TSTP Solution File: LCL498+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL498+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:27:19 EDT 2024
% Result : Theorem 11.49s 1.90s
% Output : CNFRefutation 12.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL498+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 20:51:47 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 11.49/1.90 % Refutation found
% 11.49/1.90 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.49/1.90 % SZS output start CNFRefutation for theBenchmark
% 11.49/1.90 fof(f1,axiom,(
% 11.49/1.90 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f21,axiom,(
% 11.49/1.90 ( cn3<=> (! [P] : is_a_theorem(implies(implies(not(P),P),P)) )) ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f22,axiom,(
% 11.49/1.90 ( r1<=> (! [P] : is_a_theorem(implies(or(P,P),P)) )) ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f23,axiom,(
% 11.49/1.90 ( r2<=> (! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) )) ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f24,axiom,(
% 11.49/1.90 ( r3<=> (! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) )) ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f26,axiom,(
% 11.49/1.90 ( r5<=> (! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )) ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f27,axiom,(
% 11.49/1.90 ( op_or=> (! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )) ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f28,axiom,(
% 11.49/1.90 ( op_and=> (! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )) ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f30,axiom,(
% 11.49/1.90 ( op_implies_or=> (! [X,Y] : implies(X,Y) = or(not(X),Y) )) ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f32,axiom,(
% 11.49/1.90 op_implies_or ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f33,axiom,(
% 11.49/1.90 op_and ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f35,axiom,(
% 11.49/1.90 modus_ponens ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f36,axiom,(
% 11.49/1.90 r1 ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f37,axiom,(
% 11.49/1.90 r2 ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f38,axiom,(
% 11.49/1.90 r3 ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f40,axiom,(
% 11.49/1.90 r5 ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f42,axiom,(
% 11.49/1.90 op_or ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f45,conjecture,(
% 11.49/1.90 cn3 ),
% 11.49/1.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.49/1.90 fof(f46,negated_conjecture,(
% 11.49/1.90 ~(cn3 )),
% 11.49/1.90 inference(negated_conjecture,[status(cth)],[f45])).
% 11.49/1.90 fof(f47,plain,(
% 11.49/1.90 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 11.49/1.90 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 11.49/1.90 fof(f48,plain,(
% 11.49/1.90 (~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))))),
% 11.49/1.90 inference(NNF_transformation,[status(esa)],[f47])).
% 11.49/1.90 fof(f49,plain,(
% 11.49/1.90 (~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))))),
% 11.49/1.90 inference(miniscoping,[status(esa)],[f48])).
% 11.49/1.90 fof(f50,plain,(
% 11.49/1.90 (~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)))),
% 11.49/1.90 inference(skolemization,[status(esa)],[f49])).
% 11.49/1.90 fof(f51,plain,(
% 11.49/1.90 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f50])).
% 11.49/1.90 fof(f133,plain,(
% 11.49/1.90 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|(?[P]: ~is_a_theorem(implies(implies(not(P),P),P))))),
% 11.49/1.90 inference(NNF_transformation,[status(esa)],[f21])).
% 11.49/1.90 fof(f134,plain,(
% 11.49/1.90 (~cn3|(![P]: is_a_theorem(implies(implies(not(P),P),P))))&(cn3|~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43)))),
% 11.49/1.90 inference(skolemization,[status(esa)],[f133])).
% 11.49/1.90 fof(f136,plain,(
% 11.49/1.90 cn3|~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f134])).
% 11.49/1.90 fof(f137,plain,(
% 11.49/1.90 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|(?[P]: ~is_a_theorem(implies(or(P,P),P))))),
% 11.49/1.90 inference(NNF_transformation,[status(esa)],[f22])).
% 11.49/1.90 fof(f138,plain,(
% 11.49/1.90 (~r1|(![P]: is_a_theorem(implies(or(P,P),P))))&(r1|~is_a_theorem(implies(or(sk0_44,sk0_44),sk0_44)))),
% 11.49/1.90 inference(skolemization,[status(esa)],[f137])).
% 11.49/1.90 fof(f139,plain,(
% 11.49/1.90 ![X0]: (~r1|is_a_theorem(implies(or(X0,X0),X0)))),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f138])).
