TSTP Solution File: LCL553+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL553+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 20:27:26 EDT 2024
% Result : Theorem 178.42s 22.83s
% Output : CNFRefutation 181.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : LCL553+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.35 % Computer : n032.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Apr 29 20:38:05 EDT 2024
% 0.11/0.35 % CPUTime :
% 0.11/0.36 % Drodi V3.6.0
% 178.42/22.83 % Refutation found
% 178.42/22.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 178.42/22.83 % SZS output start CNFRefutation for theBenchmark
% 178.42/22.83 fof(f2,axiom,(
% 178.42/22.83 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f5,axiom,(
% 178.42/22.83 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f27,axiom,(
% 178.42/22.83 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f29,axiom,(
% 178.42/22.83 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f31,axiom,(
% 178.42/22.83 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f33,axiom,(
% 178.42/22.83 ( modus_ponens_strict_implies<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(strict_implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f34,axiom,(
% 178.42/22.83 ( adjunction<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(Y) )=> is_a_theorem(and(X,Y)) ) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f35,axiom,(
% 178.42/22.83 ( substitution_strict_equiv<=> (! [X,Y] :( is_a_theorem(strict_equiv(X,Y))=> X = Y ) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f45,axiom,(
% 178.42/22.83 ( axiom_m1<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f46,axiom,(
% 178.42/22.83 ( axiom_m2<=> (! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f47,axiom,(
% 178.42/22.83 ( axiom_m3<=> (! [X,Y,Z] : is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z)))) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f48,axiom,(
% 178.42/22.83 ( axiom_m4<=> (! [X] : is_a_theorem(strict_implies(X,and(X,X))) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f49,axiom,(
% 178.42/22.83 ( axiom_m5<=> (! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z))) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f57,axiom,(
% 178.42/22.83 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f58,axiom,(
% 178.42/22.83 ( op_strict_equiv=> (! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) )) ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f60,axiom,(
% 178.42/22.83 op_or ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f62,axiom,(
% 178.42/22.83 op_strict_implies ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f63,axiom,(
% 178.42/22.83 op_equiv ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f64,axiom,(
% 178.42/22.83 op_strict_equiv ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f65,axiom,(
% 178.42/22.83 modus_ponens_strict_implies ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f66,axiom,(
% 178.42/22.83 substitution_strict_equiv ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f67,axiom,(
% 178.42/22.83 adjunction ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f68,axiom,(
% 178.42/22.83 axiom_m1 ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f69,axiom,(
% 178.42/22.83 axiom_m2 ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f70,axiom,(
% 178.42/22.83 axiom_m3 ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f71,axiom,(
% 178.42/22.83 axiom_m4 ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f72,axiom,(
% 178.42/22.83 axiom_m5 ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f74,axiom,(
% 178.42/22.83 op_implies_and ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f76,axiom,(
% 178.42/22.83 substitution_of_equivalents ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.42/22.83 fof(f77,conjecture,(
% 178.42/22.83 implies_2 ),
% 178.42/22.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 178.47/22.84 fof(f78,negated_conjecture,(
% 178.47/22.84 ~(implies_2 )),
% 178.47/22.84 inference(negated_conjecture,[status(cth)],[f77])).
% 178.47/22.84 fof(f87,plain,(
% 178.47/22.84 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 178.47/22.84 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 178.47/22.84 fof(f88,plain,(
% 178.47/22.84 (~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)))),
% 178.47/22.84 inference(NNF_transformation,[status(esa)],[f87])).
% 178.47/22.84 fof(f89,plain,(
% 178.47/22.84 (~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))),
% 178.47/22.84 inference(skolemization,[status(esa)],[f88])).
% 178.47/22.84 fof(f90,plain,(
% 178.47/22.84 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f89])).
% 178.47/22.84 fof(f101,plain,(
% 178.47/22.84 (~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)))))),
% 178.47/22.84 inference(NNF_transformation,[status(esa)],[f5])).
% 178.47/22.84 fof(f102,plain,(
% 178.47/22.84 (~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))))),
% 178.47/22.84 inference(skolemization,[status(esa)],[f101])).
% 178.47/22.84 fof(f104,plain,(
% 178.47/22.84 implies_2|~is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9)))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f102])).
% 178.47/22.84 fof(f189,plain,(
% 178.47/22.84 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 178.47/22.84 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 178.47/22.84 fof(f190,plain,(
% 178.47/22.84 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f189])).
% 178.47/22.84 fof(f193,plain,(
% 178.47/22.84 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 178.47/22.84 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 178.47/22.84 fof(f194,plain,(
% 178.47/22.84 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f193])).
% 178.47/22.84 fof(f197,plain,(
% 178.47/22.84 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 178.47/22.84 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 178.47/22.84 fof(f198,plain,(
% 178.47/22.84 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f197])).
% 178.47/22.84 fof(f205,plain,(
% 178.47/22.84 modus_ponens_strict_implies<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(strict_implies(X,Y)))|is_a_theorem(Y)))),
% 178.47/22.84 inference(pre_NNF_transformation,[status(esa)],[f33])).
% 178.47/22.84 fof(f206,plain,(
% 178.47/22.84 (~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))))),
% 178.47/22.84 inference(NNF_transformation,[status(esa)],[f205])).
% 178.47/22.84 fof(f207,plain,(
% 178.47/22.84 (~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))))),
% 178.47/22.84 inference(miniscoping,[status(esa)],[f206])).
% 178.47/22.84 fof(f208,plain,(
% 178.47/22.84 (~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)))),
% 178.47/22.84 inference(skolemization,[status(esa)],[f207])).
% 178.47/22.84 fof(f209,plain,(
% 178.47/22.84 ![X0,X1]: (~modus_ponens_strict_implies|~is_a_theorem(X0)|~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(X1))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f208])).
