TSTP Solution File: LCL501+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL501+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 12:19:28 EDT 2023
% Result : Theorem 219.10s 28.00s
% Output : CNFRefutation 221.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : LCL501+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n029.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 09:56:37 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.32 % Drodi V3.5.1
% 219.10/28.00 % Refutation found
% 219.10/28.00 % SZS status Theorem for theBenchmark: Theorem is valid
% 219.10/28.00 % SZS output start CNFRefutation for theBenchmark
% 219.10/28.00 fof(f1,axiom,(
% 219.10/28.00 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f2,axiom,(
% 219.10/28.00 ( substitution_of_equivalents<=> (! [X,Y] :( is_a_theorem(equiv(X,Y))=> X = Y ) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f18,axiom,(
% 219.10/28.00 ( kn3<=> (! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f22,axiom,(
% 219.10/28.00 ( r1<=> (! [P] : is_a_theorem(implies(or(P,P),P)) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f23,axiom,(
% 219.10/28.00 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f24,axiom,(
% 219.10/28.00 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f25,axiom,(
% 219.10/28.00 ( r4<=> (! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f26,axiom,(
% 219.10/28.00 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f27,axiom,(
% 219.10/28.00 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f28,axiom,(
% 219.10/28.00 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f29,axiom,(
% 219.10/28.00 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f30,axiom,(
% 219.10/28.00 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f31,axiom,(
% 219.10/28.00 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f32,axiom,(
% 219.10/28.00 op_implies_or ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f33,axiom,(
% 219.10/28.00 op_and ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f34,axiom,(
% 219.10/28.00 op_equiv ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f35,axiom,(
% 219.10/28.00 modus_ponens ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f36,axiom,(
% 219.10/28.00 r1 ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f37,axiom,(
% 219.10/28.00 r2 ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f38,axiom,(
% 219.10/28.00 r3 ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f39,axiom,(
% 219.10/28.00 r4 ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f40,axiom,(
% 219.10/28.00 r5 ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f41,axiom,(
% 219.10/28.00 substitution_of_equivalents ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f42,axiom,(
% 219.10/28.00 op_or ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f43,axiom,(
% 219.10/28.00 op_implies_and ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f45,conjecture,(
% 219.10/28.00 kn3 ),
% 219.10/28.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 219.10/28.00 fof(f46,negated_conjecture,(
% 219.10/28.00 ~(kn3 )),
% 219.10/28.00 inference(negated_conjecture,[status(cth)],[f45])).
% 219.10/28.00 fof(f47,plain,(
% 219.10/28.00 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 219.10/28.00 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 219.10/28.00 fof(f48,plain,(
% 219.10/28.00 (~modus_ponens|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y))))&(modus_ponens|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(implies(X,Y)))&~is_a_theorem(Y))))),
% 219.10/28.00 inference(NNF_transformation,[status(esa)],[f47])).
% 219.10/28.00 fof(f49,plain,(
% 219.10/28.00 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|(?[Y]: ((?[X]: (is_a_theorem(X)&is_a_theorem(implies(X,Y))))&~is_a_theorem(Y))))),
% 219.10/28.00 inference(miniscoping,[status(esa)],[f48])).
% 219.24/28.01 fof(f50,plain,(
% 219.24/28.01 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|((is_a_theorem(sk0_1)&is_a_theorem(implies(sk0_1,sk0_0)))&~is_a_theorem(sk0_0)))),
% 219.24/28.01 inference(skolemization,[status(esa)],[f49])).
% 219.24/28.01 fof(f51,plain,(
% 219.24/28.01 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f50])).
% 219.24/28.01 fof(f55,plain,(
% 219.24/28.01 substitution_of_equivalents<=>(![X,Y]: (~is_a_theorem(equiv(X,Y))|X=Y))),
% 219.24/28.01 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 219.24/28.01 fof(f56,plain,(
% 219.24/28.01 (~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)))),
% 219.24/28.01 inference(NNF_transformation,[status(esa)],[f55])).
% 219.24/28.01 fof(f57,plain,(
% 219.24/28.01 (~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))),
% 219.24/28.01 inference(skolemization,[status(esa)],[f56])).
% 219.24/28.01 fof(f58,plain,(
% 219.24/28.01 ![X0,X1]: (~substitution_of_equivalents|~is_a_theorem(equiv(X0,X1))|X0=X1)),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f57])).
% 219.24/28.01 fof(f121,plain,(
% 219.24/28.01 (~kn3|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))))&(kn3|(?[P,Q,R]: ~is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))))),
% 219.24/28.01 inference(NNF_transformation,[status(esa)],[f18])).
% 219.24/28.01 fof(f122,plain,(
% 219.24/28.01 (~kn3|(![P,Q,R]: is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))))&(kn3|~is_a_theorem(implies(implies(sk0_35,sk0_36),implies(not(and(sk0_36,sk0_37)),not(and(sk0_37,sk0_35))))))),
% 219.24/28.01 inference(skolemization,[status(esa)],[f121])).
% 219.24/28.01 fof(f124,plain,(
% 219.24/28.01 kn3|~is_a_theorem(implies(implies(sk0_35,sk0_36),implies(not(and(sk0_36,sk0_37)),not(and(sk0_37,sk0_35)))))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f122])).
