TSTP Solution File: LCL493+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL493+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 20:27:18 EDT 2024
% Result : Theorem 18.26s 2.72s
% Output : CNFRefutation 18.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL493+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.37 % Computer : n004.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Apr 29 20:07:34 EDT 2024
% 0.13/0.37 % CPUTime :
% 0.13/0.38 % Drodi V3.6.0
% 18.26/2.72 % Refutation found
% 18.26/2.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.26/2.72 % SZS output start CNFRefutation for theBenchmark
% 18.26/2.72 fof(f1,axiom,(
% 18.26/2.72 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f13,axiom,(
% 18.26/2.72 ( equivalence_1<=> (! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) )) ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f23,axiom,(
% 18.26/2.72 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f24,axiom,(
% 18.26/2.72 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f26,axiom,(
% 18.26/2.72 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f27,axiom,(
% 18.26/2.72 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f28,axiom,(
% 18.26/2.72 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f29,axiom,(
% 18.26/2.72 ( op_implies_and=> (! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )) ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f30,axiom,(
% 18.26/2.72 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f31,axiom,(
% 18.26/2.72 ( op_equiv=> (! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) )) ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f32,axiom,(
% 18.26/2.72 op_implies_or ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f33,axiom,(
% 18.26/2.72 op_and ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f34,axiom,(
% 18.26/2.72 op_equiv ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f35,axiom,(
% 18.26/2.72 modus_ponens ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f37,axiom,(
% 18.26/2.72 r2 ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f38,axiom,(
% 18.26/2.72 r3 ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f40,axiom,(
% 18.26/2.72 r5 ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f42,axiom,(
% 18.26/2.72 op_or ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f43,axiom,(
% 18.26/2.72 op_implies_and ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f45,conjecture,(
% 18.26/2.72 equivalence_1 ),
% 18.26/2.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.26/2.72 fof(f46,negated_conjecture,(
% 18.26/2.72 ~(equivalence_1 )),
% 18.26/2.72 inference(negated_conjecture,[status(cth)],[f45])).
% 18.26/2.72 fof(f47,plain,(
% 18.26/2.72 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 18.26/2.72 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 18.26/2.72 fof(f48,plain,(
% 18.26/2.72 (~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))))),
% 18.26/2.72 inference(NNF_transformation,[status(esa)],[f47])).
% 18.26/2.72 fof(f49,plain,(
% 18.26/2.72 (~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))))),
% 18.26/2.72 inference(miniscoping,[status(esa)],[f48])).
% 18.26/2.72 fof(f50,plain,(
% 18.26/2.72 (~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)))),
% 18.26/2.72 inference(skolemization,[status(esa)],[f49])).
% 18.26/2.72 fof(f51,plain,(
% 18.26/2.72 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 18.26/2.72 inference(cnf_transformation,[status(esa)],[f50])).
% 18.26/2.72 fof(f101,plain,(
% 18.26/2.72 (~equivalence_1|(![X,Y]: is_a_theorem(implies(equiv(X,Y),implies(X,Y)))))&(equivalence_1|(?[X,Y]: ~is_a_theorem(implies(equiv(X,Y),implies(X,Y)))))),
% 18.26/2.72 inference(NNF_transformation,[status(esa)],[f13])).
% 18.26/2.72 fof(f102,plain,(
% 18.26/2.72 (~equivalence_1|(![X,Y]: is_a_theorem(implies(equiv(X,Y),implies(X,Y)))))&(equivalence_1|~is_a_theorem(implies(equiv(sk0_26,sk0_27),implies(sk0_26,sk0_27))))),
% 18.50/2.73 inference(skolemization,[status(esa)],[f101])).
% 18.50/2.73 fof(f104,plain,(
% 18.50/2.73 equivalence_1|~is_a_theorem(implies(equiv(sk0_26,sk0_27),implies(sk0_26,sk0_27)))),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f102])).
% 18.50/2.73 fof(f141,plain,(
% 18.50/2.73 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 18.50/2.73 inference(NNF_transformation,[status(esa)],[f23])).
% 18.50/2.73 fof(f142,plain,(
% 18.50/2.73 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sk0_46,or(sk0_45,sk0_46))))),
% 18.50/2.73 inference(skolemization,[status(esa)],[f141])).
% 18.50/2.73 fof(f143,plain,(
% 18.50/2.73 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f142])).