% 178.47/22.84 fof(f213,plain,(
% 178.47/22.84 adjunction<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(Y))|is_a_theorem(and(X,Y))))),
% 178.47/22.84 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 178.47/22.84 fof(f214,plain,(
% 178.47/22.84 (~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)))))),
% 178.47/22.84 inference(NNF_transformation,[status(esa)],[f213])).
% 178.47/22.84 fof(f215,plain,(
% 178.47/22.84 (~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))))),
% 178.47/22.84 inference(skolemization,[status(esa)],[f214])).
% 178.47/22.84 fof(f216,plain,(
% 178.47/22.84 ![X0,X1]: (~adjunction|~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1)))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f215])).
% 178.47/22.84 fof(f220,plain,(
% 178.47/22.84 substitution_strict_equiv<=>(![X,Y]: (~is_a_theorem(strict_equiv(X,Y))|X=Y))),
% 178.47/22.84 inference(pre_NNF_transformation,[status(esa)],[f35])).
% 178.47/22.84 fof(f221,plain,(
% 178.47/22.84 (~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)))),
% 178.47/22.84 inference(NNF_transformation,[status(esa)],[f220])).
% 178.47/22.84 fof(f222,plain,(
% 178.47/22.84 (~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))),
% 178.47/22.84 inference(skolemization,[status(esa)],[f221])).
% 178.47/22.84 fof(f223,plain,(
% 178.47/22.84 ![X0,X1]: (~substitution_strict_equiv|~is_a_theorem(strict_equiv(X0,X1))|X0=X1)),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f222])).
% 178.47/22.84 fof(f262,plain,(
% 178.47/22.84 (~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)))))),
% 178.47/22.84 inference(NNF_transformation,[status(esa)],[f45])).
% 178.47/22.84 fof(f263,plain,(
% 178.47/22.84 (~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))))),
% 178.47/22.84 inference(skolemization,[status(esa)],[f262])).
% 178.47/22.84 fof(f264,plain,(
% 178.47/22.84 ![X0,X1]: (~axiom_m1|is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f263])).
% 178.47/22.84 fof(f266,plain,(
% 178.47/22.84 (~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))))),
% 178.47/22.84 inference(NNF_transformation,[status(esa)],[f46])).
% 178.47/22.84 fof(f267,plain,(
% 178.47/22.84 (~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)))),
% 178.47/22.84 inference(skolemization,[status(esa)],[f266])).
% 178.47/22.84 fof(f268,plain,(
% 178.47/22.84 ![X0,X1]: (~axiom_m2|is_a_theorem(strict_implies(and(X0,X1),X0)))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f267])).
% 178.47/22.84 fof(f270,plain,(
% 178.47/22.84 (~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))))))),
% 178.47/22.84 inference(NNF_transformation,[status(esa)],[f47])).
% 178.47/22.84 fof(f271,plain,(
% 178.47/22.84 (~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)))))),
% 178.47/22.84 inference(skolemization,[status(esa)],[f270])).
% 178.47/22.84 fof(f272,plain,(
% 178.47/22.84 ![X0,X1,X2]: (~axiom_m3|is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f271])).
% 178.47/22.84 fof(f274,plain,(
% 178.47/22.84 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|(?[X]: ~is_a_theorem(strict_implies(X,and(X,X)))))),
% 178.47/22.84 inference(NNF_transformation,[status(esa)],[f48])).
% 178.47/22.84 fof(f275,plain,(
% 178.47/22.84 (~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))))),
% 178.47/22.84 inference(skolemization,[status(esa)],[f274])).
% 178.47/22.84 fof(f276,plain,(
% 178.47/22.84 ![X0]: (~axiom_m4|is_a_theorem(strict_implies(X0,and(X0,X0))))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f275])).
% 178.47/22.84 fof(f278,plain,(
% 178.47/22.84 (~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)))))),
% 178.47/22.84 inference(NNF_transformation,[status(esa)],[f49])).
% 178.47/22.84 fof(f279,plain,(
% 178.47/22.84 (~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))))),
% 178.47/22.84 inference(skolemization,[status(esa)],[f278])).
% 178.47/22.84 fof(f280,plain,(
% 178.47/22.84 ![X0,X1,X2]: (~axiom_m5|is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f279])).
% 178.47/22.84 fof(f306,plain,(
% 178.47/22.84 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 178.47/22.84 inference(pre_NNF_transformation,[status(esa)],[f57])).
% 178.47/22.84 fof(f307,plain,(
% 178.47/22.84 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f306])).
% 178.47/22.84 fof(f308,plain,(
% 178.47/22.84 ~op_strict_equiv|(![X,Y]: strict_equiv(X,Y)=and(strict_implies(X,Y),strict_implies(Y,X)))),
% 178.47/22.84 inference(pre_NNF_transformation,[status(esa)],[f58])).
% 178.47/22.84 fof(f309,plain,(
% 178.47/22.84 ![X0,X1]: (~op_strict_equiv|strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0)))),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f308])).
% 178.47/22.84 fof(f311,plain,(
% 178.47/22.84 op_or),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f60])).
% 178.47/22.84 fof(f313,plain,(
% 178.47/22.84 op_strict_implies),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f62])).
% 178.47/22.84 fof(f314,plain,(
% 178.47/22.84 op_equiv),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f63])).
% 178.47/22.84 fof(f315,plain,(
% 178.47/22.84 op_strict_equiv),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f64])).
% 178.47/22.84 fof(f316,plain,(
% 178.47/22.84 modus_ponens_strict_implies),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f65])).