% 219.24/28.01 fof(f137,plain,(
% 219.24/28.01 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|(?[P]: ~is_a_theorem(implies(or(P,P),P))))),
% 219.24/28.01 inference(NNF_transformation,[status(esa)],[f22])).
% 219.24/28.01 fof(f138,plain,(
% 219.24/28.01 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|~is_a_theorem(implies(or(sk0_44,sk0_44),sk0_44)))),
% 219.24/28.01 inference(skolemization,[status(esa)],[f137])).
% 219.24/28.01 fof(f139,plain,(
% 219.24/28.01 ![X0]: (~r1|is_a_theorem(implies(or(X0,X0),X0)))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f138])).
% 219.24/28.01 fof(f141,plain,(
% 219.24/28.01 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 219.24/28.01 inference(NNF_transformation,[status(esa)],[f23])).
% 219.24/28.01 fof(f142,plain,(
% 219.24/28.01 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sk0_46,or(sk0_45,sk0_46))))),
% 219.24/28.01 inference(skolemization,[status(esa)],[f141])).
% 219.24/28.01 fof(f143,plain,(
% 219.24/28.01 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f142])).
% 219.24/28.01 fof(f145,plain,(
% 219.24/28.01 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|(?[P,Q]: ~is_a_theorem(implies(or(P,Q),or(Q,P)))))),
% 219.24/28.01 inference(NNF_transformation,[status(esa)],[f24])).
% 219.24/28.01 fof(f146,plain,(
% 219.24/28.01 (~r3|(![P,Q]: is_a_theorem(implies(or(P,Q),or(Q,P)))))&(r3|~is_a_theorem(implies(or(sk0_47,sk0_48),or(sk0_48,sk0_47))))),
% 219.24/28.01 inference(skolemization,[status(esa)],[f145])).
% 219.24/28.01 fof(f147,plain,(
% 219.24/28.01 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f146])).
% 219.24/28.01 fof(f149,plain,(
% 219.24/28.01 (~r4|(![P,Q,R]: is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))&(r4|(?[P,Q,R]: ~is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))),
% 219.24/28.01 inference(NNF_transformation,[status(esa)],[f25])).
% 219.24/28.01 fof(f150,plain,(
% 219.24/28.01 (~r4|(![P,Q,R]: is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))))&(r4|~is_a_theorem(implies(or(sk0_49,or(sk0_50,sk0_51)),or(sk0_50,or(sk0_49,sk0_51)))))),
% 219.24/28.01 inference(skolemization,[status(esa)],[f149])).
% 219.24/28.01 fof(f151,plain,(
% 219.24/28.01 ![X0,X1,X2]: (~r4|is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f150])).
% 219.24/28.01 fof(f153,plain,(
% 219.24/28.01 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|(?[P,Q,R]: ~is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))),
% 219.24/28.01 inference(NNF_transformation,[status(esa)],[f26])).
% 219.24/28.01 fof(f154,plain,(
% 219.24/28.01 (~r5|(![P,Q,R]: is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))))&(r5|~is_a_theorem(implies(implies(sk0_53,sk0_54),implies(or(sk0_52,sk0_53),or(sk0_52,sk0_54)))))),
% 219.24/28.01 inference(skolemization,[status(esa)],[f153])).
% 219.24/28.01 fof(f155,plain,(
% 219.24/28.01 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f154])).
% 219.24/28.01 fof(f157,plain,(
% 219.24/28.01 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 219.24/28.01 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 219.24/28.01 fof(f158,plain,(
% 219.24/28.01 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f157])).
% 219.24/28.01 fof(f159,plain,(
% 219.24/28.01 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 219.24/28.01 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 219.24/28.01 fof(f160,plain,(
% 219.24/28.01 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f159])).
% 219.24/28.01 fof(f161,plain,(
% 219.24/28.01 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 219.24/28.01 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 219.24/28.01 fof(f162,plain,(
% 219.24/28.01 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f161])).
% 219.24/28.01 fof(f163,plain,(
% 219.24/28.01 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 219.24/28.01 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 219.24/28.01 fof(f164,plain,(
% 219.24/28.01 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f163])).
% 219.24/28.01 fof(f165,plain,(
% 219.24/28.01 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 219.24/28.01 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 219.24/28.01 fof(f166,plain,(
% 219.24/28.01 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f165])).
% 219.24/28.01 fof(f167,plain,(
% 219.24/28.01 op_implies_or),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f32])).
% 219.24/28.01 fof(f168,plain,(
% 219.24/28.01 op_and),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f33])).
% 219.24/28.01 fof(f169,plain,(
% 219.24/28.01 op_equiv),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f34])).
% 219.24/28.01 fof(f170,plain,(
% 219.24/28.01 modus_ponens),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f35])).
% 219.24/28.01 fof(f171,plain,(
% 219.24/28.01 r1),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f36])).
% 219.24/28.01 fof(f172,plain,(
% 219.24/28.01 r2),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f37])).
% 219.24/28.01 fof(f173,plain,(
% 219.24/28.01 r3),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f38])).
% 219.24/28.01 fof(f174,plain,(
% 219.24/28.01 r4),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f39])).
% 219.24/28.01 fof(f175,plain,(
% 219.24/28.01 r5),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f40])).
% 219.24/28.01 fof(f176,plain,(
% 219.24/28.01 substitution_of_equivalents),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f41])).