% 18.50/2.73 fof(f145,plain,(
% 18.50/2.73 (~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)))))),
% 18.50/2.73 inference(NNF_transformation,[status(esa)],[f24])).
% 18.50/2.73 fof(f146,plain,(
% 18.50/2.73 (~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))))),
% 18.50/2.73 inference(skolemization,[status(esa)],[f145])).
% 18.50/2.73 fof(f147,plain,(
% 18.50/2.73 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f146])).
% 18.50/2.73 fof(f153,plain,(
% 18.50/2.73 (~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))))))),
% 18.50/2.73 inference(NNF_transformation,[status(esa)],[f26])).
% 18.50/2.73 fof(f154,plain,(
% 18.50/2.73 (~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)))))),
% 18.50/2.73 inference(skolemization,[status(esa)],[f153])).
% 18.50/2.73 fof(f155,plain,(
% 18.50/2.73 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f154])).
% 18.50/2.73 fof(f157,plain,(
% 18.50/2.73 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 18.50/2.73 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 18.50/2.73 fof(f158,plain,(
% 18.50/2.73 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f157])).
% 18.50/2.73 fof(f159,plain,(
% 18.50/2.73 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 18.50/2.73 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 18.50/2.73 fof(f160,plain,(
% 18.50/2.73 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f159])).
% 18.50/2.73 fof(f161,plain,(
% 18.50/2.73 ~op_implies_and|(![X,Y]: implies(X,Y)=not(and(X,not(Y))))),
% 18.50/2.73 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 18.50/2.73 fof(f162,plain,(
% 18.50/2.73 ![X0,X1]: (~op_implies_and|implies(X0,X1)=not(and(X0,not(X1))))),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f161])).
% 18.50/2.73 fof(f163,plain,(
% 18.50/2.73 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 18.50/2.73 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 18.50/2.73 fof(f164,plain,(
% 18.50/2.73 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f163])).
% 18.50/2.73 fof(f165,plain,(
% 18.50/2.73 ~op_equiv|(![X,Y]: equiv(X,Y)=and(implies(X,Y),implies(Y,X)))),
% 18.50/2.73 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 18.50/2.73 fof(f166,plain,(
% 18.50/2.73 ![X0,X1]: (~op_equiv|equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0)))),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f165])).
% 18.50/2.73 fof(f167,plain,(
% 18.50/2.73 op_implies_or),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f32])).
% 18.50/2.73 fof(f168,plain,(
% 18.50/2.73 op_and),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f33])).
% 18.50/2.73 fof(f169,plain,(
% 18.50/2.73 op_equiv),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f34])).
% 18.50/2.73 fof(f170,plain,(
% 18.50/2.73 modus_ponens),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f35])).
% 18.50/2.73 fof(f172,plain,(
% 18.50/2.73 r2),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f37])).
% 18.50/2.73 fof(f173,plain,(
% 18.50/2.73 r3),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f38])).
% 18.50/2.73 fof(f175,plain,(
% 18.50/2.73 r5),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f40])).
% 18.50/2.73 fof(f177,plain,(
% 18.50/2.73 op_or),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f42])).
% 18.50/2.73 fof(f178,plain,(
% 18.50/2.73 op_implies_and),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f43])).
% 18.50/2.73 fof(f180,plain,(
% 18.50/2.73 ~equivalence_1),
% 18.50/2.73 inference(cnf_transformation,[status(esa)],[f46])).
% 18.50/2.73 fof(f181,plain,(
% 18.50/2.73 spl0_0 <=> modus_ponens),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f183,plain,(
% 18.50/2.73 ~modus_ponens|spl0_0),
% 18.50/2.73 inference(component_clause,[status(thm)],[f181])).
% 18.50/2.73 fof(f184,plain,(
% 18.50/2.73 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f185,plain,(
% 18.50/2.73 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f184])).
% 18.50/2.73 fof(f187,plain,(
% 18.50/2.73 ~spl0_0|spl0_1),
% 18.50/2.73 inference(split_clause,[status(thm)],[f51,f181,f184])).
% 18.50/2.73 fof(f262,plain,(
% 18.50/2.73 spl0_22 <=> is_a_theorem(implies(and(X0,X1),X0))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f263,plain,(
% 18.50/2.73 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_22)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f262])).
% 18.50/2.73 fof(f295,plain,(
% 18.50/2.73 spl0_31 <=> is_a_theorem(implies(X0,or(X0,X1)))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f296,plain,(
% 18.50/2.73 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_31)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f295])).