% 178.47/22.84 fof(f317,plain,(
% 178.47/22.84 substitution_strict_equiv),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f66])).
% 178.47/22.84 fof(f318,plain,(
% 178.47/22.84 adjunction),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f67])).
% 178.47/22.84 fof(f319,plain,(
% 178.47/22.84 axiom_m1),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f68])).
% 178.47/22.84 fof(f320,plain,(
% 178.47/22.84 axiom_m2),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f69])).
% 178.47/22.84 fof(f321,plain,(
% 178.47/22.84 axiom_m3),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f70])).
% 178.47/22.84 fof(f322,plain,(
% 178.47/22.84 axiom_m4),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f71])).
% 178.47/22.84 fof(f323,plain,(
% 178.47/22.84 axiom_m5),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f72])).
% 178.47/22.84 fof(f325,plain,(
% 178.47/22.84 op_implies_and),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f74])).
% 178.47/22.84 fof(f327,plain,(
% 178.47/22.84 substitution_of_equivalents),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f76])).
% 178.47/22.84 fof(f328,plain,(
% 178.47/22.84 ~implies_2),
% 178.47/22.84 inference(cnf_transformation,[status(esa)],[f78])).
% 178.47/22.84 fof(f348,plain,(
% 178.47/22.84 spl0_5 <=> substitution_of_equivalents),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f350,plain,(
% 178.47/22.84 ~substitution_of_equivalents|spl0_5),
% 178.47/22.84 inference(component_clause,[status(thm)],[f348])).
% 178.47/22.84 fof(f351,plain,(
% 178.47/22.84 spl0_6 <=> ~is_a_theorem(equiv(X0,X1))|X0=X1),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f352,plain,(
% 178.47/22.84 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~spl0_6)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f351])).
% 178.47/22.84 fof(f354,plain,(
% 178.47/22.84 ~spl0_5|spl0_6),
% 178.47/22.84 inference(split_clause,[status(thm)],[f90,f348,f351])).
% 178.47/22.84 fof(f385,plain,(
% 178.47/22.84 spl0_15 <=> implies_2),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f386,plain,(
% 178.47/22.84 implies_2|~spl0_15),
% 178.47/22.84 inference(component_clause,[status(thm)],[f385])).
% 178.47/22.84 fof(f392,plain,(
% 178.47/22.84 spl0_17 <=> is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9)))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f394,plain,(
% 178.47/22.84 ~is_a_theorem(implies(implies(sk0_8,implies(sk0_8,sk0_9)),implies(sk0_8,sk0_9)))|spl0_17),
% 178.47/22.84 inference(component_clause,[status(thm)],[f392])).
% 178.47/22.84 fof(f395,plain,(
% 178.47/22.84 spl0_15|~spl0_17),
% 178.47/22.84 inference(split_clause,[status(thm)],[f104,f385,f392])).
% 178.47/22.84 fof(f410,plain,(
% 178.47/22.84 spl0_22 <=> is_a_theorem(implies(and(X0,X1),X0))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f411,plain,(
% 178.47/22.84 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_22)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f410])).
% 178.47/22.84 fof(f618,plain,(
% 178.47/22.84 spl0_78 <=> op_or),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f620,plain,(
% 178.47/22.84 ~op_or|spl0_78),
% 178.47/22.84 inference(component_clause,[status(thm)],[f618])).
% 178.47/22.84 fof(f621,plain,(
% 178.47/22.84 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f622,plain,(
% 178.47/22.84 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f621])).
% 178.47/22.84 fof(f624,plain,(
% 178.47/22.84 ~spl0_78|spl0_79),
% 178.47/22.84 inference(split_clause,[status(thm)],[f190,f618,f621])).
% 178.47/22.84 fof(f632,plain,(
% 178.47/22.84 spl0_82 <=> op_implies_and),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f634,plain,(
% 178.47/22.84 ~op_implies_and|spl0_82),
% 178.47/22.84 inference(component_clause,[status(thm)],[f632])).
% 178.47/22.84 fof(f635,plain,(
% 178.47/22.84 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f636,plain,(
% 178.47/22.84 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f635])).
% 178.47/22.84 fof(f638,plain,(
% 178.47/22.84 ~spl0_82|spl0_83),
% 178.47/22.84 inference(split_clause,[status(thm)],[f194,f632,f635])).
% 178.47/22.84 fof(f646,plain,(
% 178.47/22.84 spl0_86 <=> op_equiv),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f648,plain,(
% 178.47/22.84 ~op_equiv|spl0_86),
% 178.47/22.84 inference(component_clause,[status(thm)],[f646])).
% 178.47/22.84 fof(f649,plain,(
% 178.47/22.84 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f650,plain,(
% 178.47/22.84 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f649])).
% 178.47/22.84 fof(f652,plain,(
% 178.47/22.84 ~spl0_86|spl0_87),
% 178.47/22.84 inference(split_clause,[status(thm)],[f198,f646,f649])).
% 178.47/22.84 fof(f668,plain,(
% 178.47/22.84 spl0_92 <=> modus_ponens_strict_implies),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f670,plain,(
% 178.47/22.84 ~modus_ponens_strict_implies|spl0_92),
% 178.47/22.84 inference(component_clause,[status(thm)],[f668])).
% 178.47/22.84 fof(f671,plain,(
% 178.47/22.84 spl0_93 <=> ~is_a_theorem(X0)|~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(X1)),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f672,plain,(
% 178.47/22.84 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(strict_implies(X0,X1))|is_a_theorem(X1)|~spl0_93)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f671])).
% 178.47/22.84 fof(f674,plain,(
% 178.47/22.84 ~spl0_92|spl0_93),
% 178.47/22.84 inference(split_clause,[status(thm)],[f209,f668,f671])).