% 219.24/28.01 fof(f177,plain,(
% 219.24/28.01 op_or),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f42])).
% 219.24/28.01 fof(f178,plain,(
% 219.24/28.01 op_implies_and),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f43])).
% 219.24/28.01 fof(f180,plain,(
% 219.24/28.01 ~kn3),
% 219.24/28.01 inference(cnf_transformation,[status(esa)],[f46])).
% 219.24/28.01 fof(f181,plain,(
% 219.24/28.01 spl0_0 <=> modus_ponens),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f183,plain,(
% 219.24/28.01 ~modus_ponens|spl0_0),
% 219.24/28.01 inference(component_clause,[status(thm)],[f181])).
% 219.24/28.01 fof(f184,plain,(
% 219.24/28.01 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f185,plain,(
% 219.24/28.01 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f184])).
% 219.24/28.01 fof(f187,plain,(
% 219.24/28.01 ~spl0_0|spl0_1),
% 219.24/28.01 inference(split_clause,[status(thm)],[f51,f181,f184])).
% 219.24/28.01 fof(f200,plain,(
% 219.24/28.01 spl0_5 <=> substitution_of_equivalents),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f202,plain,(
% 219.24/28.01 ~substitution_of_equivalents|spl0_5),
% 219.24/28.01 inference(component_clause,[status(thm)],[f200])).
% 219.24/28.01 fof(f203,plain,(
% 219.24/28.01 spl0_6 <=> ~is_a_theorem(equiv(X0,X1))|X0=X1),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f204,plain,(
% 219.24/28.01 ![X0,X1]: (~is_a_theorem(equiv(X0,X1))|X0=X1|~spl0_6)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f203])).
% 219.24/28.01 fof(f206,plain,(
% 219.24/28.01 ~spl0_5|spl0_6),
% 219.24/28.01 inference(split_clause,[status(thm)],[f58,f200,f203])).
% 219.24/28.01 fof(f251,plain,(
% 219.24/28.01 spl0_19 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f252,plain,(
% 219.24/28.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))|~spl0_19)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f251])).
% 219.24/28.01 fof(f306,plain,(
% 219.24/28.01 spl0_34 <=> is_a_theorem(implies(X0,or(X1,X0)))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f307,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~spl0_34)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f306])).
% 219.24/28.01 fof(f350,plain,(
% 219.24/28.01 spl0_46 <=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f351,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))|~spl0_46)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f350])).
% 219.24/28.01 fof(f377,plain,(
% 219.24/28.01 spl0_53 <=> kn3),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f378,plain,(
% 219.24/28.01 kn3|~spl0_53),
% 219.24/28.01 inference(component_clause,[status(thm)],[f377])).
% 219.24/28.01 fof(f384,plain,(
% 219.24/28.01 spl0_55 <=> is_a_theorem(implies(implies(sk0_35,sk0_36),implies(not(and(sk0_36,sk0_37)),not(and(sk0_37,sk0_35)))))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f386,plain,(
% 219.24/28.01 ~is_a_theorem(implies(implies(sk0_35,sk0_36),implies(not(and(sk0_36,sk0_37)),not(and(sk0_37,sk0_35)))))|spl0_55),
% 219.24/28.01 inference(component_clause,[status(thm)],[f384])).
% 219.24/28.01 fof(f387,plain,(
% 219.24/28.01 spl0_53|~spl0_55),
% 219.24/28.01 inference(split_clause,[status(thm)],[f124,f377,f384])).
% 219.24/28.01 fof(f418,plain,(
% 219.24/28.01 spl0_64 <=> r1),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f420,plain,(
% 219.24/28.01 ~r1|spl0_64),
% 219.24/28.01 inference(component_clause,[status(thm)],[f418])).
% 219.24/28.01 fof(f421,plain,(
% 219.24/28.01 spl0_65 <=> is_a_theorem(implies(or(X0,X0),X0))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f422,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(implies(or(X0,X0),X0))|~spl0_65)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f421])).
% 219.24/28.01 fof(f424,plain,(
% 219.24/28.01 ~spl0_64|spl0_65),
% 219.24/28.01 inference(split_clause,[status(thm)],[f139,f418,f421])).
% 219.24/28.01 fof(f429,plain,(
% 219.24/28.01 spl0_67 <=> r2),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f431,plain,(
% 219.24/28.01 ~r2|spl0_67),
% 219.24/28.01 inference(component_clause,[status(thm)],[f429])).
% 219.24/28.01 fof(f432,plain,(
% 219.24/28.01 ~spl0_67|spl0_34),
% 219.24/28.01 inference(split_clause,[status(thm)],[f143,f429,f306])).
% 219.24/28.01 fof(f437,plain,(
% 219.24/28.01 spl0_69 <=> r3),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f439,plain,(
% 219.24/28.01 ~r3|spl0_69),
% 219.24/28.01 inference(component_clause,[status(thm)],[f437])).
% 219.24/28.01 fof(f440,plain,(
% 219.24/28.01 spl0_70 <=> is_a_theorem(implies(or(X0,X1),or(X1,X0)))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f441,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_70)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f440])).
% 219.24/28.01 fof(f443,plain,(
% 219.24/28.01 ~spl0_69|spl0_70),
% 219.24/28.01 inference(split_clause,[status(thm)],[f147,f437,f440])).