% 11.49/1.90 fof(f141,plain,(
% 11.49/1.90 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|(?[P,Q]: ~is_a_theorem(implies(Q,or(P,Q)))))),
% 11.49/1.90 inference(NNF_transformation,[status(esa)],[f23])).
% 11.49/1.90 fof(f142,plain,(
% 11.49/1.90 (~r2|(![P,Q]: is_a_theorem(implies(Q,or(P,Q)))))&(r2|~is_a_theorem(implies(sk0_46,or(sk0_45,sk0_46))))),
% 11.49/1.90 inference(skolemization,[status(esa)],[f141])).
% 11.49/1.90 fof(f143,plain,(
% 11.49/1.90 ![X0,X1]: (~r2|is_a_theorem(implies(X0,or(X1,X0))))),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f142])).
% 11.49/1.90 fof(f145,plain,(
% 11.49/1.90 (~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)))))),
% 11.49/1.90 inference(NNF_transformation,[status(esa)],[f24])).
% 11.49/1.90 fof(f146,plain,(
% 11.49/1.90 (~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))))),
% 11.49/1.90 inference(skolemization,[status(esa)],[f145])).
% 11.49/1.90 fof(f147,plain,(
% 11.49/1.90 ![X0,X1]: (~r3|is_a_theorem(implies(or(X0,X1),or(X1,X0))))),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f146])).
% 11.49/1.90 fof(f153,plain,(
% 11.49/1.90 (~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))))))),
% 11.49/1.90 inference(NNF_transformation,[status(esa)],[f26])).
% 11.49/1.90 fof(f154,plain,(
% 11.49/1.90 (~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)))))),
% 11.49/1.90 inference(skolemization,[status(esa)],[f153])).
% 11.49/1.90 fof(f155,plain,(
% 11.49/1.90 ![X0,X1,X2]: (~r5|is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f154])).
% 11.49/1.90 fof(f157,plain,(
% 11.49/1.90 ~op_or|(![X,Y]: or(X,Y)=not(and(not(X),not(Y))))),
% 11.49/1.90 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 11.49/1.90 fof(f158,plain,(
% 11.49/1.90 ![X0,X1]: (~op_or|or(X0,X1)=not(and(not(X0),not(X1))))),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f157])).
% 11.49/1.90 fof(f159,plain,(
% 11.49/1.90 ~op_and|(![X,Y]: and(X,Y)=not(or(not(X),not(Y))))),
% 11.49/1.90 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 11.49/1.90 fof(f160,plain,(
% 11.49/1.90 ![X0,X1]: (~op_and|and(X0,X1)=not(or(not(X0),not(X1))))),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f159])).
% 11.49/1.90 fof(f163,plain,(
% 11.49/1.90 ~op_implies_or|(![X,Y]: implies(X,Y)=or(not(X),Y))),
% 11.49/1.90 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 11.49/1.90 fof(f164,plain,(
% 11.49/1.90 ![X0,X1]: (~op_implies_or|implies(X0,X1)=or(not(X0),X1))),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f163])).
% 11.49/1.90 fof(f167,plain,(
% 11.49/1.90 op_implies_or),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f32])).
% 11.49/1.90 fof(f168,plain,(
% 11.49/1.90 op_and),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f33])).
% 11.49/1.90 fof(f170,plain,(
% 11.49/1.90 modus_ponens),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f35])).
% 11.49/1.90 fof(f171,plain,(
% 11.49/1.90 r1),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f36])).
% 11.49/1.90 fof(f172,plain,(
% 11.49/1.90 r2),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f37])).
% 11.49/1.90 fof(f173,plain,(
% 11.49/1.90 r3),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f38])).
% 11.49/1.90 fof(f175,plain,(
% 11.49/1.90 r5),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f40])).
% 11.49/1.90 fof(f177,plain,(
% 11.49/1.90 op_or),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f42])).
% 11.49/1.90 fof(f180,plain,(
% 11.49/1.90 ~cn3),
% 11.49/1.90 inference(cnf_transformation,[status(esa)],[f46])).