% 178.47/22.84 fof(f687,plain,(
% 178.47/22.84 spl0_97 <=> adjunction),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f689,plain,(
% 178.47/22.84 ~adjunction|spl0_97),
% 178.47/22.84 inference(component_clause,[status(thm)],[f687])).
% 178.47/22.84 fof(f690,plain,(
% 178.47/22.84 spl0_98 <=> ~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f691,plain,(
% 178.47/22.84 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(X1)|is_a_theorem(and(X0,X1))|~spl0_98)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f690])).
% 178.47/22.84 fof(f693,plain,(
% 178.47/22.84 ~spl0_97|spl0_98),
% 178.47/22.84 inference(split_clause,[status(thm)],[f216,f687,f690])).
% 178.47/22.84 fof(f706,plain,(
% 178.47/22.84 spl0_102 <=> substitution_strict_equiv),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f708,plain,(
% 178.47/22.84 ~substitution_strict_equiv|spl0_102),
% 178.47/22.84 inference(component_clause,[status(thm)],[f706])).
% 178.47/22.84 fof(f709,plain,(
% 178.47/22.84 spl0_103 <=> ~is_a_theorem(strict_equiv(X0,X1))|X0=X1),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f710,plain,(
% 178.47/22.84 ![X0,X1]: (~is_a_theorem(strict_equiv(X0,X1))|X0=X1|~spl0_103)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f709])).
% 178.47/22.84 fof(f712,plain,(
% 178.47/22.84 ~spl0_102|spl0_103),
% 178.47/22.84 inference(split_clause,[status(thm)],[f223,f706,f709])).
% 178.47/22.84 fof(f820,plain,(
% 178.47/22.84 spl0_133 <=> axiom_m1),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f822,plain,(
% 178.47/22.84 ~axiom_m1|spl0_133),
% 178.47/22.84 inference(component_clause,[status(thm)],[f820])).
% 178.47/22.84 fof(f823,plain,(
% 178.47/22.84 spl0_134 <=> is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f824,plain,(
% 178.47/22.84 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))|~spl0_134)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f823])).
% 178.47/22.84 fof(f826,plain,(
% 178.47/22.84 ~spl0_133|spl0_134),
% 178.47/22.84 inference(split_clause,[status(thm)],[f264,f820,f823])).
% 178.47/22.84 fof(f831,plain,(
% 178.47/22.84 spl0_136 <=> axiom_m2),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f833,plain,(
% 178.47/22.84 ~axiom_m2|spl0_136),
% 178.47/22.84 inference(component_clause,[status(thm)],[f831])).
% 178.47/22.84 fof(f834,plain,(
% 178.47/22.84 spl0_137 <=> is_a_theorem(strict_implies(and(X0,X1),X0))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f835,plain,(
% 178.47/22.84 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),X0))|~spl0_137)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f834])).
% 178.47/22.84 fof(f837,plain,(
% 178.47/22.84 ~spl0_136|spl0_137),
% 178.47/22.84 inference(split_clause,[status(thm)],[f268,f831,f834])).
% 178.47/22.84 fof(f842,plain,(
% 178.47/22.84 spl0_139 <=> axiom_m3),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f844,plain,(
% 178.47/22.84 ~axiom_m3|spl0_139),
% 178.47/22.84 inference(component_clause,[status(thm)],[f842])).
% 178.47/22.84 fof(f845,plain,(
% 178.47/22.84 spl0_140 <=> is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f846,plain,(
% 178.47/22.84 ![X0,X1,X2]: (is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))|~spl0_140)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f845])).
% 178.47/22.84 fof(f848,plain,(
% 178.47/22.84 ~spl0_139|spl0_140),
% 178.47/22.84 inference(split_clause,[status(thm)],[f272,f842,f845])).
% 178.47/22.84 fof(f853,plain,(
% 178.47/22.84 spl0_142 <=> axiom_m4),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f855,plain,(
% 178.47/22.84 ~axiom_m4|spl0_142),
% 178.47/22.84 inference(component_clause,[status(thm)],[f853])).
% 178.47/22.84 fof(f856,plain,(
% 178.47/22.84 spl0_143 <=> is_a_theorem(strict_implies(X0,and(X0,X0)))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f857,plain,(
% 178.47/22.84 ![X0]: (is_a_theorem(strict_implies(X0,and(X0,X0)))|~spl0_143)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f856])).
% 178.47/22.84 fof(f859,plain,(
% 178.47/22.84 ~spl0_142|spl0_143),
% 178.47/22.84 inference(split_clause,[status(thm)],[f276,f853,f856])).
% 178.47/22.84 fof(f864,plain,(
% 178.47/22.84 spl0_145 <=> axiom_m5),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f866,plain,(
% 178.47/22.84 ~axiom_m5|spl0_145),
% 178.47/22.84 inference(component_clause,[status(thm)],[f864])).
% 178.47/22.84 fof(f867,plain,(
% 178.47/22.84 spl0_146 <=> is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f868,plain,(
% 178.47/22.84 ![X0,X1,X2]: (is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))|~spl0_146)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f867])).
% 178.47/22.84 fof(f870,plain,(
% 178.47/22.84 ~spl0_145|spl0_146),
% 178.47/22.84 inference(split_clause,[status(thm)],[f280,f864,f867])).
% 178.47/22.84 fof(f944,plain,(
% 178.47/22.84 spl0_167 <=> op_strict_implies),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f946,plain,(
% 178.47/22.84 ~op_strict_implies|spl0_167),
% 178.47/22.84 inference(component_clause,[status(thm)],[f944])).