% 219.24/28.01 fof(f448,plain,(
% 219.24/28.01 spl0_72 <=> r4),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f450,plain,(
% 219.24/28.01 ~r4|spl0_72),
% 219.24/28.01 inference(component_clause,[status(thm)],[f448])).
% 219.24/28.01 fof(f451,plain,(
% 219.24/28.01 spl0_73 <=> is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f452,plain,(
% 219.24/28.01 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))|~spl0_73)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f451])).
% 219.24/28.01 fof(f454,plain,(
% 219.24/28.01 ~spl0_72|spl0_73),
% 219.24/28.01 inference(split_clause,[status(thm)],[f151,f448,f451])).
% 219.24/28.01 fof(f459,plain,(
% 219.24/28.01 spl0_75 <=> r5),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f461,plain,(
% 219.24/28.01 ~r5|spl0_75),
% 219.24/28.01 inference(component_clause,[status(thm)],[f459])).
% 219.24/28.01 fof(f462,plain,(
% 219.24/28.01 spl0_76 <=> is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f463,plain,(
% 219.24/28.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))|~spl0_76)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f462])).
% 219.24/28.01 fof(f465,plain,(
% 219.24/28.01 ~spl0_75|spl0_76),
% 219.24/28.01 inference(split_clause,[status(thm)],[f155,f459,f462])).
% 219.24/28.01 fof(f470,plain,(
% 219.24/28.01 spl0_78 <=> op_or),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f472,plain,(
% 219.24/28.01 ~op_or|spl0_78),
% 219.24/28.01 inference(component_clause,[status(thm)],[f470])).
% 219.24/28.01 fof(f473,plain,(
% 219.24/28.01 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f474,plain,(
% 219.24/28.01 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f473])).
% 219.24/28.01 fof(f476,plain,(
% 219.24/28.01 ~spl0_78|spl0_79),
% 219.24/28.01 inference(split_clause,[status(thm)],[f158,f470,f473])).
% 219.24/28.01 fof(f477,plain,(
% 219.24/28.01 spl0_80 <=> op_and),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f479,plain,(
% 219.24/28.01 ~op_and|spl0_80),
% 219.24/28.01 inference(component_clause,[status(thm)],[f477])).
% 219.24/28.01 fof(f480,plain,(
% 219.24/28.01 spl0_81 <=> and(X0,X1)=not(or(not(X0),not(X1)))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f481,plain,(
% 219.24/28.01 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1)))|~spl0_81)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f480])).
% 219.24/28.01 fof(f483,plain,(
% 219.24/28.01 ~spl0_80|spl0_81),
% 219.24/28.01 inference(split_clause,[status(thm)],[f160,f477,f480])).
% 219.24/28.01 fof(f484,plain,(
% 219.24/28.01 spl0_82 <=> op_implies_and),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f486,plain,(
% 219.24/28.01 ~op_implies_and|spl0_82),
% 219.24/28.01 inference(component_clause,[status(thm)],[f484])).
% 219.24/28.01 fof(f487,plain,(
% 219.24/28.01 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f488,plain,(
% 219.24/28.01 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f487])).
% 219.24/28.01 fof(f490,plain,(
% 219.24/28.01 ~spl0_82|spl0_83),
% 219.24/28.01 inference(split_clause,[status(thm)],[f162,f484,f487])).
% 219.24/28.01 fof(f491,plain,(
% 219.24/28.01 spl0_84 <=> op_implies_or),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f493,plain,(
% 219.24/28.01 ~op_implies_or|spl0_84),
% 219.24/28.01 inference(component_clause,[status(thm)],[f491])).
% 219.24/28.01 fof(f494,plain,(
% 219.24/28.01 spl0_85 <=> implies(X0,X1)=or(not(X0),X1)),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f495,plain,(
% 219.24/28.01 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~spl0_85)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f494])).
% 219.24/28.01 fof(f497,plain,(
% 219.24/28.01 ~spl0_84|spl0_85),
% 219.24/28.01 inference(split_clause,[status(thm)],[f164,f491,f494])).
% 219.24/28.01 fof(f498,plain,(
% 219.24/28.01 spl0_86 <=> op_equiv),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f500,plain,(
% 219.24/28.01 ~op_equiv|spl0_86),
% 219.24/28.01 inference(component_clause,[status(thm)],[f498])).
% 219.24/28.01 fof(f501,plain,(
% 219.24/28.01 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 219.24/28.01 introduced(split_symbol_definition)).
% 219.24/28.01 fof(f502,plain,(
% 219.24/28.01 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 219.24/28.01 inference(component_clause,[status(thm)],[f501])).
% 219.24/28.01 fof(f504,plain,(
% 219.24/28.01 ~spl0_86|spl0_87),
% 219.24/28.01 inference(split_clause,[status(thm)],[f166,f498,f501])).
% 219.24/28.01 fof(f505,plain,(
% 219.24/28.01 $false|spl0_86),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f500,f169])).
% 219.24/28.01 fof(f506,plain,(
% 219.24/28.01 spl0_86),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f505])).
% 219.24/28.01 fof(f507,plain,(
% 219.24/28.01 $false|spl0_0),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f183,f170])).
% 219.24/28.01 fof(f508,plain,(
% 219.24/28.01 spl0_0),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f507])).
% 219.24/28.01 fof(f509,plain,(
% 219.24/28.01 $false|spl0_5),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f202,f176])).