% 11.49/1.90 fof(f181,plain,(
% 11.49/1.90 spl0_0 <=> modus_ponens),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f183,plain,(
% 11.49/1.90 ~modus_ponens|spl0_0),
% 11.49/1.90 inference(component_clause,[status(thm)],[f181])).
% 11.49/1.90 fof(f184,plain,(
% 11.49/1.90 spl0_1 <=> ~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f185,plain,(
% 11.49/1.90 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1)|~spl0_1)),
% 11.49/1.90 inference(component_clause,[status(thm)],[f184])).
% 11.49/1.90 fof(f187,plain,(
% 11.49/1.90 ~spl0_0|spl0_1),
% 11.49/1.90 inference(split_clause,[status(thm)],[f51,f181,f184])).
% 11.49/1.90 fof(f229,plain,(
% 11.49/1.90 spl0_13 <=> is_a_theorem(implies(X0,implies(X1,X0)))),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f230,plain,(
% 11.49/1.90 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~spl0_13)),
% 11.49/1.90 inference(component_clause,[status(thm)],[f229])).
% 11.49/1.90 fof(f306,plain,(
% 11.49/1.90 spl0_34 <=> is_a_theorem(implies(X0,or(X1,X0)))),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f307,plain,(
% 11.49/1.90 ![X0,X1]: (is_a_theorem(implies(X0,or(X1,X0)))|~spl0_34)),
% 11.49/1.90 inference(component_clause,[status(thm)],[f306])).
% 11.49/1.90 fof(f407,plain,(
% 11.49/1.90 spl0_61 <=> cn3),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f408,plain,(
% 11.49/1.90 cn3|~spl0_61),
% 11.49/1.90 inference(component_clause,[status(thm)],[f407])).
% 11.49/1.90 fof(f410,plain,(
% 11.49/1.90 spl0_62 <=> is_a_theorem(implies(implies(not(X0),X0),X0))),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f411,plain,(
% 11.49/1.90 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0))|~spl0_62)),
% 11.49/1.90 inference(component_clause,[status(thm)],[f410])).
% 11.49/1.90 fof(f414,plain,(
% 11.49/1.90 spl0_63 <=> is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f416,plain,(
% 11.49/1.90 ~is_a_theorem(implies(implies(not(sk0_43),sk0_43),sk0_43))|spl0_63),
% 11.49/1.90 inference(component_clause,[status(thm)],[f414])).
% 11.49/1.90 fof(f417,plain,(
% 11.49/1.90 spl0_61|~spl0_63),
% 11.49/1.90 inference(split_clause,[status(thm)],[f136,f407,f414])).
% 11.49/1.90 fof(f418,plain,(
% 11.49/1.90 spl0_64 <=> r1),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f420,plain,(
% 11.49/1.90 ~r1|spl0_64),
% 11.49/1.90 inference(component_clause,[status(thm)],[f418])).
% 11.49/1.90 fof(f421,plain,(
% 11.49/1.90 spl0_65 <=> is_a_theorem(implies(or(X0,X0),X0))),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f422,plain,(
% 11.49/1.90 ![X0]: (is_a_theorem(implies(or(X0,X0),X0))|~spl0_65)),
% 11.49/1.90 inference(component_clause,[status(thm)],[f421])).
% 11.49/1.90 fof(f424,plain,(
% 11.49/1.90 ~spl0_64|spl0_65),
% 11.49/1.90 inference(split_clause,[status(thm)],[f139,f418,f421])).
% 11.49/1.90 fof(f429,plain,(
% 11.49/1.90 spl0_67 <=> r2),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f431,plain,(
% 11.49/1.90 ~r2|spl0_67),
% 11.49/1.90 inference(component_clause,[status(thm)],[f429])).
% 11.49/1.90 fof(f432,plain,(
% 11.49/1.90 ~spl0_67|spl0_34),
% 11.49/1.90 inference(split_clause,[status(thm)],[f143,f429,f306])).