% 18.50/2.73 fof(f306,plain,(
% 18.50/2.73 spl0_34 <=> is_a_theorem(implies(X0,or(X1,X0)))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f307,plain,(
% 18.50/2.73 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~spl0_34)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f306])).
% 18.50/2.73 fof(f325,plain,(
% 18.50/2.73 spl0_39 <=> equivalence_1),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f326,plain,(
% 18.50/2.73 equivalence_1|~spl0_39),
% 18.50/2.73 inference(component_clause,[status(thm)],[f325])).
% 18.50/2.73 fof(f328,plain,(
% 18.50/2.73 spl0_40 <=> is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f329,plain,(
% 18.50/2.73 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))|~spl0_40)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f328])).
% 18.50/2.73 fof(f332,plain,(
% 18.50/2.73 spl0_41 <=> is_a_theorem(implies(equiv(sk0_26,sk0_27),implies(sk0_26,sk0_27)))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f334,plain,(
% 18.50/2.73 ~is_a_theorem(implies(equiv(sk0_26,sk0_27),implies(sk0_26,sk0_27)))|spl0_41),
% 18.50/2.73 inference(component_clause,[status(thm)],[f332])).
% 18.50/2.73 fof(f335,plain,(
% 18.50/2.73 spl0_39|~spl0_41),
% 18.50/2.73 inference(split_clause,[status(thm)],[f104,f325,f332])).
% 18.50/2.73 fof(f429,plain,(
% 18.50/2.73 spl0_67 <=> r2),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f431,plain,(
% 18.50/2.73 ~r2|spl0_67),
% 18.50/2.73 inference(component_clause,[status(thm)],[f429])).
% 18.50/2.73 fof(f432,plain,(
% 18.50/2.73 ~spl0_67|spl0_34),
% 18.50/2.73 inference(split_clause,[status(thm)],[f143,f429,f306])).
% 18.50/2.73 fof(f437,plain,(
% 18.50/2.73 spl0_69 <=> r3),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f439,plain,(
% 18.50/2.73 ~r3|spl0_69),
% 18.50/2.73 inference(component_clause,[status(thm)],[f437])).
% 18.50/2.73 fof(f440,plain,(
% 18.50/2.73 spl0_70 <=> is_a_theorem(implies(or(X0,X1),or(X1,X0)))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f441,plain,(
% 18.50/2.73 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_70)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f440])).
% 18.50/2.73 fof(f443,plain,(
% 18.50/2.73 ~spl0_69|spl0_70),
% 18.50/2.73 inference(split_clause,[status(thm)],[f147,f437,f440])).
% 18.50/2.73 fof(f459,plain,(
% 18.50/2.73 spl0_75 <=> r5),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f461,plain,(
% 18.50/2.73 ~r5|spl0_75),
% 18.50/2.73 inference(component_clause,[status(thm)],[f459])).
% 18.50/2.73 fof(f462,plain,(
% 18.50/2.73 spl0_76 <=> is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f463,plain,(
% 18.50/2.73 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))|~spl0_76)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f462])).
% 18.50/2.73 fof(f465,plain,(
% 18.50/2.73 ~spl0_75|spl0_76),
% 18.50/2.73 inference(split_clause,[status(thm)],[f155,f459,f462])).
% 18.50/2.73 fof(f470,plain,(
% 18.50/2.73 spl0_78 <=> op_or),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f472,plain,(
% 18.50/2.73 ~op_or|spl0_78),
% 18.50/2.73 inference(component_clause,[status(thm)],[f470])).
% 18.50/2.73 fof(f473,plain,(
% 18.50/2.73 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f474,plain,(
% 18.50/2.73 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f473])).
% 18.50/2.73 fof(f476,plain,(
% 18.50/2.73 ~spl0_78|spl0_79),
% 18.50/2.73 inference(split_clause,[status(thm)],[f158,f470,f473])).
% 18.50/2.73 fof(f477,plain,(
% 18.50/2.73 spl0_80 <=> op_and),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f479,plain,(
% 18.50/2.73 ~op_and|spl0_80),
% 18.50/2.73 inference(component_clause,[status(thm)],[f477])).
% 18.50/2.73 fof(f480,plain,(
% 18.50/2.73 spl0_81 <=> and(X0,X1)=not(or(not(X0),not(X1)))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f481,plain,(
% 18.50/2.73 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1)))|~spl0_81)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f480])).