% 219.24/28.01 fof(f510,plain,(
% 219.24/28.01 spl0_5),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f509])).
% 219.24/28.01 fof(f511,plain,(
% 219.24/28.01 $false|spl0_84),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f493,f167])).
% 219.24/28.01 fof(f512,plain,(
% 219.24/28.01 spl0_84),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f511])).
% 219.24/28.01 fof(f513,plain,(
% 219.24/28.01 $false|spl0_82),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f486,f178])).
% 219.24/28.01 fof(f514,plain,(
% 219.24/28.01 spl0_82),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f513])).
% 219.24/28.01 fof(f515,plain,(
% 219.24/28.01 $false|spl0_80),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f479,f168])).
% 219.24/28.01 fof(f516,plain,(
% 219.24/28.01 spl0_80),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f515])).
% 219.24/28.01 fof(f517,plain,(
% 219.24/28.01 $false|spl0_78),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f472,f177])).
% 219.24/28.01 fof(f518,plain,(
% 219.24/28.01 spl0_78),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f517])).
% 219.24/28.01 fof(f520,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(implies(implies(X0,not(X0)),not(X0)))|~spl0_65|~spl0_85)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f495,f422])).
% 219.24/28.01 fof(f523,plain,(
% 219.24/28.01 $false|spl0_67),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f431,f172])).
% 219.24/28.01 fof(f524,plain,(
% 219.24/28.01 spl0_67),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f523])).
% 219.24/28.01 fof(f527,plain,(
% 219.24/28.01 $false|spl0_64),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f420,f171])).
% 219.24/28.01 fof(f528,plain,(
% 219.24/28.01 spl0_64),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f527])).
% 219.24/28.01 fof(f554,plain,(
% 219.24/28.01 $false|spl0_69),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f439,f173])).
% 219.24/28.01 fof(f555,plain,(
% 219.24/28.01 spl0_69),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f554])).
% 219.24/28.01 fof(f556,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0))))|~spl0_70|~spl0_85)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f495,f441])).
% 219.24/28.01 fof(f557,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0)))|~spl0_70|~spl0_85)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f495,f441])).
% 219.24/28.01 fof(f560,plain,(
% 219.24/28.01 ![X0]: (~is_a_theorem(or(X0,X0))|is_a_theorem(X0)|~spl0_1|~spl0_65)),
% 219.24/28.01 inference(resolution,[status(thm)],[f185,f422])).
% 219.24/28.01 fof(f582,plain,(
% 219.24/28.01 ![X0,X1,X2]: (implies(X0,and(X1,not(X2)))=not(and(X0,implies(X1,X2)))|~spl0_83)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f488,f488])).
% 219.24/28.01 fof(f640,plain,(
% 219.24/28.01 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1)))|~spl0_85|~spl0_81)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f495,f481])).
% 219.24/28.01 fof(f641,plain,(
% 219.24/28.01 ![X0,X1,X2]: (and(X0,implies(X1,not(X2)))=not(implies(X0,and(X1,X2)))|~spl0_85|~spl0_81)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f640,f640])).
% 219.24/28.01 fof(f650,plain,(
% 219.24/28.01 ![X0,X1,X2]: (implies(implies(X0,not(X1)),X2)=or(and(X0,X1),X2)|~spl0_85|~spl0_81)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f640,f495])).
% 219.24/28.01 fof(f651,plain,(
% 219.24/28.01 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f488,f474])).
% 219.24/28.01 fof(f653,plain,(
% 219.24/28.01 ![X0,X1,X2]: (or(and(X0,not(X1)),X2)=implies(implies(X0,X1),X2)|~spl0_79|~spl0_83)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f488,f651])).
% 219.24/28.01 fof(f663,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(or(X0,or(X1,not(X0))))|~spl0_34|~spl0_83|~spl0_79)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f651,f307])).
% 219.24/28.01 fof(f665,plain,(
% 219.24/28.01 ![X0,X1]: (equiv(not(X0),X1)=and(or(X0,X1),implies(X1,not(X0)))|~spl0_87|~spl0_83|~spl0_79)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f651,f502])).
% 219.24/28.01 fof(f735,plain,(
% 219.24/28.01 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(or(X1,not(X0)))|~spl0_70|~spl0_85|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f556,f185])).
% 219.24/28.01 fof(f746,plain,(
% 219.24/28.01 $false|spl0_75),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f461,f175])).
% 219.24/28.01 fof(f747,plain,(
% 219.24/28.01 spl0_75),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f746])).
% 219.24/28.01 fof(f748,plain,(
% 219.24/28.01 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(or(X2,X0),or(X2,X1)))|~spl0_76|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f463,f185])).
% 219.24/28.01 fof(f754,plain,(
% 219.24/28.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1))))|~spl0_76|~spl0_85)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f495,f463])).
% 219.24/28.01 fof(f755,plain,(
% 219.24/28.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))|~spl0_76|~spl0_85)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f495,f754])).
% 219.24/28.01 fof(f760,plain,(
% 219.24/28.01 $false|spl0_72),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f450,f174])).
% 219.24/28.01 fof(f761,plain,(
% 219.24/28.01 spl0_72),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f760])).
% 219.24/28.01 fof(f762,plain,(
% 219.24/28.01 ![X0,X1,X2]: (~is_a_theorem(or(X0,or(X1,X2)))|is_a_theorem(or(X1,or(X0,X2)))|~spl0_73|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f452,f185])).