% 178.47/22.84 fof(f947,plain,(
% 178.47/22.84 spl0_168 <=> strict_implies(X0,X1)=necessarily(implies(X0,X1))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f948,plain,(
% 178.47/22.84 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1))|~spl0_168)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f947])).
% 178.47/22.84 fof(f950,plain,(
% 178.47/22.84 ~spl0_167|spl0_168),
% 178.47/22.84 inference(split_clause,[status(thm)],[f307,f944,f947])).
% 178.47/22.84 fof(f951,plain,(
% 178.47/22.84 spl0_169 <=> op_strict_equiv),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f953,plain,(
% 178.47/22.84 ~op_strict_equiv|spl0_169),
% 178.47/22.84 inference(component_clause,[status(thm)],[f951])).
% 178.47/22.84 fof(f954,plain,(
% 178.47/22.84 spl0_170 <=> strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))),
% 178.47/22.84 introduced(split_symbol_definition)).
% 178.47/22.84 fof(f955,plain,(
% 178.47/22.84 ![X0,X1]: (strict_equiv(X0,X1)=and(strict_implies(X0,X1),strict_implies(X1,X0))|~spl0_170)),
% 178.47/22.84 inference(component_clause,[status(thm)],[f954])).
% 178.47/22.84 fof(f957,plain,(
% 178.47/22.84 ~spl0_169|spl0_170),
% 178.47/22.84 inference(split_clause,[status(thm)],[f309,f951,f954])).
% 178.47/22.84 fof(f958,plain,(
% 178.47/22.84 $false|spl0_169),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f953,f315])).
% 178.47/22.84 fof(f959,plain,(
% 178.47/22.84 spl0_169),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f958])).
% 178.47/22.84 fof(f960,plain,(
% 178.47/22.84 $false|spl0_97),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f689,f318])).
% 178.47/22.84 fof(f961,plain,(
% 178.47/22.84 spl0_97),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f960])).
% 178.47/22.84 fof(f962,plain,(
% 178.47/22.84 $false|spl0_92),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f670,f316])).
% 178.47/22.84 fof(f963,plain,(
% 178.47/22.84 spl0_92),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f962])).
% 178.47/22.84 fof(f964,plain,(
% 178.47/22.84 $false|spl0_102),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f708,f317])).
% 178.47/22.84 fof(f965,plain,(
% 178.47/22.84 spl0_102),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f964])).
% 178.47/22.84 fof(f966,plain,(
% 178.47/22.84 $false|spl0_5),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f350,f327])).
% 178.47/22.84 fof(f967,plain,(
% 178.47/22.84 spl0_5),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f966])).
% 178.47/22.84 fof(f968,plain,(
% 178.47/22.84 $false|spl0_167),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f946,f313])).
% 178.47/22.84 fof(f969,plain,(
% 178.47/22.84 spl0_167),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f968])).
% 178.47/22.84 fof(f972,plain,(
% 178.47/22.84 $false|spl0_86),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f648,f314])).
% 178.47/22.84 fof(f973,plain,(
% 178.47/22.84 spl0_86),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f972])).
% 178.47/22.84 fof(f974,plain,(
% 178.47/22.84 $false|spl0_82),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f634,f325])).
% 178.47/22.84 fof(f975,plain,(
% 178.47/22.84 spl0_82),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f974])).
% 178.47/22.84 fof(f976,plain,(
% 178.47/22.84 $false|spl0_78),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f620,f311])).
% 178.47/22.84 fof(f977,plain,(
% 178.47/22.84 spl0_78),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f976])).
% 178.47/22.84 fof(f989,plain,(
% 178.47/22.84 $false|spl0_142),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f855,f322])).
% 178.47/22.84 fof(f990,plain,(
% 178.47/22.84 spl0_142),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f989])).
% 178.47/22.84 fof(f993,plain,(
% 178.47/22.84 $false|spl0_136),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f833,f320])).
% 178.47/22.84 fof(f994,plain,(
% 178.47/22.84 spl0_136),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f993])).
% 178.47/22.84 fof(f1024,plain,(
% 178.47/22.84 $false|spl0_133),
% 178.47/22.84 inference(forward_subsumption_resolution,[status(thm)],[f822,f319])).
% 178.47/22.84 fof(f1025,plain,(
% 178.47/22.84 spl0_133),
% 178.47/22.84 inference(contradiction_clause,[status(thm)],[f1024])).
% 178.47/22.84 fof(f1055,plain,(
% 178.47/22.84 ![X0,X1]: (~is_a_theorem(and(X0,X1))|is_a_theorem(and(X1,X0))|~spl0_134|~spl0_93)),
% 178.47/22.84 inference(resolution,[status(thm)],[f824,f672])).
% 178.47/22.84 fof(f1069,plain,(
% 178.47/22.84 ![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)),
% 178.47/22.84 inference(paramodulation,[status(thm)],[f955,f691])).
% 178.47/22.84 fof(f1071,plain,(
% 178.47/22.84 ![X0,X1]: (is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X1)))|~spl0_137|~spl0_170)),
% 178.47/22.84 inference(paramodulation,[status(thm)],[f955,f835])).
% 178.47/22.84 fof(f1072,plain,(
% 178.47/22.84 ![X0]: (is_a_theorem(strict_implies(strict_implies(X0,X0),strict_equiv(X0,X0)))|~spl0_143|~spl0_170)),
% 178.47/22.84 inference(paramodulation,[status(thm)],[f955,f857])).
% 178.47/22.84 fof(f1101,plain,(
% 178.47/22.84 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(X1,X0))|is_a_theorem(equiv(X0,X1))|~spl0_98|~spl0_87)),
% 178.47/22.84 inference(paramodulation,[status(thm)],[f650,f691])).