% 18.50/2.73 fof(f483,plain,(
% 18.50/2.73 ~spl0_80|spl0_81),
% 18.50/2.73 inference(split_clause,[status(thm)],[f160,f477,f480])).
% 18.50/2.73 fof(f484,plain,(
% 18.50/2.73 spl0_82 <=> op_implies_and),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f486,plain,(
% 18.50/2.73 ~op_implies_and|spl0_82),
% 18.50/2.73 inference(component_clause,[status(thm)],[f484])).
% 18.50/2.73 fof(f487,plain,(
% 18.50/2.73 spl0_83 <=> implies(X0,X1)=not(and(X0,not(X1)))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f488,plain,(
% 18.50/2.73 ![X0,X1]: (implies(X0,X1)=not(and(X0,not(X1)))|~spl0_83)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f487])).
% 18.50/2.73 fof(f490,plain,(
% 18.50/2.73 ~spl0_82|spl0_83),
% 18.50/2.73 inference(split_clause,[status(thm)],[f162,f484,f487])).
% 18.50/2.73 fof(f491,plain,(
% 18.50/2.73 spl0_84 <=> op_implies_or),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f493,plain,(
% 18.50/2.73 ~op_implies_or|spl0_84),
% 18.50/2.73 inference(component_clause,[status(thm)],[f491])).
% 18.50/2.73 fof(f494,plain,(
% 18.50/2.73 spl0_85 <=> implies(X0,X1)=or(not(X0),X1)),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f495,plain,(
% 18.50/2.73 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~spl0_85)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f494])).
% 18.50/2.73 fof(f497,plain,(
% 18.50/2.73 ~spl0_84|spl0_85),
% 18.50/2.73 inference(split_clause,[status(thm)],[f164,f491,f494])).
% 18.50/2.73 fof(f498,plain,(
% 18.50/2.73 spl0_86 <=> op_equiv),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f500,plain,(
% 18.50/2.73 ~op_equiv|spl0_86),
% 18.50/2.73 inference(component_clause,[status(thm)],[f498])).
% 18.50/2.73 fof(f501,plain,(
% 18.50/2.73 spl0_87 <=> equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))),
% 18.50/2.73 introduced(split_symbol_definition)).
% 18.50/2.73 fof(f502,plain,(
% 18.50/2.73 ![X0,X1]: (equiv(X0,X1)=and(implies(X0,X1),implies(X1,X0))|~spl0_87)),
% 18.50/2.73 inference(component_clause,[status(thm)],[f501])).
% 18.50/2.73 fof(f504,plain,(
% 18.50/2.73 ~spl0_86|spl0_87),
% 18.50/2.73 inference(split_clause,[status(thm)],[f166,f498,f501])).
% 18.50/2.73 fof(f505,plain,(
% 18.50/2.73 $false|spl0_86),
% 18.50/2.73 inference(forward_subsumption_resolution,[status(thm)],[f500,f169])).
% 18.50/2.73 fof(f506,plain,(
% 18.50/2.73 spl0_86),
% 18.50/2.73 inference(contradiction_clause,[status(thm)],[f505])).
% 18.50/2.73 fof(f507,plain,(
% 18.50/2.73 $false|spl0_0),
% 18.50/2.73 inference(forward_subsumption_resolution,[status(thm)],[f183,f170])).
% 18.50/2.73 fof(f508,plain,(
% 18.50/2.73 spl0_0),
% 18.50/2.73 inference(contradiction_clause,[status(thm)],[f507])).
% 18.50/2.73 fof(f511,plain,(
% 18.50/2.73 $false|spl0_84),
% 18.50/2.73 inference(forward_subsumption_resolution,[status(thm)],[f493,f167])).
% 18.50/2.73 fof(f512,plain,(
% 18.50/2.73 spl0_84),
% 18.50/2.73 inference(contradiction_clause,[status(thm)],[f511])).
% 18.50/2.73 fof(f513,plain,(
% 18.50/2.73 $false|spl0_82),
% 18.50/2.73 inference(forward_subsumption_resolution,[status(thm)],[f486,f178])).
% 18.50/2.73 fof(f514,plain,(
% 18.50/2.73 spl0_82),
% 18.50/2.73 inference(contradiction_clause,[status(thm)],[f513])).
% 18.50/2.73 fof(f515,plain,(
% 18.50/2.73 $false|spl0_80),
% 18.50/2.73 inference(forward_subsumption_resolution,[status(thm)],[f479,f168])).