% 11.49/1.90 fof(f437,plain,(
% 11.49/1.90 spl0_69 <=> r3),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f439,plain,(
% 11.49/1.90 ~r3|spl0_69),
% 11.49/1.90 inference(component_clause,[status(thm)],[f437])).
% 11.49/1.90 fof(f440,plain,(
% 11.49/1.90 spl0_70 <=> is_a_theorem(implies(or(X0,X1),or(X1,X0)))),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f441,plain,(
% 11.49/1.90 ![X0,X1]: (is_a_theorem(implies(or(X0,X1),or(X1,X0)))|~spl0_70)),
% 11.49/1.90 inference(component_clause,[status(thm)],[f440])).
% 11.49/1.90 fof(f443,plain,(
% 11.49/1.90 ~spl0_69|spl0_70),
% 11.49/1.90 inference(split_clause,[status(thm)],[f147,f437,f440])).
% 11.49/1.90 fof(f459,plain,(
% 11.49/1.90 spl0_75 <=> r5),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f461,plain,(
% 11.49/1.90 ~r5|spl0_75),
% 11.49/1.90 inference(component_clause,[status(thm)],[f459])).
% 11.49/1.90 fof(f462,plain,(
% 11.49/1.90 spl0_76 <=> is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f463,plain,(
% 11.49/1.90 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))|~spl0_76)),
% 11.49/1.90 inference(component_clause,[status(thm)],[f462])).
% 11.49/1.90 fof(f465,plain,(
% 11.49/1.90 ~spl0_75|spl0_76),
% 11.49/1.90 inference(split_clause,[status(thm)],[f155,f459,f462])).
% 11.49/1.90 fof(f470,plain,(
% 11.49/1.90 spl0_78 <=> op_or),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f472,plain,(
% 11.49/1.90 ~op_or|spl0_78),
% 11.49/1.90 inference(component_clause,[status(thm)],[f470])).
% 11.49/1.90 fof(f473,plain,(
% 11.49/1.90 spl0_79 <=> or(X0,X1)=not(and(not(X0),not(X1)))),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f474,plain,(
% 11.49/1.90 ![X0,X1]: (or(X0,X1)=not(and(not(X0),not(X1)))|~spl0_79)),
% 11.49/1.90 inference(component_clause,[status(thm)],[f473])).
% 11.49/1.90 fof(f476,plain,(
% 11.49/1.90 ~spl0_78|spl0_79),
% 11.49/1.90 inference(split_clause,[status(thm)],[f158,f470,f473])).
% 11.49/1.90 fof(f477,plain,(
% 11.49/1.90 spl0_80 <=> op_and),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f479,plain,(
% 11.49/1.90 ~op_and|spl0_80),
% 11.49/1.90 inference(component_clause,[status(thm)],[f477])).
% 11.49/1.90 fof(f480,plain,(
% 11.49/1.90 spl0_81 <=> and(X0,X1)=not(or(not(X0),not(X1)))),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f481,plain,(
% 11.49/1.90 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1)))|~spl0_81)),
% 11.49/1.90 inference(component_clause,[status(thm)],[f480])).
% 11.49/1.90 fof(f483,plain,(
% 11.49/1.90 ~spl0_80|spl0_81),
% 11.49/1.90 inference(split_clause,[status(thm)],[f160,f477,f480])).
% 11.49/1.90 fof(f491,plain,(
% 11.49/1.90 spl0_84 <=> op_implies_or),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f493,plain,(
% 11.49/1.90 ~op_implies_or|spl0_84),
% 11.49/1.90 inference(component_clause,[status(thm)],[f491])).
% 11.49/1.90 fof(f494,plain,(
% 11.49/1.90 spl0_85 <=> implies(X0,X1)=or(not(X0),X1)),
% 11.49/1.90 introduced(split_symbol_definition)).
% 11.49/1.90 fof(f495,plain,(
% 11.49/1.90 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1)|~spl0_85)),
% 11.49/1.90 inference(component_clause,[status(thm)],[f494])).
% 11.49/1.90 fof(f497,plain,(
% 11.49/1.90 ~spl0_84|spl0_85),
% 11.49/1.90 inference(split_clause,[status(thm)],[f164,f491,f494])).