% 178.47/22.84 fof(f1116,plain,(
% 178.47/22.84 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 178.47/22.84 inference(forward_demodulation,[status(thm)],[f636,f622])).
% 178.47/22.85 fof(f1118,plain,(
% 178.47/22.85 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~spl0_79|~spl0_83)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f636,f1116])).
% 178.47/22.85 fof(f1128,plain,(
% 178.47/22.85 ![X0,X1]: (equiv(X0,not(X1))=and(implies(X0,not(X1)),or(X1,X0))|~spl0_87|~spl0_83|~spl0_79)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1116,f650])).
% 178.47/22.85 fof(f1130,plain,(
% 178.47/22.85 ![X0,X1]: (strict_implies(not(X0),X1)=necessarily(or(X0,X1))|~spl0_168|~spl0_83|~spl0_79)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1116,f948])).
% 178.47/22.85 fof(f1140,plain,(
% 178.47/22.85 ![X0]: (is_a_theorem(necessarily(or(X0,and(not(X0),not(X0)))))|~spl0_143|~spl0_168|~spl0_83|~spl0_79)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1130,f857])).
% 178.47/22.85 fof(f1142,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1130,f1071])).
% 178.47/22.85 fof(f1246,plain,(
% 178.47/22.85 $false|spl0_145),
% 178.47/22.85 inference(forward_subsumption_resolution,[status(thm)],[f866,f323])).
% 178.47/22.85 fof(f1247,plain,(
% 178.47/22.85 spl0_145),
% 178.47/22.85 inference(contradiction_clause,[status(thm)],[f1246])).
% 178.47/22.85 fof(f1248,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f868,f672])).
% 178.47/22.85 fof(f1249,plain,(
% 178.47/22.85 ![X0,X1]: (is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X0)))|~spl0_146|~spl0_170)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f955,f868])).
% 178.47/22.85 fof(f1292,plain,(
% 178.47/22.85 $false|spl0_139),
% 178.47/22.85 inference(forward_subsumption_resolution,[status(thm)],[f844,f321])).
% 178.47/22.85 fof(f1293,plain,(
% 178.47/22.85 spl0_139),
% 178.47/22.85 inference(contradiction_clause,[status(thm)],[f1292])).
% 178.47/22.85 fof(f1343,plain,(
% 178.47/22.85 ![X0,X1]: (~is_a_theorem(strict_implies(X0,X1))|~is_a_theorem(strict_implies(X1,X0))|X0=X1|~spl0_98|~spl0_170|~spl0_103)),
% 178.47/22.85 inference(resolution,[status(thm)],[f1069,f710])).
% 178.47/22.85 fof(f1351,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f1343,f1072])).
% 178.47/22.85 fof(f1352,plain,(
% 178.47/22.85 ![X0]: (strict_equiv(X0,X0)=strict_implies(X0,X0)|~spl0_146|~spl0_98|~spl0_103|~spl0_143|~spl0_170)),
% 178.47/22.85 inference(forward_subsumption_resolution,[status(thm)],[f1351,f1249])).
% 178.47/22.85 fof(f1358,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f1343,f824])).
% 178.47/22.85 fof(f1359,plain,(
% 178.47/22.85 ![X0,X1]: (and(X0,X1)=and(X1,X0)|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 178.47/22.85 inference(forward_subsumption_resolution,[status(thm)],[f1358,f824])).
% 178.47/22.85 fof(f1360,plain,(
% 178.47/22.85 ![X0,X1]: (~is_a_theorem(strict_implies(X0,and(X0,X1)))|X0=and(X0,X1)|~spl0_98|~spl0_170|~spl0_103|~spl0_137)),
% 178.47/22.85 inference(resolution,[status(thm)],[f1343,f835])).
% 178.47/22.85 fof(f1361,plain,(
% 178.47/22.85 ![X0]: (~is_a_theorem(strict_implies(and(X0,X0),X0))|and(X0,X0)=X0|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 178.47/22.85 inference(resolution,[status(thm)],[f1343,f857])).
% 178.47/22.85 fof(f1362,plain,(
% 178.47/22.85 ![X0]: (and(X0,X0)=X0|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 178.47/22.85 inference(forward_subsumption_resolution,[status(thm)],[f1361,f835])).
% 178.47/22.85 fof(f1364,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(backward_demodulation,[status(thm)],[f1362,f1140])).
% 178.47/22.85 fof(f1368,plain,(
% 178.47/22.85 ![X0]: (is_a_theorem(strict_implies(X0,X0))|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 178.47/22.85 inference(backward_demodulation,[status(thm)],[f1362,f857])).
% 178.47/22.85 fof(f1379,plain,(
% 178.47/22.85 ![X0]: (implies(not(X0),X0)=not(not(X0))|~spl0_83|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1362,f636])).
% 178.47/22.85 fof(f1380,plain,(
% 178.47/22.85 ![X0]: (or(X0,X0)=not(not(X0))|~spl0_79|~spl0_83|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1116,f1379])).
% 178.47/22.85 fof(f1475,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1359,f1118])).
% 178.47/22.85 fof(f1477,plain,(
% 178.47/22.85 ![X0,X1]: (implies(X0,X1)=not(and(not(X1),X0))|~spl0_83|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1359,f636])).
% 178.47/22.85 fof(f1481,plain,(
% 178.47/22.85 ![X0,X1]: (is_a_theorem(strict_implies(and(X0,X1),X1))|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1359,f835])).
% 178.47/22.85 fof(f1552,plain,(
% 178.47/22.85 ![X0,X1]: (implies(not(X0),X1)=implies(not(X1),X0)|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f636,f1477])).
% 178.47/22.85 fof(f1553,plain,(
% 178.47/22.85 ![X0,X1]: (or(X0,X1)=implies(not(X1),X0)|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1116,f1552])).