% 219.24/28.01 fof(f767,plain,(
% 219.24/28.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2))))|~spl0_73|~spl0_85)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f495,f452])).
% 219.24/28.01 fof(f768,plain,(
% 219.24/28.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2))))|~spl0_73|~spl0_85)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f495,f767])).
% 219.24/28.01 fof(f777,plain,(
% 219.24/28.01 ![X0,X1]: (~is_a_theorem(or(X0,not(X1)))|is_a_theorem(implies(X1,X0))|~spl0_70|~spl0_85|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f557,f185])).
% 219.24/28.01 fof(f909,plain,(
% 219.24/28.01 ~is_a_theorem(implies(implies(sk0_35,sk0_36),or(and(sk0_36,sk0_37),not(and(sk0_37,sk0_35)))))|~spl0_83|~spl0_79|spl0_55),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f651,f386])).
% 219.24/28.01 fof(f959,plain,(
% 219.24/28.01 ![X0,X1,X2]: (~is_a_theorem(implies(implies(or(X0,X1),or(X1,X0)),X2))|is_a_theorem(X2)|~spl0_70|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f441,f185])).
% 219.24/28.01 fof(f1733,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(or(not(X0),not(implies(X0,not(X0)))))|~spl0_70|~spl0_1|~spl0_65|~spl0_85)),
% 219.24/28.01 inference(resolution,[status(thm)],[f735,f520])).
% 219.24/28.01 fof(f1734,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(implies(X0,not(implies(X0,not(X0)))))|~spl0_70|~spl0_1|~spl0_65|~spl0_85)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f495,f1733])).
% 219.24/28.01 fof(f1735,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(implies(X0,and(X0,X0)))|~spl0_81|~spl0_70|~spl0_1|~spl0_65|~spl0_85)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f640,f1734])).
% 219.24/28.01 fof(f1761,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(implies(implies(X0,X0),equiv(X0,X0)))|~spl0_81|~spl0_70|~spl0_1|~spl0_65|~spl0_85|~spl0_87)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f502,f1735])).
% 219.24/28.01 fof(f1846,plain,(
% 219.24/28.01 ![X0,X1]: (implies(implies(X0,X1),and(X1,not(X0)))=not(equiv(X0,X1))|~spl0_83|~spl0_87)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f502,f582])).
% 219.24/28.01 fof(f2875,plain,(
% 219.24/28.01 ![X0,X1]: (equiv(not(X0),X1)=not(implies(or(X0,X1),and(X1,X0)))|~spl0_85|~spl0_81|~spl0_87|~spl0_83|~spl0_79)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f641,f665])).
% 219.24/28.01 fof(f2884,plain,(
% 219.24/28.01 ![X0,X1]: (equiv(not(not(X0)),X1)=not(implies(implies(X0,X1),and(X1,not(X0))))|~spl0_81|~spl0_87|~spl0_83|~spl0_79|~spl0_85)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f495,f2875])).
% 219.24/28.01 fof(f2946,plain,(
% 219.24/28.01 ![X0,X1,X2]: (is_a_theorem(implies(or(X0,implies(X1,X2)),or(X0,or(X2,not(X1)))))|~spl0_76|~spl0_1|~spl0_70|~spl0_85)),
% 219.24/28.01 inference(resolution,[status(thm)],[f748,f556])).
% 219.24/28.01 fof(f3062,plain,(
% 219.24/28.01 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))),X3))|is_a_theorem(X3)|~spl0_76|~spl0_85|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f755,f185])).
% 219.24/28.01 fof(f3096,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(or(X0,or(X1,not(X1))))|~spl0_73|~spl0_1|~spl0_34|~spl0_83|~spl0_79)),
% 219.24/28.01 inference(resolution,[status(thm)],[f762,f663])).
% 219.24/28.01 fof(f3170,plain,(
% 219.24/28.01 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(X0,implies(implies(X1,X2),X3)),or(and(X1,not(X2)),implies(X0,X3))))|~spl0_73|~spl0_85|~spl0_79|~spl0_83)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f653,f768])).
% 219.24/28.01 fof(f3171,plain,(
% 219.24/28.01 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(X0,implies(implies(X1,X2),X3)),implies(implies(X1,X2),implies(X0,X3))))|~spl0_73|~spl0_85|~spl0_79|~spl0_83)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f653,f3170])).
% 219.24/28.01 fof(f3380,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(or(X0,not(X0)))|~spl0_73|~spl0_34|~spl0_83|~spl0_79|~spl0_1|~spl0_65)),
% 219.24/28.01 inference(resolution,[status(thm)],[f3096,f560])).
% 219.24/28.01 fof(f3408,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_73|~spl0_34|~spl0_83|~spl0_79|~spl0_65|~spl0_70|~spl0_85|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f3380,f777])).
% 219.24/28.01 fof(f3427,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(implies(X0,not(not(X0))))|~spl0_73|~spl0_34|~spl0_83|~spl0_79|~spl0_1|~spl0_65|~spl0_85)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f495,f3380])).
% 219.24/28.01 fof(f3444,plain,(
% 219.24/28.01 ![X0,X1]: (~is_a_theorem(implies(implies(X0,X0),X1))|is_a_theorem(X1)|~spl0_73|~spl0_34|~spl0_83|~spl0_79|~spl0_65|~spl0_70|~spl0_85|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f3408,f185])).
