1026,f1212,f1223,f30060,f80879,f81117])).
% 92.97/12.99 % SZS output end CNFRefutation for theBenchmark.p
% 92.97/12.99 % Elapsed time: 12.431834 seconds
% 92.97/12.99 % CPU time: 85.418446 seconds
% 92.97/12.99 % Memory used: 1.344 GB
%------------------------------------------------------------------------------