% 178.47/22.85 fof(f1554,plain,(
% 178.47/22.85 ![X0,X1]: (or(X0,X1)=or(X1,X0)|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1116,f1553])).
% 178.47/22.85 fof(f1600,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1554,f1142])).
% 178.47/22.85 fof(f1618,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1359,f1360])).
% 178.47/22.85 fof(f1759,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1362,f846])).
% 178.47/22.85 fof(f2006,plain,(
% 178.47/22.85 ![X0,X1]: (and(X0,X1)=and(and(X0,X1),X0)|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 178.47/22.85 inference(resolution,[status(thm)],[f1759,f1618])).
% 178.47/22.85 fof(f2041,plain,(
% 178.47/22.85 ![X0,X1]: (and(X0,X1)=and(and(X1,X0),X0)|~spl0_140|~spl0_143|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1359,f2006])).
% 178.47/22.85 fof(f2132,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f2041,f636])).
% 178.47/22.85 fof(f2133,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1477,f2132])).
% 178.47/22.85 fof(f2221,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1116,f1101])).
% 178.47/22.85 fof(f2258,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f2133,f948])).
% 178.47/22.85 fof(f2259,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f948,f2258])).
% 178.47/22.85 fof(f2380,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1130,f1248])).
% 178.47/22.85 fof(f2381,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1359,f2380])).
% 178.47/22.85 fof(f3221,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1118,f1475])).
% 178.47/22.85 fof(f3222,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1116,f3221])).
% 178.47/22.85 fof(f3223,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1116,f3222])).
% 178.47/22.85 fof(f3225,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1554,f1475])).
% 178.47/22.85 fof(f3298,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f3223,f948])).
% 178.47/22.85 fof(f3299,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f948,f3298])).
% 178.47/22.85 fof(f3346,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f3299,f1368])).
% 178.47/22.85 fof(f3378,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f3346,f672])).
% 178.47/22.85 fof(f3468,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f1600,f672])).
% 178.47/22.85 fof(f3861,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1352,f3468])).
% 178.47/22.85 fof(f3862,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1130,f3861])).
% 178.47/22.85 fof(f3863,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_subsumption_resolution,[status(thm)],[f3862,f1364])).
% 178.47/22.85 fof(f8169,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f1481,f691])).
% 178.47/22.85 fof(f8223,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f3863,f691])).
% 178.47/22.85 fof(f8224,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f3863,f672])).
% 178.47/22.85 fof(f10544,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f8169,f1248])).
% 178.47/22.85 fof(f10546,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f8169,f1055])).
% 178.47/22.85 fof(f10895,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f2041,f10544])).
% 178.47/22.85 fof(f11180,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f10546,f1248])).
% 178.47/22.85 fof(f12442,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f2259,f11180])).
% 178.47/22.85 fof(f12443,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1130,f12442])).
% 178.47/22.85 fof(f12444,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1380,f12443])).
% 178.47/22.85 fof(f16321,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f8223,f1055])).
% 178.47/22.85 fof(f17720,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f16321,f2381])).
% 178.47/22.85 fof(f17901,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f17720,f835])).
% 178.47/22.85 fof(f18007,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f17901,f10895])).
% 178.47/22.85 fof(f18339,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f18007,f17720])).
% 178.47/22.85 fof(f18340,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1477,f18339])).
% 178.47/22.85 fof(f20852,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f2259,f18340])).
% 178.47/22.85 fof(f20853,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1130,f20852])).
% 178.47/22.85 fof(f21008,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1554,f20853])).
% 178.47/22.85 fof(f21018,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1116,f20853])).
% 178.47/22.85 fof(f21177,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1116,f21008])).
% 178.47/22.85 fof(f21247,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1380,f21018])).
% 178.47/22.85 fof(f21419,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1380,f21177])).
% 178.47/22.85 fof(f21847,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f3225,f21247])).
% 178.47/22.85 fof(f21848,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f948,f21847])).
% 178.47/22.85 fof(f21849,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1477,f21848])).
% 178.47/22.85 fof(f28508,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f21849,f1343])).
% 178.47/22.85 fof(f28509,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1130,f28508])).
% 178.47/22.85 fof(f28510,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1554,f28509])).
% 178.47/22.85 fof(f28511,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_subsumption_resolution,[status(thm)],[f28510,f1364])).
% 178.47/22.85 fof(f28643,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f28511,f12444])).
% 178.47/22.85 fof(f28644,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f948,f28643])).
% 178.47/22.85 fof(f29965,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f28644,f8224])).
% 178.47/22.85 fof(f30138,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f29965,f835])).
% 178.47/22.85 fof(f30139,plain,(
% 178.47/22.85 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),
% 178.47/22.85 inference(split_clause,[status(thm)],[f30138,f410,f845,f947,f621,f823,f635,f867,f690,f709,f856,f954,f671,f834])).
% 178.47/22.85 fof(f30144,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f29965,f1368])).
% 178.47/22.85 fof(f30157,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1130,f29965])).
% 178.47/22.85 fof(f30158,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1116,f30157])).
% 178.47/22.85 fof(f30228,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1116,f30144])).
% 178.47/22.85 fof(f30235,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f30228,f3378])).
% 178.47/22.85 fof(f30303,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f30235,f691])).
% 178.47/22.85 fof(f37742,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f30158,f21419])).
% 178.47/22.85 fof(f39595,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f37742,f2221])).
% 178.47/22.85 fof(f39596,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1116,f39595])).
% 178.47/22.85 fof(f39597,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_subsumption_resolution,[status(thm)],[f39596,f30235])).