% 219.24/28.01 fof(f3755,plain,(
% 219.24/28.01 $false|~spl0_53),
% 219.24/28.01 inference(forward_subsumption_resolution,[status(thm)],[f378,f180])).
% 219.24/28.01 fof(f3756,plain,(
% 219.24/28.01 ~spl0_53),
% 219.24/28.01 inference(contradiction_clause,[status(thm)],[f3755])).
% 219.24/28.01 fof(f4079,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(or(X0,implies(or(X1,X0),X1)))|~spl0_70|~spl0_1|~spl0_73|~spl0_85)),
% 219.24/28.01 inference(resolution,[status(thm)],[f959,f768])).
% 219.24/28.01 fof(f4642,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(equiv(X0,X0))|~spl0_73|~spl0_34|~spl0_83|~spl0_79|~spl0_81|~spl0_70|~spl0_1|~spl0_65|~spl0_85|~spl0_87)),
% 219.24/28.01 inference(resolution,[status(thm)],[f3444,f1761])).
% 219.24/28.01 fof(f4677,plain,(
% 219.24/28.01 ![X0,X1]: (~is_a_theorem(implies(equiv(X0,X0),X1))|is_a_theorem(X1)|~spl0_73|~spl0_34|~spl0_83|~spl0_79|~spl0_81|~spl0_70|~spl0_65|~spl0_85|~spl0_87|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f4642,f185])).
% 219.24/28.01 fof(f5553,plain,(
% 219.24/28.01 ![X0,X1,X2]: (~is_a_theorem(implies(or(X0,implies(or(X1,X0),X1)),X2))|is_a_theorem(X2)|~spl0_70|~spl0_73|~spl0_85|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f4079,f185])).
% 219.24/28.01 fof(f5845,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(not(not(equiv(X0,X0))))|~spl0_81|~spl0_70|~spl0_87|~spl0_73|~spl0_34|~spl0_83|~spl0_79|~spl0_1|~spl0_65|~spl0_85)),
% 219.24/28.01 inference(resolution,[status(thm)],[f4677,f3427])).
% 219.24/28.01 fof(f45841,plain,(
% 219.24/28.01 ![X0,X1]: (equiv(not(not(X0)),X1)=not(not(equiv(X0,X1)))|~spl0_81|~spl0_87|~spl0_83|~spl0_79|~spl0_85)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f1846,f2884])).
% 219.24/28.01 fof(f45845,plain,(
% 219.24/28.01 ![X0]: (is_a_theorem(equiv(not(not(X0)),X0))|~spl0_81|~spl0_70|~spl0_87|~spl0_73|~spl0_34|~spl0_83|~spl0_79|~spl0_1|~spl0_65|~spl0_85)),
% 219.24/28.01 inference(backward_demodulation,[status(thm)],[f45841,f5845])).
% 219.24/28.01 fof(f47004,plain,(
% 219.24/28.01 ![X0]: (not(not(X0))=X0|~spl0_81|~spl0_70|~spl0_87|~spl0_73|~spl0_34|~spl0_83|~spl0_79|~spl0_1|~spl0_65|~spl0_85|~spl0_6)),
% 219.24/28.01 inference(resolution,[status(thm)],[f45845,f204])).
% 219.24/28.01 fof(f47132,plain,(
% 219.24/28.01 ![X0,X1]: (not(and(X0,X1))=implies(X0,not(X1))|~spl0_70|~spl0_87|~spl0_73|~spl0_34|~spl0_83|~spl0_79|~spl0_1|~spl0_65|~spl0_6|~spl0_85|~spl0_81)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f640,f47004])).
% 219.24/28.01 fof(f49970,plain,(
% 219.24/28.01 ~is_a_theorem(implies(implies(sk0_35,sk0_36),or(and(sk0_36,sk0_37),implies(sk0_37,not(sk0_35)))))|~spl0_70|~spl0_87|~spl0_73|~spl0_34|~spl0_1|~spl0_65|~spl0_6|~spl0_85|~spl0_81|~spl0_83|~spl0_79|spl0_55),
% 219.24/28.01 inference(backward_demodulation,[status(thm)],[f47132,f909])).
% 219.24/28.01 fof(f69369,plain,(
% 219.24/28.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))|~spl0_73|~spl0_79|~spl0_83|~spl0_76|~spl0_85|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f3171,f3062])).
% 219.24/28.01 fof(f69370,plain,(
% 219.24/28.01 spl0_19|~spl0_73|~spl0_79|~spl0_83|~spl0_76|~spl0_85|~spl0_1),
% 219.24/28.01 inference(split_clause,[status(thm)],[f69369,f251,f451,f473,f487,f462,f494,f184])).
% 219.24/28.01 fof(f69550,plain,(
% 219.24/28.01 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),implies(X0,not(X2)))))|~spl0_19|~spl0_85|~spl0_81)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f650,f252])).
% 219.24/28.01 fof(f213323,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(or(X0,or(X1,not(or(X1,X0)))))|~spl0_73|~spl0_76|~spl0_1|~spl0_70|~spl0_85)),
% 219.24/28.01 inference(resolution,[status(thm)],[f5553,f2946])).