% 18.50/2.73 fof(f516,plain,(
% 18.50/2.73 spl0_80),
% 18.50/2.73 inference(contradiction_clause,[status(thm)],[f515])).
% 18.50/2.73 fof(f517,plain,(
% 18.50/2.73 $false|spl0_78),
% 18.50/2.73 inference(forward_subsumption_resolution,[status(thm)],[f472,f177])).
% 18.50/2.73 fof(f518,plain,(
% 18.50/2.73 spl0_78),
% 18.50/2.73 inference(contradiction_clause,[status(thm)],[f517])).
% 18.50/2.73 fof(f519,plain,(
% 18.50/2.73 ![X0,X1]: (is_a_theorem(implies(not(X0),implies(X0,X1)))|~spl0_31|~spl0_85)),
% 18.50/2.73 inference(paramodulation,[status(thm)],[f495,f296])).
% 18.50/2.73 fof(f532,plain,(
% 18.50/2.73 $false|spl0_67),
% 18.50/2.73 inference(forward_subsumption_resolution,[status(thm)],[f431,f172])).
% 18.50/2.73 fof(f533,plain,(
% 18.50/2.73 spl0_67),
% 18.50/2.73 inference(contradiction_clause,[status(thm)],[f532])).
% 18.50/2.73 fof(f558,plain,(
% 18.50/2.73 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1)))|~spl0_85|~spl0_81)),
% 18.50/2.73 inference(forward_demodulation,[status(thm)],[f495,f481])).
% 18.50/2.73 fof(f563,plain,(
% 18.50/2.73 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1)|~spl0_83|~spl0_79)),
% 18.50/2.73 inference(forward_demodulation,[status(thm)],[f488,f474])).
% 18.50/2.73 fof(f570,plain,(
% 18.50/2.73 ![X0,X1,X2]: (or(implies(X0,not(X1)),X2)=implies(and(X0,X1),X2)|~spl0_83|~spl0_79|~spl0_85|~spl0_81)),
% 18.50/2.73 inference(paramodulation,[status(thm)],[f558,f563])).
% 18.50/2.73 fof(f1665,plain,(
% 18.50/2.73 ![X0,X1]: (~is_a_theorem(or(X0,X1))|is_a_theorem(or(X1,X0))|~spl0_70|~spl0_1)),
% 18.50/2.73 inference(resolution,[status(thm)],[f441,f185])).
% 18.63/2.74 fof(f1697,plain,(
% 18.63/2.74 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1))))|~spl0_76|~spl0_85)),
% 18.63/2.74 inference(paramodulation,[status(thm)],[f495,f463])).
% 18.63/2.74 fof(f1698,plain,(
% 18.63/2.74 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))|~spl0_76|~spl0_85)),
% 18.63/2.74 inference(forward_demodulation,[status(thm)],[f495,f1697])).
% 18.63/2.74 fof(f2015,plain,(
% 18.63/2.74 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))|~spl0_76|~spl0_85|~spl0_1)),
% 18.63/2.74 inference(resolution,[status(thm)],[f1698,f185])).
% 18.63/2.74 fof(f2026,plain,(
% 18.63/2.74 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,or(X1,X2)),implies(X0,or(X2,X1))))|~spl0_76|~spl0_85|~spl0_1|~spl0_70)),
% 18.63/2.74 inference(resolution,[status(thm)],[f2015,f441])).
% 18.63/2.74 fof(f2161,plain,(
% 18.63/2.74 $false|spl0_75),
% 18.63/2.74 inference(forward_subsumption_resolution,[status(thm)],[f461,f175])).
% 18.63/2.74 fof(f2162,plain,(
% 18.63/2.74 spl0_75),
% 18.63/2.74 inference(contradiction_clause,[status(thm)],[f2161])).
% 18.63/2.74 fof(f2725,plain,(
% 18.63/2.74 ![X0,X1,X2]: (~is_a_theorem(implies(X0,or(X1,X2)))|is_a_theorem(implies(X0,or(X2,X1)))|~spl0_76|~spl0_85|~spl0_70|~spl0_1)),
% 18.63/2.74 inference(resolution,[status(thm)],[f2026,f185])).