% 11.49/1.90 fof(f507,plain,(
% 11.49/1.90 $false|spl0_84),
% 11.49/1.90 inference(forward_subsumption_resolution,[status(thm)],[f493,f167])).
% 11.49/1.90 fof(f508,plain,(
% 11.49/1.90 spl0_84),
% 11.49/1.90 inference(contradiction_clause,[status(thm)],[f507])).
% 11.49/1.90 fof(f509,plain,(
% 11.49/1.90 $false|spl0_80),
% 11.49/1.90 inference(forward_subsumption_resolution,[status(thm)],[f479,f168])).
% 11.49/1.90 fof(f510,plain,(
% 11.49/1.90 spl0_80),
% 11.49/1.90 inference(contradiction_clause,[status(thm)],[f509])).
% 11.49/1.90 fof(f511,plain,(
% 11.49/1.90 $false|spl0_78),
% 11.49/1.90 inference(forward_subsumption_resolution,[status(thm)],[f472,f177])).
% 11.49/1.90 fof(f512,plain,(
% 11.49/1.90 spl0_78),
% 11.49/1.90 inference(contradiction_clause,[status(thm)],[f511])).
% 11.49/1.90 fof(f513,plain,(
% 11.49/1.90 $false|spl0_0),
% 11.49/1.90 inference(forward_subsumption_resolution,[status(thm)],[f183,f170])).
% 11.49/1.90 fof(f514,plain,(
% 11.49/1.90 spl0_0),
% 11.49/1.90 inference(contradiction_clause,[status(thm)],[f513])).
% 11.49/1.90 fof(f517,plain,(
% 11.49/1.90 ![X0,X1]: (and(X0,X1)=not(implies(X0,not(X1)))|~spl0_85|~spl0_81)),
% 11.49/1.90 inference(forward_demodulation,[status(thm)],[f495,f481])).
% 11.49/1.90 fof(f532,plain,(
% 11.49/1.90 $false|~spl0_62|spl0_63),
% 11.49/1.90 inference(backward_subsumption_resolution,[status(thm)],[f416,f411])).
% 11.49/1.90 fof(f533,plain,(
% 11.49/1.90 ~spl0_62|spl0_63),
% 11.49/1.90 inference(contradiction_clause,[status(thm)],[f532])).
% 11.49/1.90 fof(f566,plain,(
% 11.49/1.90 $false|spl0_75),
% 11.49/1.90 inference(forward_subsumption_resolution,[status(thm)],[f461,f175])).
% 11.49/1.90 fof(f567,plain,(
% 11.49/1.90 spl0_75),
% 11.49/1.90 inference(contradiction_clause,[status(thm)],[f566])).
% 11.49/1.90 fof(f570,plain,(
% 11.49/1.90 $false|spl0_69),
% 11.49/1.90 inference(forward_subsumption_resolution,[status(thm)],[f439,f173])).
% 11.49/1.90 fof(f571,plain,(
% 11.49/1.90 spl0_69),
% 11.49/1.90 inference(contradiction_clause,[status(thm)],[f570])).
% 11.49/1.90 fof(f572,plain,(
% 11.49/1.90 $false|spl0_64),
% 11.49/1.90 inference(forward_subsumption_resolution,[status(thm)],[f420,f171])).
% 11.49/1.90 fof(f573,plain,(
% 11.49/1.90 spl0_64),
% 11.49/1.90 inference(contradiction_clause,[status(thm)],[f572])).
% 11.49/1.90 fof(f574,plain,(
% 11.49/1.90 $false|spl0_67),
% 11.49/1.90 inference(forward_subsumption_resolution,[status(thm)],[f431,f172])).
% 11.49/1.90 fof(f575,plain,(
% 11.49/1.90 spl0_67),
% 11.49/1.90 inference(contradiction_clause,[status(thm)],[f574])).
% 11.49/1.90 fof(f576,plain,(
% 11.49/1.90 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0)))|~spl0_34|~spl0_85)),
% 11.49/1.90 inference(paramodulation,[status(thm)],[f495,f307])).