% 219.24/28.01 fof(f213615,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(or(X0,or(X1,not(or(X0,X1)))))|~spl0_76|~spl0_70|~spl0_85|~spl0_73|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f213323,f762])).
% 219.24/28.01 fof(f213865,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,not(or(not(X0),X1)))))|~spl0_76|~spl0_70|~spl0_73|~spl0_1|~spl0_85)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f495,f213615])).
% 219.24/28.01 fof(f213866,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,not(implies(X0,X1)))))|~spl0_76|~spl0_70|~spl0_73|~spl0_1|~spl0_85)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f495,f213865])).
% 219.24/28.01 fof(f214985,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,not(implies(X0,not(X1))))))|~spl0_76|~spl0_70|~spl0_73|~spl0_1|~spl0_85)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f495,f213866])).
% 219.24/28.01 fof(f214986,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1))))|~spl0_81|~spl0_76|~spl0_70|~spl0_73|~spl0_1|~spl0_85)),
% 219.24/28.01 inference(forward_demodulation,[status(thm)],[f640,f214985])).
% 219.24/28.01 fof(f215201,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))|~spl0_81|~spl0_76|~spl0_70|~spl0_73|~spl0_1|~spl0_85|~spl0_87)),
% 219.24/28.01 inference(paramodulation,[status(thm)],[f502,f214986])).
% 219.24/28.01 fof(f215202,plain,(
% 219.24/28.01 spl0_46|~spl0_81|~spl0_76|~spl0_70|~spl0_73|~spl0_1|~spl0_85|~spl0_87),
% 219.24/28.01 inference(split_clause,[status(thm)],[f215201,f350,f480,f462,f440,f451,f184,f494,f501])).
% 219.24/28.01 fof(f216202,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(implies(implies(or(X0,X1),or(X1,X0)),equiv(or(X1,X0),or(X0,X1))))|~spl0_46|~spl0_70|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f351,f959])).
% 219.24/28.01 fof(f246683,plain,(
% 219.24/28.01 ![X0,X1]: (is_a_theorem(equiv(or(X0,X1),or(X1,X0)))|~spl0_46|~spl0_70|~spl0_1)),
% 219.24/28.01 inference(resolution,[status(thm)],[f216202,f959])).
% 219.24/28.01 fof(f247057,plain,(
% 219.24/28.01 ![X0,X1]: (or(X0,X1)=or(X1,X0)|~spl0_46|~spl0_70|~spl0_1|~spl0_6)),
% 219.24/28.01 inference(resolution,[status(thm)],[f246683,f204])).
% 221.40/28.34 fof(f247160,plain,(
% 221.40/28.34 ![X0,X1]: (implies(X0,X1)=or(X1,not(X0))|~spl0_46|~spl0_70|~spl0_1|~spl0_6|~spl0_85)),
% 221.40/28.34 inference(paramodulation,[status(thm)],[f495,f247057])).
% 221.40/28.34 fof(f249611,plain,(
% 221.40/28.34 ![X0,X1]: (implies(X0,not(X1))=implies(X1,not(X0))|~spl0_46|~spl0_70|~spl0_1|~spl0_6|~spl0_85)),
% 221.40/28.34 inference(paramodulation,[status(thm)],[f495,f247160])).
% 221.40/28.34 fof(f253693,plain,(
% 221.40/28.34 ~is_a_theorem(implies(implies(sk0_35,sk0_36),or(and(sk0_36,sk0_37),implies(sk0_35,not(sk0_37)))))|~spl0_87|~spl0_73|~spl0_34|~spl0_65|~spl0_81|~spl0_83|~spl0_79|spl0_55|~spl0_46|~spl0_70|~spl0_1|~spl0_6|~spl0_85),
% 221.40/28.34 inference(paramodulation,[status(thm)],[f249611,f49970])).
% 221.40/28.34 fof(f253694,plain,(
% 221.40/28.34 $false|~spl0_19|~spl0_87|~spl0_73|~spl0_34|~spl0_65|~spl0_81|~spl0_83|~spl0_79|spl0_55|~spl0_46|~spl0_70|~spl0_1|~spl0_6|~spl0_85),
% 221.40/28.34 inference(forward_subsumption_resolution,[status(thm)],[f253693,f69550])).
% 221.40/28.34 fof(f253695,plain,(
% 221.40/28.34 ~spl0_19|~spl0_87|~spl0_73|~spl0_34|~spl0_65|~spl0_81|~spl0_83|~spl0_79|spl0_55|~spl0_46|~spl0_70|~spl0_1|~spl0_6|~spl0_85),
% 221.40/28.34 inference(contradiction_clause,[status(thm)],[f253694])).
% 221.40/28.34 fof(f253696,plain,(
% 221.40/28.34 $false),
% 221.40/28.34 inference(sat_refutation,[status(thm)],[f187,f206,f387,f424,f432,f443,f454,f465,f476,f483,f490,f497,f504,f506,f508,f510,f512,f514,f516,f518,f524,f528,f555,f747,f761,f3756,f69370,f215202,f253695])).
% 221.40/28.34 % SZS output end CNFRefutation for theBenchmark.p
% 225.12/29.43 % Elapsed time: 28.899670 seconds
% 225.12/29.43 % CPU time: 200.865167 seconds
% 225.12/29.43 % Memory used: 1.941 GB
%------------------------------------------------------------------------------