% 18.63/2.74 fof(f2778,plain,(
% 18.63/2.74 ![X0,X1]: (is_a_theorem(implies(X0,or(X0,X1)))|~spl0_76|~spl0_85|~spl0_70|~spl0_1|~spl0_34)),
% 18.63/2.74 inference(resolution,[status(thm)],[f2725,f307])).
% 18.63/2.74 fof(f2779,plain,(
% 18.63/2.74 spl0_31|~spl0_76|~spl0_85|~spl0_70|~spl0_1|~spl0_34),
% 18.63/2.74 inference(split_clause,[status(thm)],[f2778,f295,f462,f494,f440,f184,f306])).
% 18.63/2.74 fof(f2784,plain,(
% 18.63/2.74 ![X0,X1]: (is_a_theorem(or(X0,implies(X0,X1)))|~spl0_83|~spl0_79|~spl0_31|~spl0_85)),
% 18.63/2.74 inference(forward_demodulation,[status(thm)],[f563,f519])).
% 18.63/2.74 fof(f2796,plain,(
% 18.63/2.74 $false|spl0_69),
% 18.63/2.74 inference(forward_subsumption_resolution,[status(thm)],[f439,f173])).
% 18.63/2.74 fof(f2797,plain,(
% 18.63/2.74 spl0_69),
% 18.63/2.74 inference(contradiction_clause,[status(thm)],[f2796])).
% 18.63/2.74 fof(f6377,plain,(
% 18.63/2.74 ![X0,X1]: (is_a_theorem(or(implies(X0,X1),X0))|~spl0_70|~spl0_1|~spl0_83|~spl0_79|~spl0_31|~spl0_85)),
% 18.63/2.74 inference(resolution,[status(thm)],[f1665,f2784])).
% 18.63/2.74 fof(f6763,plain,(
% 18.63/2.74 ![X0,X1]: (is_a_theorem(implies(and(X0,X1),X0))|~spl0_70|~spl0_1|~spl0_31|~spl0_83|~spl0_79|~spl0_85|~spl0_81)),
% 18.63/2.74 inference(paramodulation,[status(thm)],[f570,f6377])).
% 18.63/2.74 fof(f6764,plain,(
% 18.63/2.74 spl0_22|~spl0_70|~spl0_1|~spl0_31|~spl0_83|~spl0_79|~spl0_85|~spl0_81),
% 18.63/2.74 inference(split_clause,[status(thm)],[f6763,f262,f440,f184,f295,f487,f473,f494,f480])).
% 18.63/2.74 fof(f6784,plain,(
% 18.63/2.74 ![X0,X1]: (is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))|~spl0_22|~spl0_87)),
% 18.63/2.74 inference(paramodulation,[status(thm)],[f502,f263])).
% 18.63/2.74 fof(f6785,plain,(
% 18.63/2.74 spl0_40|~spl0_22|~spl0_87),
% 18.63/2.74 inference(split_clause,[status(thm)],[f6784,f328,f262,f501])).
% 18.63/2.74 fof(f8483,plain,(
% 18.63/2.74 $false|~spl0_40|spl0_41),
% 18.63/2.74 inference(backward_subsumption_resolution,[status(thm)],[f334,f329])).
% 18.63/2.74 fof(f8484,plain,(
% 18.63/2.74 ~spl0_40|spl0_41),
% 18.63/2.74 inference(contradiction_clause,[status(thm)],[f8483])).
% 18.63/2.74 fof(f8500,plain,(
% 18.63/2.74 $false|~spl0_39),
% 18.63/2.74 inference(forward_subsumption_resolution,[status(thm)],[f326,f180])).
% 18.63/2.74 fof(f8501,plain,(
% 18.63/2.74 ~spl0_39),
% 18.63/2.74 inference(contradiction_clause,[status(thm)],[f8500])).
% 18.63/2.74 fof(f8502,plain,(
% 18.63/2.74 $false),
% 18.63/2.74 inference(sat_refutation,[status(thm)],[f187,f335,f432,f443,f465,f476,f483,f490,f497,f504,f506,f508,f512,f514,f516,f518,f533,f2162,f2779,f2797,f6764,f6785,f8484,f8501])).
% 18.63/2.74 % SZS output end CNFRefutation for theBenchmark.p
% 18.63/2.81 % Elapsed time: 2.420022 seconds
% 18.63/2.81 % CPU time: 18.910750 seconds
% 18.63/2.81 % Total memory used: 414.533 MB
% 18.63/2.81 % Net memory used: 392.710 MB
%------------------------------------------------------------------------------