% 11.49/1.90 fof(f577,plain,(
% 11.49/1.90 spl0_13|~spl0_34|~spl0_85),
% 11.49/1.90 inference(split_clause,[status(thm)],[f576,f229,f306,f494])).
% 11.49/1.90 fof(f587,plain,(
% 11.49/1.90 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),or(X1,not(X0))))|~spl0_70|~spl0_85)),
% 11.49/1.90 inference(paramodulation,[status(thm)],[f495,f441])).
% 11.49/1.90 fof(f601,plain,(
% 11.49/1.90 ![X0,X1]: (is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0))))|~spl0_70|~spl0_85)),
% 11.49/1.90 inference(paramodulation,[status(thm)],[f495,f587])).
% 11.49/1.90 fof(f604,plain,(
% 11.49/1.90 ![X0,X1]: (~is_a_theorem(implies(X0,not(X1)))|is_a_theorem(implies(X1,not(X0)))|~spl0_70|~spl0_85|~spl0_1)),
% 11.49/1.90 inference(resolution,[status(thm)],[f601,f185])).
% 11.49/1.90 fof(f1340,plain,(
% 11.49/1.90 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1))))|~spl0_76|~spl0_85)),
% 11.49/1.90 inference(paramodulation,[status(thm)],[f495,f463])).
% 11.49/1.90 fof(f1341,plain,(
% 11.49/1.90 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))|~spl0_76|~spl0_85)),
% 11.49/1.90 inference(forward_demodulation,[status(thm)],[f495,f1340])).
% 11.49/1.90 fof(f1498,plain,(
% 11.49/1.90 ![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)),
% 11.49/1.90 inference(resolution,[status(thm)],[f1341,f185])).
% 11.49/1.90 fof(f1509,plain,(
% 11.49/1.90 ![X0,X1]: (is_a_theorem(implies(implies(X0,or(X1,X1)),implies(X0,X1)))|~spl0_76|~spl0_85|~spl0_1|~spl0_65)),
% 11.49/1.90 inference(resolution,[status(thm)],[f1498,f422])).
% 11.49/1.90 fof(f1520,plain,(
% 11.49/1.90 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X2,X1))))|~spl0_76|~spl0_85|~spl0_1|~spl0_13)),
% 12.22/1.93 inference(resolution,[status(thm)],[f1498,f230])).
% 12.22/1.93 fof(f1524,plain,(
% 12.22/1.93 ![X0,X1]: (~is_a_theorem(implies(X0,or(X1,X1)))|is_a_theorem(implies(X0,X1))|~spl0_76|~spl0_85|~spl0_65|~spl0_1)),
% 12.22/1.93 inference(resolution,[status(thm)],[f1509,f185])).
% 12.22/1.93 fof(f1541,plain,(
% 12.22/1.93 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(X0,implies(X2,X1)))|~spl0_76|~spl0_85|~spl0_13|~spl0_1)),
% 12.22/1.93 inference(resolution,[status(thm)],[f1520,f185])).
% 12.22/1.93 fof(f1689,plain,(
% 12.22/1.93 ![X0]: (is_a_theorem(implies(X0,X0))|~spl0_76|~spl0_85|~spl0_65|~spl0_1|~spl0_34)),
% 12.22/1.93 inference(resolution,[status(thm)],[f1524,f307])).
% 12.22/1.93 fof(f1692,plain,(
% 12.22/1.93 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X1,not(X1))))|is_a_theorem(implies(X0,not(X1)))|~spl0_76|~spl0_65|~spl0_1|~spl0_85)),
% 12.22/1.93 inference(paramodulation,[status(thm)],[f495,f1524])).
% 12.22/1.93 fof(f1697,plain,(
% 12.22/1.93 ![X0]: (is_a_theorem(implies(X0,not(not(X0))))|~spl0_76|~spl0_65|~spl0_34|~spl0_70|~spl0_85|~spl0_1)),
% 12.22/1.93 inference(resolution,[status(thm)],[f1689,f604])).
% 12.22/1.93 fof(f1728,plain,(
% 12.22/1.93 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(X0,not(not(X1)))))|~spl0_65|~spl0_34|~spl0_70|~spl0_76|~spl0_85|~spl0_1)),
% 12.22/1.93 inference(resolution,[status(thm)],[f1697,f1498])).