% 178.47/22.85 fof(f46275,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f39597,f352])).
% 178.47/22.85 fof(f46741,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f46275,f1477])).
% 178.47/22.85 fof(f46742,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1477,f46741])).
% 178.47/22.85 fof(f63539,plain,(
% 178.47/22.85 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_22|~spl0_137|~spl0_98|~spl0_170|~spl0_103|~spl0_143)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1362,f411])).
% 178.47/22.85 fof(f79716,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1128,f30303])).
% 178.47/22.85 fof(f79717,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f46742,f79716])).
% 178.47/22.85 fof(f79718,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(forward_subsumption_resolution,[status(thm)],[f79717,f63539])).
% 178.47/22.85 fof(f79784,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(resolution,[status(thm)],[f79718,f352])).
% 178.47/22.85 fof(f79862,plain,(
% 178.47/22.85 ![X0,X1]: (and(not(X0),X1)=not(implies(X1,X0))|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_79|~spl0_6|~spl0_83|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1477,f79784])).
% 178.47/22.85 fof(f80015,plain,(
% 178.47/22.85 ![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)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f79784,f1116])).
% 178.47/22.85 fof(f80539,plain,(
% 178.47/22.85 ![X0,X1]: (or(X0,not(X1))=implies(X1,X0)|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_6|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f1554,f80015])).
% 178.47/22.85 fof(f95445,plain,(
% 178.47/22.85 $false|~spl0_15),
% 178.47/22.85 inference(forward_subsumption_resolution,[status(thm)],[f386,f328])).
% 178.47/22.85 fof(f95446,plain,(
% 178.47/22.85 ~spl0_15),
% 178.47/22.85 inference(contradiction_clause,[status(thm)],[f95445])).
% 178.47/22.85 fof(f105708,plain,(
% 178.47/22.85 ![X0,X1]: (implies(not(implies(not(X0),X1)),X0)=implies(not(X1),X0)|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_79|~spl0_6|~spl0_83|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 178.47/22.85 inference(paramodulation,[status(thm)],[f79862,f2133])).
% 178.47/22.85 fof(f105709,plain,(
% 178.47/22.85 ![X0,X1]: (or(implies(not(X0),X1),X0)=implies(not(X1),X0)|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_79|~spl0_6|~spl0_83|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 178.47/22.85 inference(forward_demodulation,[status(thm)],[f1116,f105708])).
% 178.47/22.85 fof(f105710,plain,(
% 178.47/22.85 ![X0,X1]: (or(or(X0,X1),X0)=implies(not(X1),X0)|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_79|~spl0_6|~spl0_83|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 181.00/23.20 inference(forward_demodulation,[status(thm)],[f1116,f105709])).
% 181.00/23.20 fof(f105711,plain,(
% 181.00/23.20 ![X0,X1]: (or(or(X0,X1),X0)=or(X1,X0)|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_79|~spl0_6|~spl0_83|~spl0_98|~spl0_170|~spl0_103|~spl0_134)),
% 181.00/23.20 inference(forward_demodulation,[status(thm)],[f1116,f105710])).
% 181.00/23.20 fof(f105998,plain,(
% 181.00/23.20 ![X0,X1]: (implies(X0,or(not(X0),X1))=or(X1,not(X0))|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_6|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 181.00/23.20 inference(paramodulation,[status(thm)],[f80539,f105711])).
% 181.00/23.20 fof(f105999,plain,(
% 181.00/23.20 ![X0,X1]: (implies(X0,implies(X0,X1))=or(X1,not(X0))|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_6|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 181.00/23.20 inference(forward_demodulation,[status(thm)],[f80015,f105998])).
% 181.00/23.20 fof(f106000,plain,(
% 181.00/23.20 ![X0,X1]: (implies(X0,implies(X0,X1))=implies(X0,X1)|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_6|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83)),
% 181.00/23.20 inference(forward_demodulation,[status(thm)],[f80539,f105999])).
% 181.00/23.20 fof(f107544,plain,(
% 181.00/23.20 ~is_a_theorem(implies(implies(sk0_8,sk0_9),implies(sk0_8,sk0_9)))|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_6|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83|spl0_17),
% 181.00/23.20 inference(backward_demodulation,[status(thm)],[f106000,f394])).
% 181.00/23.20 fof(f107545,plain,(
% 181.00/23.20 $false|~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_6|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83|spl0_17),
% 181.00/23.20 inference(forward_subsumption_resolution,[status(thm)],[f107544,f63539])).
% 181.00/23.20 fof(f107546,plain,(
% 181.00/23.20 ~spl0_22|~spl0_140|~spl0_146|~spl0_137|~spl0_143|~spl0_168|~spl0_93|~spl0_87|~spl0_6|~spl0_79|~spl0_98|~spl0_170|~spl0_103|~spl0_134|~spl0_83|spl0_17),
% 181.00/23.20 inference(contradiction_clause,[status(thm)],[f107545])).
% 181.00/23.20 fof(f107547,plain,(
% 181.00/23.20 $false),
% 181.00/23.20 inference(sat_refutation,[status(thm)],[f354,f395,f624,f638,f652,f674,f693,f712,f826,f837,f848,f859,f870,f950,f957,f959,f961,f963,f965,f967,f969,f973,f975,f977,f990,f994,f1025,f1247,f1293,f30139,f95446,f107546])).
% 181.00/23.20 % SZS output end CNFRefutation for theBenchmark.p
% 182.85/24.28 % Elapsed time: 23.702651 seconds
% 182.85/24.28 % CPU time: 172.997261 seconds
% 182.85/24.28 % Total memory used: 1.776 GB
% 182.85/24.28 % Net memory used: 1.705 GB
%------------------------------------------------------------------------------