% 12.22/1.93 fof(f2229,plain,(
% 12.22/1.93 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(X0,not(not(X1))))|~spl0_65|~spl0_34|~spl0_70|~spl0_76|~spl0_85|~spl0_1)),
% 12.22/1.93 inference(resolution,[status(thm)],[f1728,f185])).
% 12.22/1.93 fof(f6171,plain,(
% 12.22/1.93 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),not(not(X0))))|~spl0_65|~spl0_34|~spl0_70|~spl0_76|~spl0_85|~spl0_1)),
% 12.22/1.93 inference(resolution,[status(thm)],[f1692,f1728])).
% 12.22/1.93 fof(f6256,plain,(
% 12.22/1.93 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),X0),implies(X1,not(not(X0)))))|~spl0_65|~spl0_34|~spl0_70|~spl0_76|~spl0_85|~spl0_13|~spl0_1)),
% 12.22/1.93 inference(resolution,[status(thm)],[f6171,f1541])).
% 12.22/1.93 fof(f6432,plain,(
% 12.22/1.93 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),X0),not(not(implies(X1,not(not(X0)))))))|~spl0_13|~spl0_65|~spl0_34|~spl0_70|~spl0_76|~spl0_85|~spl0_1)),
% 12.22/1.93 inference(resolution,[status(thm)],[f6256,f2229])).
% 12.22/1.93 fof(f6433,plain,(
% 12.22/1.93 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),X0),not(and(X1,not(X0)))))|~spl0_81|~spl0_13|~spl0_65|~spl0_34|~spl0_70|~spl0_76|~spl0_85|~spl0_1)),
% 12.22/1.93 inference(forward_demodulation,[status(thm)],[f517,f6432])).
% 12.22/1.93 fof(f6556,plain,(
% 12.22/1.93 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),X0),or(X1,X0)))|~spl0_81|~spl0_13|~spl0_65|~spl0_34|~spl0_70|~spl0_76|~spl0_85|~spl0_1|~spl0_79)),
% 12.22/1.93 inference(paramodulation,[status(thm)],[f474,f6433])).
% 12.22/1.93 fof(f6568,plain,(
% 12.22/1.93 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0))|~spl0_81|~spl0_13|~spl0_34|~spl0_70|~spl0_79|~spl0_76|~spl0_85|~spl0_65|~spl0_1)),
% 12.22/1.93 inference(resolution,[status(thm)],[f6556,f1524])).
% 12.22/1.93 fof(f6569,plain,(
% 12.22/1.93 spl0_62|~spl0_81|~spl0_13|~spl0_34|~spl0_70|~spl0_79|~spl0_76|~spl0_85|~spl0_65|~spl0_1),
% 12.22/1.93 inference(split_clause,[status(thm)],[f6568,f410,f480,f229,f306,f440,f473,f462,f494,f421,f184])).
% 12.22/1.93 fof(f6601,plain,(
% 12.22/1.93 $false|~spl0_61),
% 12.22/1.93 inference(forward_subsumption_resolution,[status(thm)],[f408,f180])).
% 12.22/1.93 fof(f6602,plain,(
% 12.22/1.93 ~spl0_61),
% 12.22/1.93 inference(contradiction_clause,[status(thm)],[f6601])).
% 12.22/1.93 fof(f6603,plain,(
% 12.22/1.93 $false),
% 12.22/1.93 inference(sat_refutation,[status(thm)],[f187,f417,f424,f432,f443,f465,f476,f483,f497,f508,f510,f512,f514,f533,f567,f571,f573,f575,f577,f6569,f6602])).
% 12.22/1.93 % SZS output end CNFRefutation for theBenchmark.p
% 12.22/1.98 % Elapsed time: 1.612158 seconds
% 12.22/1.98 % CPU time: 12.340147 seconds
% 12.22/1.98 % Total memory used: 242.140 MB
% 12.22/1.98 % Net memory used: 236.070 MB
%------------------------------------------------------------------------------